TSTP Solution File: SWW350+1 by CSE---1.7
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW350+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n025.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 18:08:07 EDT 2024
% Result : Theorem 155.90s 155.59s
% Output : CNFRefutation 155.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW350+1 : TPTP v8.2.0. Released v5.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.32 % Computer : n025.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jun 19 06:00:54 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.20/0.55 start to proof:theBenchmark
% 155.39/155.43 %-------------------------------------------
% 155.39/155.43 % File :CSE---1.7
% 155.39/155.43 % Problem :theBenchmark
% 155.39/155.43 % Transform :cnf
% 155.39/155.43 % Format :tptp:raw
% 155.39/155.43 % Command :java -jar mcs_scs.jar %d %s
% 155.39/155.43
% 155.39/155.43 % Result :Theorem 140.760000s
% 155.39/155.43 % Output :CNFRefutation 140.760000s
% 155.39/155.43 %-------------------------------------------
% 155.39/155.44 %------------------------------------------------------------------------------
% 155.39/155.44 % File : SWW350+1 : TPTP v8.2.0. Released v5.2.0.
% 155.39/155.44 % Domain : Software Verification
% 155.39/155.44 % Problem : Hoare's Logic with Procedures 435264, 5000 axioms selected
% 155.39/155.44 % Version : Especial.
% 155.39/155.44 % English :
% 155.39/155.44
% 155.39/155.44 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 155.39/155.44 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 155.39/155.44 % Source : [Bla11]
% 155.39/155.44 % Names : hoare_435264.5000.p [Bla11]
% 155.39/155.44
% 155.39/155.44 % Status : Theorem
% 155.39/155.44 % Rating : 0.69 v8.2.0, 0.75 v8.1.0, 0.69 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
% 155.39/155.44 % Syntax : Number of formulae : 5229 (1731 unt; 0 def)
% 155.39/155.44 % Number of atoms : 12573 (4522 equ)
% 155.39/155.44 % Maximal formula atoms : 13 ( 2 avg)
% 155.39/155.44 % Number of connectives : 8368 (1024 ~; 154 |; 717 &)
% 155.39/155.44 % ( 878 <=>;5595 =>; 0 <=; 0 <~>)
% 155.39/155.44 % Maximal formula depth : 22 ( 6 avg)
% 155.39/155.44 % Maximal term depth : 19 ( 2 avg)
% 155.39/155.44 % Number of predicates : 139 ( 138 usr; 2 prp; 0-7 aty)
% 155.39/155.44 % Number of functors : 370 ( 370 usr; 63 con; 0-10 aty)
% 155.39/155.44 % Number of variables : 16850 (16701 !; 149 ?)
% 155.39/155.44 % SPC : FOF_THM_RFO_SEQ
% 155.39/155.44
% 155.39/155.44 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 155.39/155.44 % 2011-03-01 12:19:22
% 155.39/155.44 %------------------------------------------------------------------------------
% 155.39/155.44 %----Relevant facts (4985)
% 155.39/155.44 fof(fact_ext,axiom,
% 155.39/155.44 ! [V_g_2,V_f_2] :
% 155.39/155.44 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 155.39/155.44 => V_f_2 = V_g_2 ) ).
% 155.39/155.44
% 155.39/155.44 fof(fact_com__det,axiom,
% 155.39/155.44 ! [V_u,V_t,V_s,V_c] :
% 155.39/155.44 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 155.39/155.44 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
% 155.39/155.44 => V_u = V_t ) ) ).
% 155.39/155.44
% 155.39/155.44 fof(fact_state__not__singleton__def,axiom,
% 155.39/155.44 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 155.39/155.44 <=> ? [B_s,B_t] : B_s != B_t ) ).
% 155.39/155.44
% 155.39/155.44 fof(fact_single__stateE,axiom,
% 155.39/155.44 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 155.39/155.44 => ! [B_t] :
% 155.39/155.44 ~ ! [B_s] : B_s = B_t ) ).
% 155.39/155.44
% 155.39/155.44 fof(fact_evalc_OSkip,axiom,
% 155.39/155.44 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 155.39/155.44
% 155.39/155.44 fof(fact_evalc__elim__cases_I1_J,axiom,
% 155.39/155.44 ! [V_t,V_s] :
% 155.39/155.44 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
% 155.39/155.44 => V_t = V_s ) ).
% 155.39/155.44
% 155.39/155.44 fof(fact_evalc_OSemi,axiom,
% 155.39/155.44 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 155.39/155.44 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
% 155.39/155.44 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
% 155.39/155.44 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 155.39/155.44
% 155.39/155.44 fof(fact_evalc_OIfFalse,axiom,
% 155.39/155.44 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
% 155.39/155.44 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.44 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
% 155.39/155.44 => 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)) ) ) ).
% 155.39/155.44
% 155.39/155.45 fof(fact_evalc_OIfTrue,axiom,
% 155.39/155.45 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
% 155.39/155.45 ( hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.45 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
% 155.39/155.45 => 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)) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_evalc__elim__cases_I5_J,axiom,
% 155.39/155.45 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 155.39/155.45 ( 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))
% 155.39/155.45 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.45 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
% 155.39/155.45 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.45 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_evalc_OWhileFalse,axiom,
% 155.39/155.45 ! [V_ca_2,V_s_2,V_b_2] :
% 155.39/155.45 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.45 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_s_2)) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_evalc_OWhileTrue,axiom,
% 155.39/155.45 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_b_2] :
% 155.39/155.45 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 155.39/155.45 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2))
% 155.39/155.45 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_s2_2))
% 155.39/155.45 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_evalc_Oequations_I1_J,axiom,
% 155.39/155.45 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_evalc_Oequations_I8_J,axiom,
% 155.39/155.45 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 155.39/155.45 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 155.39/155.45 <=> ( ( V_a5_2 = V_a2_2
% 155.39/155.45 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 155.39/155.45 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.45 & ? [B_s1] :
% 155.39/155.45 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 155.39/155.45 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_evalc_Oequations_I7_J,axiom,
% 155.39/155.45 ! [V_a2_2,V_a3_2,V_a1_2] :
% 155.39/155.45 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 155.39/155.45 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.45 => ? [B_s1] :
% 155.39/155.45 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 155.39/155.45 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_evalc_Oequations_I6_J,axiom,
% 155.39/155.45 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 155.39/155.45 ( 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))
% 155.39/155.45 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.45 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) )
% 155.39/155.45 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.45 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_evalc_Oequations_I5_J,axiom,
% 155.39/155.45 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 155.39/155.45 ( 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))
% 155.39/155.45 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.45 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) )
% 155.39/155.45 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.45 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_evalc_Oequations_I4_J,axiom,
% 155.39/155.45 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 155.39/155.45 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 155.39/155.45 <=> ? [B_s1] :
% 155.39/155.45 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1))
% 155.39/155.45 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I12_J,axiom,
% 155.39/155.45 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I13_J,axiom,
% 155.39/155.45 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I14_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I15_J,axiom,
% 155.39/155.45 ! [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 ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I44_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I45_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I16_J,axiom,
% 155.39/155.45 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I17_J,axiom,
% 155.39/155.45 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I46_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I47_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I53_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I52_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I5_J,axiom,
% 155.39/155.45 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 155.39/155.45 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 155.39/155.45 <=> ( V_fun_2 = V_fun_H_2
% 155.39/155.45 & V_com_2 = V_com_H_2 ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I4_J,axiom,
% 155.39/155.45 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 155.39/155.45 ( 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)
% 155.39/155.45 <=> ( V_fun_2 = V_fun_H_2
% 155.39/155.45 & V_com1_2 = V_com1_H_2
% 155.39/155.45 & V_com2_2 = V_com2_H_2 ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I3_J,axiom,
% 155.39/155.45 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 155.39/155.45 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 155.39/155.45 <=> ( V_com1_2 = V_com1_H_2
% 155.39/155.45 & V_com2_2 = V_com2_H_2 ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_evalc__elim__cases_I4_J,axiom,
% 155.39/155.45 ! [V_t,V_s,V_c2,V_c1] :
% 155.39/155.45 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t))
% 155.39/155.45 => ~ ! [B_s1] :
% 155.39/155.45 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1))
% 155.39/155.45 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_evalc__WHILE__case,axiom,
% 155.39/155.45 ! [V_t_2,V_s_2,V_ca_2,V_b_2] :
% 155.39/155.45 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_t_2))
% 155.39/155.45 => ( ( V_t_2 = V_s_2
% 155.39/155.45 => hBOOL(hAPP(V_b_2,V_s_2)) )
% 155.39/155.45 => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.45 => ! [B_s1] :
% 155.39/155.45 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),B_s1))
% 155.39/155.45 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),B_s1),V_t_2)) ) ) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I64_J,axiom,
% 155.39/155.45 ! [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 ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I67_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I68_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I69_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Orecs_I1_J,axiom,
% 155.39/155.45 ! [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 ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Orecs_I4_J,axiom,
% 155.39/155.45 ! [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)) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Orecs_I5_J,axiom,
% 155.39/155.45 ! [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)) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Orecs_I6_J,axiom,
% 155.39/155.45 ! [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)) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_WTs__elim__cases_I4_J,axiom,
% 155.39/155.45 ! [V_c2,V_c1] :
% 155.39/155.45 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 155.39/155.45 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 155.39/155.45 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_WTs__elim__cases_I6_J,axiom,
% 155.39/155.45 ! [V_ca_2,V_b_2] :
% 155.39/155.45 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2)))
% 155.39/155.45 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_WTs__elim__cases_I5_J,axiom,
% 155.39/155.45 ! [V_c2_2,V_c1_2,V_b_2] :
% 155.39/155.45 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
% 155.39/155.45 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 155.39/155.45 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_WT_Oequations_I6_J,axiom,
% 155.39/155.45 ! [V_a1_2,V_a2_2] :
% 155.39/155.45 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 155.39/155.45 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_While,axiom,
% 155.39/155.45 ! [V_b_2,V_ca_2] :
% 155.39/155.45 ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 155.39/155.45 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_WT_Oequations_I5_J,axiom,
% 155.39/155.45 ! [V_a2_2,V_a1_2,V_a3_2] :
% 155.39/155.45 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 155.39/155.45 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 155.39/155.45 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_WT_OIf,axiom,
% 155.39/155.45 ! [V_b_2,V_c1_2,V_c0_2] :
% 155.39/155.45 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 155.39/155.45 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 155.39/155.45 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_WT_Oequations_I4_J,axiom,
% 155.39/155.45 ! [V_a2_2,V_a1_2] :
% 155.39/155.45 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 155.39/155.45 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 155.39/155.45 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_WT_OSemi,axiom,
% 155.39/155.45 ! [V_c1,V_c0] :
% 155.39/155.45 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 155.39/155.45 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 155.39/155.45 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_WT_OSkip,axiom,
% 155.39/155.45 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_WT_Oequations_I1_J,axiom,
% 155.39/155.45 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_WTs__elim__cases_I3_J,axiom,
% 155.39/155.45 ! [V_ca_2,V_a_2,V_Y_2] :
% 155.39/155.45 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)))
% 155.39/155.45 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I66_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I71_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Osimps_I65_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Orecs_I3_J,axiom,
% 155.39/155.45 ! [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)) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Orecs_I8_J,axiom,
% 155.39/155.45 ! [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) ).
% 155.39/155.45
% 155.39/155.45 fof(fact_com_Orecs_I2_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I70_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_OSkip,axiom,
% 155.39/155.46 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln__elim__cases_I1_J,axiom,
% 155.39/155.46 ! [V_t,V_n,V_s] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t))
% 155.39/155.46 => V_t = V_s ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_OSemi,axiom,
% 155.39/155.46 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1))
% 155.39/155.46 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2))
% 155.39/155.46 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_OWhileTrue,axiom,
% 155.39/155.46 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_b_2] :
% 155.39/155.46 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 155.39/155.46 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s0_2),V_n_2),V_s1_2))
% 155.39/155.46 => ( 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))
% 155.39/155.46 => 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)) ) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_OWhileFalse,axiom,
% 155.39/155.46 ! [V_n_2,V_ca_2,V_s_2,V_b_2] :
% 155.39/155.46 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.46 => 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)) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln__elim__cases_I5_J,axiom,
% 155.39/155.46 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 155.39/155.46 ( 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))
% 155.39/155.46 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.46 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) )
% 155.39/155.46 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.46 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_OIfTrue,axiom,
% 155.39/155.46 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
% 155.39/155.46 ( hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.46 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2))
% 155.39/155.46 => 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)) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_OIfFalse,axiom,
% 155.39/155.46 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
% 155.39/155.46 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.46 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2))
% 155.39/155.46 => 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)) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_WTs__elim__cases_I8_J,axiom,
% 155.39/155.46 ! [V_a_2,V_P_2,V_X_2] :
% 155.39/155.46 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)))
% 155.39/155.46 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I31_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I62_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I41_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I30_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I32_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I22_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I63_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I40_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I33_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I23_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I43_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I42_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I6_J,axiom,
% 155.39/155.46 ! [V_pname_H_2,V_pname_2] :
% 155.39/155.46 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 155.39/155.46 <=> V_pname_2 = V_pname_H_2 ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I1_J,axiom,
% 155.39/155.46 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
% 155.39/155.46 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
% 155.39/155.46 <=> ( V_vname_2 = V_vname_H_2
% 155.39/155.46 & V_fun_2 = V_fun_H_2 ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I7_J,axiom,
% 155.39/155.46 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
% 155.39/155.46 ( 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)
% 155.39/155.46 <=> ( V_vname_2 = V_vname_H_2
% 155.39/155.46 & V_pname_2 = V_pname_H_2
% 155.39/155.46 & V_fun_2 = V_fun_H_2 ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I2_J,axiom,
% 155.39/155.46 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 155.39/155.46 ( 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)
% 155.39/155.46 <=> ( V_loc_2 = V_loc_H_2
% 155.39/155.46 & V_fun_2 = V_fun_H_2
% 155.39/155.46 & V_com_2 = V_com_H_2 ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_WT_Oequations_I8_J,axiom,
% 155.39/155.46 ! [V_a3_2,V_a1_2,V_a2_2] :
% 155.39/155.46 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
% 155.39/155.46 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_WT_OCall,axiom,
% 155.39/155.46 ! [V_a_2,V_X_2,V_pn_2] :
% 155.39/155.46 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2)))
% 155.39/155.46 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_eval__eq,axiom,
% 155.39/155.46 ! [V_t_2,V_s_2,V_ca_2] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2))
% 155.39/155.46 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),B_n),V_t_2)) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln__evalc,axiom,
% 155.39/155.46 ! [V_t,V_n,V_s,V_c] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 155.39/155.46 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_Oequations_I8_J,axiom,
% 155.39/155.46 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 155.39/155.46 ( 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))
% 155.39/155.46 <=> ( ( V_a6_2 = V_a2_2
% 155.39/155.46 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 155.39/155.46 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.46 & ? [B_s1] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 155.39/155.46 & 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)) ) ) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_Oequations_I7_J,axiom,
% 155.39/155.46 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 155.39/155.46 ( 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))
% 155.39/155.46 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.46 => ? [B_s1] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 155.39/155.46 & 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)) ) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_Oequations_I6_J,axiom,
% 155.39/155.46 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 155.39/155.46 ( 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))
% 155.39/155.46 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.46 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) )
% 155.39/155.46 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.46 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_Oequations_I5_J,axiom,
% 155.39/155.46 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 155.39/155.46 ( 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))
% 155.39/155.46 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.46 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) )
% 155.39/155.46 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 155.39/155.46 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_Oequations_I4_J,axiom,
% 155.39/155.46 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 155.39/155.46 ( 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))
% 155.39/155.46 <=> ? [B_s1] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1))
% 155.39/155.46 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_Oequations_I1_J,axiom,
% 155.39/155.46 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I58_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I59_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I54_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I55_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I48_J,axiom,
% 155.39/155.46 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I49_J,axiom,
% 155.39/155.46 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I19_J,axiom,
% 155.39/155.46 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I18_J,axiom,
% 155.39/155.46 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_WT_OAssign,axiom,
% 155.39/155.46 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_WT_Oequations_I2_J,axiom,
% 155.39/155.46 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_WT_Oequations_I3_J,axiom,
% 155.39/155.46 ! [V_a1_2,V_a3_2,V_a2_2] :
% 155.39/155.46 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 155.39/155.46 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_WT_OLocal,axiom,
% 155.39/155.46 ! [V_a_2,V_Y_2,V_ca_2] :
% 155.39/155.46 ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 155.39/155.46 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I29_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I28_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I38_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I61_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I39_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I60_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I27_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I26_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I36_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I37_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I56_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I57_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I25_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I24_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I9_J,axiom,
% 155.39/155.46 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I8_J,axiom,
% 155.39/155.46 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Orecs_I7_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I34_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I51_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I35_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I50_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I11_J,axiom,
% 155.39/155.46 ! [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 ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I21_J,axiom,
% 155.39/155.46 ! [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 ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I10_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_com_Osimps_I20_J,axiom,
% 155.39/155.46 ! [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) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln__elim__cases_I4_J,axiom,
% 155.39/155.46 ! [V_t,V_n,V_s,V_c2,V_c1] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_n),V_t))
% 155.39/155.46 => ~ ! [B_s1] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s),V_n),B_s1))
% 155.39/155.46 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2),B_s1),V_n),V_t)) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evalc_OAssign,axiom,
% 155.39/155.46 ! [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)))) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evalc__elim__cases_I2_J,axiom,
% 155.39/155.46 ! [V_t_2,V_s_2,V_a_2,V_X_2] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2))
% 155.39/155.46 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_OAssign,axiom,
% 155.39/155.46 ! [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)))) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln__elim__cases_I2_J,axiom,
% 155.39/155.46 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] :
% 155.39/155.46 ( 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))
% 155.39/155.46 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln__WHILE__case,axiom,
% 155.39/155.46 ! [V_t_2,V_n_2,V_s_2,V_ca_2,V_b_2] :
% 155.39/155.46 ( 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))
% 155.39/155.46 => ( ( V_t_2 = V_s_2
% 155.39/155.46 => hBOOL(hAPP(V_b_2,V_s_2)) )
% 155.39/155.46 => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
% 155.39/155.46 => ! [B_s1] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),V_n_2),B_s1))
% 155.39/155.46 => ~ 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)) ) ) ) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evalc__evaln,axiom,
% 155.39/155.46 ! [V_t,V_s,V_c] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 155.39/155.46 => ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),B_n),V_t)) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evalc_Oequations_I2_J,axiom,
% 155.39/155.46 ! [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)))) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln_Oequations_I2_J,axiom,
% 155.39/155.46 ! [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)))) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evalc_OBody,axiom,
% 155.39/155.46 ! [V_s1,V_s0,V_pn] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 155.39/155.46 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evalc__elim__cases_I6_J,axiom,
% 155.39/155.46 ! [V_s1,V_s,V_P] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 155.39/155.46 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 155.39/155.46
% 155.39/155.46 fof(fact_evaln__max2,axiom,
% 155.39/155.46 ! [V_t2,V_n2,V_s2,V_c2,V_t1,V_n1,V_s1,V_c1] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n1),V_t1))
% 155.39/155.46 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2),V_s2),V_n2),V_t2))
% 155.39/155.46 => ? [B_n] :
% 155.39/155.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),B_n),V_t1))
% 155.39/155.47 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2),V_s2),B_n),V_t2)) ) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evalc_Oequations_I9_J,axiom,
% 155.39/155.47 ! [V_a3_2,V_a2_2,V_a1_2] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 155.39/155.47 <=> 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)) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evaln_OBody,axiom,
% 155.39/155.47 ! [V_s1,V_n,V_s0,V_pn] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => 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)) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evaln_Oequations_I9_J,axiom,
% 155.39/155.47 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 155.39/155.47 ( 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))
% 155.39/155.47 <=> 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)) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_WT_OBody,axiom,
% 155.39/155.47 ! [V_pn] :
% 155.39/155.47 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 155.39/155.47 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_WT_Oequations_I7_J,axiom,
% 155.39/155.47 ! [V_a_2] :
% 155.39/155.47 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 155.39/155.47 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evaln__elim__cases_I6_J,axiom,
% 155.39/155.47 ! [V_s1,V_n,V_s,V_P] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1))
% 155.39/155.47 => ~ ! [B_n] :
% 155.39/155.47 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 155.39/155.47 => ~ 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)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evalc_OLocal,axiom,
% 155.39/155.47 ! [V_s1_2,V_a_2,V_Y_2,V_s0_2,V_ca_2] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => 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)))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evaln_OLocal,axiom,
% 155.39/155.47 ! [V_s1_2,V_n_2,V_a_2,V_Y_2,V_s0_2,V_ca_2] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => 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)))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evalc_Oequations_I3_J,axiom,
% 155.39/155.47 ! [V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 <=> ? [B_s1] :
% 155.39/155.47 ( 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))
% 155.39/155.47 & 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)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evaln_Oequations_I3_J,axiom,
% 155.39/155.47 ! [V_a6_2,V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 <=> ? [B_s1] :
% 155.39/155.47 ( 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))
% 155.39/155.47 & 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)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_WTs__elim__cases_I7_J,axiom,
% 155.39/155.47 ! [V_P] :
% 155.39/155.47 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 155.39/155.47 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_WT__bodiesD,axiom,
% 155.39/155.47 ! [V_b,V_pn] :
% 155.39/155.47 ( c_Com_OWT__bodies
% 155.39/155.47 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 155.39/155.47 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Osimps_I2_J,axiom,
% 155.39/155.47 ! [V_loc_H_2,V_loc_2] :
% 155.39/155.47 ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2)
% 155.39/155.47 <=> V_loc_2 = V_loc_H_2 ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evaln__Suc,axiom,
% 155.39/155.47 ! [V_s_H,V_n,V_s,V_c] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H))
% 155.39/155.47 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evalc__elim__cases_I3_J,axiom,
% 155.39/155.47 ! [V_t_2,V_s_2,V_ca_2,V_a_2,V_Y_2] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => ~ ! [B_s1] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => ~ 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)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evaln__elim__cases_I3_J,axiom,
% 155.39/155.47 ! [V_t_2,V_n_2,V_s_2,V_ca_2,V_a_2,V_Y_2] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => ~ ! [B_s1] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => ~ 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)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_the_Osimps,axiom,
% 155.39/155.47 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 155.39/155.47
% 155.39/155.47 fof(fact_not__None__eq,axiom,
% 155.39/155.47 ! [T_a,V_x_2] :
% 155.39/155.47 ( V_x_2 != c_Option_Ooption_ONone(T_a)
% 155.39/155.47 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_not__Some__eq,axiom,
% 155.39/155.47 ! [T_a,V_x_2] :
% 155.39/155.47 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y)
% 155.39/155.47 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option_Osimps_I3_J,axiom,
% 155.39/155.47 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option_Osimps_I2_J,axiom,
% 155.39/155.47 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Orecs_I2_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Osimps_I6_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option_Oinject,axiom,
% 155.39/155.47 ! [V_a_H_2,V_a_2,T_a] :
% 155.39/155.47 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2)
% 155.39/155.47 <=> V_a_2 = V_a_H_2 ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option_Orecs_I2_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option_Osimps_I5_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option_Orecs_I1_J,axiom,
% 155.39/155.47 ! [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 ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option_Osimps_I4_J,axiom,
% 155.39/155.47 ! [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 ).
% 155.39/155.47
% 155.39/155.47 fof(fact_is__none__code_I2_J,axiom,
% 155.39/155.47 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_is__none__code_I1_J,axiom,
% 155.39/155.47 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_is__none__def,axiom,
% 155.39/155.47 ! [V_x_2,T_a] :
% 155.39/155.47 ( c_Option_Ois__none(T_a,V_x_2)
% 155.39/155.47 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Osimps_I5_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Orecs_I1_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_n__not__Suc__n,axiom,
% 155.39/155.47 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Suc__n__not__n,axiom,
% 155.39/155.47 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Osimps_I1_J,axiom,
% 155.39/155.47 ! [V_glb_H_2,V_glb_2] :
% 155.39/155.47 ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2)
% 155.39/155.47 <=> V_glb_2 = V_glb_H_2 ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Osimps_I3_J,axiom,
% 155.39/155.47 ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Osimps_I4_J,axiom,
% 155.39/155.47 ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Suc__inject,axiom,
% 155.39/155.47 ! [V_y,V_x] :
% 155.39/155.47 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 155.39/155.47 => V_x = V_y ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_nat_Oinject,axiom,
% 155.39/155.47 ! [V_nat_H_2,V_nat_2] :
% 155.39/155.47 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 155.39/155.47 <=> V_nat_2 = V_nat_H_2 ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evalc_OCall,axiom,
% 155.39/155.47 ! [V_X_2,V_s1_2,V_a_2,V_s0_2,V_pn_2] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => 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)))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evaln_OCall,axiom,
% 155.39/155.47 ! [V_X_2,V_s1_2,V_n_2,V_a_2,V_s0_2,V_pn_2] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => 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)))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 155.39/155.47 ! [V_i_2,V_n_2,V_inc_2,T_a] :
% 155.39/155.47 ( class_Rings_Osemiring__1(T_a)
% 155.39/155.47 => 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)) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evalc_Oequations_I10_J,axiom,
% 155.39/155.47 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a5_2] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 <=> ? [B_s1] :
% 155.39/155.47 ( 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))
% 155.39/155.47 & 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)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evaln_Oequations_I10_J,axiom,
% 155.39/155.47 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a6_2] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 <=> ? [B_s1] :
% 155.39/155.47 ( 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))
% 155.39/155.47 & 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)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Body__triple__valid__Suc,axiom,
% 155.39/155.47 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] :
% 155.39/155.47 ( 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))
% 155.39/155.47 <=> 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)) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option_Oexhaust,axiom,
% 155.39/155.47 ! [T_a,V_y] :
% 155.39/155.47 ( V_y != c_Option_Ooption_ONone(T_a)
% 155.39/155.47 => ~ ! [B_a] : V_y != hAPP(c_Option_Ooption_OSome(T_a),B_a) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_nat__case__Suc,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__comp__None__iff,axiom,
% 155.39/155.47 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 155.39/155.47 ( 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)
% 155.39/155.47 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 155.39/155.47 | ? [B_k_H] :
% 155.39/155.47 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 155.39/155.47 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_bind__lunit,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_bind__runit,axiom,
% 155.39/155.47 ! [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 ).
% 155.39/155.47
% 155.39/155.47 fof(fact_triple_Oinject,axiom,
% 155.39/155.47 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] :
% 155.39/155.47 ( 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)
% 155.39/155.47 <=> ( V_fun1_2 = V_fun1_H_2
% 155.39/155.47 & V_com_2 = V_com_H_2
% 155.39/155.47 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_triple__valid__def2,axiom,
% 155.39/155.47 ! [V_Q_2,V_ca_2,V_P_2,V_n_2,T_a] :
% 155.39/155.47 ( 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))
% 155.39/155.47 <=> ! [B_Z,B_s] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 155.39/155.47 => ! [B_s_H] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),B_s),V_n_2),B_s_H))
% 155.39/155.47 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__comp__simps_I1_J,axiom,
% 155.39/155.47 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] :
% 155.39/155.47 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 155.39/155.47 => 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) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__comp__Some__iff,axiom,
% 155.39/155.47 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 155.39/155.47 ( 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)
% 155.39/155.47 <=> ? [B_k_H] :
% 155.39/155.47 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 155.39/155.47 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__comp__simps_I2_J,axiom,
% 155.39/155.47 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] :
% 155.39/155.47 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2)
% 155.39/155.47 => 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) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_triple__valid__Suc,axiom,
% 155.39/155.47 ! [V_t,V_n,T_a] :
% 155.39/155.47 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 155.39/155.47 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_bind__lzero,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evalc__elim__cases_I7_J,axiom,
% 155.39/155.47 ! [V_s1_2,V_s_2,V_a_2,V_P_2,V_X_2] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => ~ ! [B_s1] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => ~ 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)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_evaln__elim__cases_I7_J,axiom,
% 155.39/155.47 ! [V_s1_2,V_n_2,V_s_2,V_a_2,V_P_2,V_X_2] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => ~ ! [B_s1] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => ~ 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)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_triple_Orecs,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_triple_Osimps_I2_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Body__triple__valid__0,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__add__Some__iff,axiom,
% 155.39/155.47 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 155.39/155.47 ( 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)
% 155.39/155.47 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 155.39/155.47 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 155.39/155.47 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__add__SomeD,axiom,
% 155.39/155.47 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 155.39/155.47 ( 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)
% 155.39/155.47 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 155.39/155.47 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 155.39/155.47 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_triples__valid__Suc,axiom,
% 155.39/155.47 ! [V_n_2,V_ts_2,T_a] :
% 155.39/155.47 ( ! [B_x] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 155.39/155.47 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 155.39/155.47 => ! [B_x] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 155.39/155.47 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_hoare__derivs_OCall,axiom,
% 155.39/155.47 ! [V_a_2,V_X_2,V_s_H_2,V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 => 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)))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_nat__rec__Suc,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 155.39/155.47 ! [V_i_2,V_inc_2,T_a] :
% 155.39/155.47 ( class_Rings_Osemiring__1(T_a)
% 155.39/155.47 => 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 ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__add__def,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__add__assoc,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_LoopF,axiom,
% 155.39/155.47 ! [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)))) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__add__empty,axiom,
% 155.39/155.47 ! [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 ).
% 155.39/155.47
% 155.39/155.47 fof(fact_empty__map__add,axiom,
% 155.39/155.47 ! [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 ).
% 155.39/155.47
% 155.39/155.47 fof(fact_derivs__insertD,axiom,
% 155.39/155.47 ! [V_ts_2,V_t_2,V_Ga_2,T_a] :
% 155.39/155.47 ( 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))
% 155.39/155.47 => ( 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))))
% 155.39/155.47 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_hoare__derivs_Oinsert,axiom,
% 155.39/155.47 ! [V_ts_2,V_t_2,V_Ga_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
% 155.39/155.47 => 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)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_cut,axiom,
% 155.39/155.47 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] :
% 155.39/155.47 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 155.39/155.47 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_G_H_2)
% 155.39/155.47 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 155.39/155.47 ! [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))) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_empty,axiom,
% 155.39/155.47 ! [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))) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_nat__rec__0,axiom,
% 155.39/155.47 ! [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 ).
% 155.39/155.47
% 155.39/155.47 fof(fact_hoare__derivs_Oequations_I8_J,axiom,
% 155.39/155.47 ! [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)))) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Ass,axiom,
% 155.39/155.47 ! [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)))) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_bind__assoc,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Comp,axiom,
% 155.39/155.47 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_Ga_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 => ( 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))))
% 155.39/155.47 => 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)))) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_hoare__derivs_OSkip,axiom,
% 155.39/155.47 ! [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)))) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 155.39/155.47 ! [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)))) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_hoare__derivs_OLocal,axiom,
% 155.39/155.47 ! [V_a_2,V_s_H_2,V_X_2,V_Q_2,V_ca_2,V_P_2,V_Ga_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 => 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)))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_bind__rzero,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__comp__empty_I2_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__comp__empty_I1_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__comp__def,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Suc__neq__Zero,axiom,
% 155.39/155.47 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Zero__neq__Suc,axiom,
% 155.39/155.47 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_nat_Osimps_I3_J,axiom,
% 155.39/155.47 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Suc__not__Zero,axiom,
% 155.39/155.47 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_nat_Osimps_I2_J,axiom,
% 155.39/155.47 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Zero__not__Suc,axiom,
% 155.39/155.47 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__add__None,axiom,
% 155.39/155.47 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 155.39/155.47 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a)
% 155.39/155.47 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 155.39/155.47 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_map__add__find__right,axiom,
% 155.39/155.47 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] :
% 155.39/155.47 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2)
% 155.39/155.47 => 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) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_nat__case__0,axiom,
% 155.39/155.47 ! [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 ).
% 155.39/155.47
% 155.39/155.47 fof(fact_weak__Body,axiom,
% 155.39/155.47 ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 => 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)))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_BodyN,axiom,
% 155.39/155.47 ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 => 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)))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_triple_Osize_I1_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Osize_I1_J,axiom,
% 155.39/155.47 ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Osize_I2_J,axiom,
% 155.39/155.47 ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_triple_Osize_I2_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_bot__fun__def,axiom,
% 155.39/155.47 ! [V_x_2,T_b,T_a] :
% 155.39/155.47 ( class_Orderings_Obot(T_a)
% 155.39/155.47 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Osize_I3_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 155.39/155.47 ! [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))) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_vname_Osize_I4_J,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_hoare__valids__def,axiom,
% 155.39/155.47 ! [V_ts_2,V_Ga_2,T_a] :
% 155.39/155.47 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2)
% 155.39/155.47 <=> ! [B_n] :
% 155.39/155.47 ( ! [B_x] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2))
% 155.39/155.47 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) )
% 155.39/155.47 => ! [B_x] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 155.39/155.47 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_ball__empty,axiom,
% 155.39/155.47 ! [V_P_2,T_a,B_x] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 155.39/155.47 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_singleton__inject,axiom,
% 155.39/155.47 ! [V_b_2,V_a_2,T_a] :
% 155.39/155.47 ( 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)))
% 155.39/155.47 => V_a_2 = V_b_2 ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_bot__nat__def,axiom,
% 155.39/155.47 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_hoare__sound,axiom,
% 155.39/155.47 ! [V_ts_2,V_Ga_2,T_a] :
% 155.39/155.47 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
% 155.39/155.47 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_insert__absorb2,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_insert__commute,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_insert__code,axiom,
% 155.39/155.47 ! [V_x_2,V_A_2,V_y_2,T_a] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2))
% 155.39/155.47 <=> ( V_y_2 = V_x_2
% 155.39/155.47 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_set__empty__eq,axiom,
% 155.39/155.47 ! [V_xo_2,T_a] :
% 155.39/155.47 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.39/155.47 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_bot__apply,axiom,
% 155.39/155.47 ! [V_x_2,T_b,T_a] :
% 155.39/155.47 ( class_Orderings_Obot(T_a)
% 155.39/155.47 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_empty__not__insert,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_insert__not__empty,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_doubleton__eq__iff,axiom,
% 155.39/155.47 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 <=> ( ( V_a_2 = V_ca_2
% 155.39/155.47 & V_b_2 = V_d_2 )
% 155.39/155.47 | ( V_a_2 = V_d_2
% 155.39/155.47 & V_b_2 = V_ca_2 ) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_the__elem__eq,axiom,
% 155.39/155.47 ! [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 ).
% 155.39/155.47
% 155.39/155.47 fof(fact_MGT__def,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_escape,axiom,
% 155.39/155.47 ! [V_Q_2,V_ca_2,V_Ga_2,T_a,V_P_2] :
% 155.39/155.47 ( ! [B_Z,B_s] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 155.39/155.47 => 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)))) )
% 155.39/155.47 => 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)))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_conseq1,axiom,
% 155.39/155.47 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_Ga_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 => ( ! [B_Z,B_s] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 155.39/155.47 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 155.39/155.47 => 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)))) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_conseq2,axiom,
% 155.39/155.47 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_Ga_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 => ( ! [B_Z,B_s] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 155.39/155.47 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
% 155.39/155.47 => 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)))) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Option_Omap__def,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_ran__empty,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Loop__sound__lemma,axiom,
% 155.39/155.47 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 => 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)))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Least__Suc,axiom,
% 155.39/155.47 ! [V_n_2,V_P_2] :
% 155.39/155.47 ( hBOOL(hAPP(V_P_2,V_n_2))
% 155.39/155.47 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 155.39/155.47 => 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))) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_com_Osize_I1_J,axiom,
% 155.39/155.47 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_LeastI__ex,axiom,
% 155.39/155.47 ! [V_P_2,T_a] :
% 155.39/155.47 ( class_Orderings_Owellorder(T_a)
% 155.39/155.47 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 155.39/155.47 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_a,V_P_2))) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option__map__comp,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Option_Omap_Ocompositionality,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Option_Omap_Ocomp,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_LeastI,axiom,
% 155.39/155.47 ! [V_k_2,V_P_2,T_a] :
% 155.39/155.47 ( class_Orderings_Owellorder(T_a)
% 155.39/155.47 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 155.39/155.47 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_a,V_P_2))) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_peek__and__def,axiom,
% 155.39/155.47 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] :
% 155.39/155.47 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2))
% 155.39/155.47 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2))
% 155.39/155.47 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option__map__is__None,axiom,
% 155.39/155.47 ! [V_opt_2,V_f_2,T_a,T_b] :
% 155.39/155.47 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a)
% 155.39/155.47 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option__map__None,axiom,
% 155.39/155.47 ! [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) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option__map__eq__Some,axiom,
% 155.39/155.47 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] :
% 155.39/155.47 ( 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)
% 155.39/155.47 <=> ? [B_z] :
% 155.39/155.47 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z)
% 155.39/155.47 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_option__map__Some,axiom,
% 155.39/155.47 ! [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)) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_Loop,axiom,
% 155.39/155.47 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 => 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)))) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_hoare__derivs_OIf,axiom,
% 155.39/155.47 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] :
% 155.39/155.47 ( 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))))
% 155.39/155.47 => ( 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))))
% 155.39/155.47 => 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)))) ) ) ).
% 155.39/155.47
% 155.39/155.47 fof(fact_com_Osize_I7_J,axiom,
% 155.39/155.47 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I2_J,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I8_J,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_MGT__alternI,axiom,
% 155.39/155.48 ! [V_ca_2,V_Ga_2] :
% 155.39/155.48 ( 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))))
% 155.39/155.48 => 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)))) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_the__elem__def,axiom,
% 155.39/155.48 ! [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))))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_o__def,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_K__record__comp,axiom,
% 155.39/155.48 ! [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 ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I4_J,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I3_J,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I5_J,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I6_J,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_ran__map__upd,axiom,
% 155.39/155.48 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] :
% 155.39/155.48 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a)
% 155.39/155.48 => 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)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_Least__Suc2,axiom,
% 155.39/155.48 ! [V_m_2,V_Q_2,V_n_2,V_P_2] :
% 155.39/155.48 ( hBOOL(hAPP(V_P_2,V_n_2))
% 155.39/155.48 => ( hBOOL(hAPP(V_Q_2,V_m_2))
% 155.39/155.48 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 155.39/155.48 => ( ! [B_k] :
% 155.39/155.48 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k)))
% 155.39/155.48 <=> hBOOL(hAPP(V_Q_2,B_k)) )
% 155.39/155.48 => 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)) ) ) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I9_J,axiom,
% 155.39/155.48 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_fun__upd__triv,axiom,
% 155.39/155.48 ! [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 ).
% 155.39/155.48
% 155.39/155.48 fof(fact_fun__upd__def,axiom,
% 155.39/155.48 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] :
% 155.39/155.48 ( ( V_x_2 = V_a_2
% 155.39/155.48 => 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 )
% 155.39/155.48 & ( V_x_2 != V_a_2
% 155.39/155.48 => 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) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_nat__add__right__cancel,axiom,
% 155.39/155.48 ! [V_n_2,V_k_2,V_m_2] :
% 155.39/155.48 ( 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)
% 155.39/155.48 <=> V_m_2 = V_n_2 ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_nat__add__left__cancel,axiom,
% 155.39/155.48 ! [V_n_2,V_m_2,V_k_2] :
% 155.39/155.48 ( 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)
% 155.39/155.48 <=> V_m_2 = V_n_2 ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_nat__add__assoc,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_nat__add__left__commute,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_nat__add__commute,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_fun__upd__idem__iff,axiom,
% 155.39/155.48 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 155.39/155.48 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2
% 155.39/155.48 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_fun__upd__upd,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_fun__upd__same,axiom,
% 155.39/155.48 ! [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 ).
% 155.39/155.48
% 155.39/155.48 fof(fact_fun__upd__apply,axiom,
% 155.39/155.48 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 155.39/155.48 ( ( V_z_2 = V_x_2
% 155.39/155.48 => 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 )
% 155.39/155.48 & ( V_z_2 != V_x_2
% 155.39/155.48 => 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) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_fun__upd__twist,axiom,
% 155.39/155.48 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] :
% 155.39/155.48 ( V_a_2 != V_ca_2
% 155.39/155.48 => 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) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_fun__upd__other,axiom,
% 155.39/155.48 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 155.39/155.48 ( V_z_2 != V_x_2
% 155.39/155.48 => 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) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_fun__upd__idem,axiom,
% 155.39/155.48 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] :
% 155.39/155.48 ( hAPP(V_f_2,V_x_2) = V_y_2
% 155.39/155.48 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_fun__upd__comp,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_option__map__o__map__upd,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__eq__self__zero,axiom,
% 155.39/155.48 ! [V_n,V_m] :
% 155.39/155.48 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 155.39/155.48 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__is__0,axiom,
% 155.39/155.48 ! [V_n_2,V_m_2] :
% 155.39/155.48 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.39/155.48 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.39/155.48 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_Nat_Oadd__0__right,axiom,
% 155.39/155.48 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 155.39/155.48
% 155.39/155.48 fof(fact_plus__nat_Oadd__0,axiom,
% 155.39/155.48 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__Suc__right,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__Suc,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__Suc__shift,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_map__upd__Some__unfold,axiom,
% 155.39/155.48 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] :
% 155.39/155.48 ( 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)
% 155.39/155.48 <=> ( ( V_x_2 = V_a_2
% 155.39/155.48 & V_b_2 = V_y_2 )
% 155.39/155.48 | ( V_x_2 != V_a_2
% 155.39/155.48 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_map__upd__triv,axiom,
% 155.39/155.48 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] :
% 155.39/155.48 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 155.39/155.48 => 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 ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_map__upd__eqD1,axiom,
% 155.39/155.48 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] :
% 155.39/155.48 ( 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))
% 155.39/155.48 => V_x_2 = V_y_2 ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_empty__upd__none,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_triple__valid__def,axiom,
% 155.39/155.48 ! [V_t_2,V_n_2,T_a] :
% 155.39/155.48 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2)
% 155.39/155.48 <=> 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)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I14_J,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I13_J,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I11_J,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I12_J,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__is__1,axiom,
% 155.39/155.48 ! [V_n_2,V_m_2] :
% 155.39/155.48 ( 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))
% 155.39/155.48 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 155.39/155.48 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 155.39/155.48 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.39/155.48 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_one__is__add,axiom,
% 155.39/155.48 ! [V_n_2,V_m_2] :
% 155.39/155.48 ( 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)
% 155.39/155.48 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 155.39/155.48 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 155.39/155.48 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.39/155.48 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_map__add__upd,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_option__map__o__empty,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_map__upd__nonempty,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_o__assoc,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_o__apply,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_o__eq__dest__lhs,axiom,
% 155.39/155.48 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 155.39/155.48 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2
% 155.39/155.48 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_o__eq__dest,axiom,
% 155.39/155.48 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 155.39/155.48 ( 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)
% 155.39/155.48 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_o__eq__elim,axiom,
% 155.39/155.48 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 155.39/155.48 ( 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)
% 155.39/155.48 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I15_J,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I10_J,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_com_Osize_I16_J,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_option_Osize_I2_J,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__0__left,axiom,
% 155.39/155.48 ! [V_a,T_a] :
% 155.39/155.48 ( class_Groups_Omonoid__add(T_a)
% 155.39/155.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 155.39/155.48 ! [V_a,T_a] :
% 155.39/155.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.39/155.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__0,axiom,
% 155.39/155.48 ! [V_a,T_a] :
% 155.39/155.48 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.39/155.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_double__zero__sym,axiom,
% 155.39/155.48 ! [V_a_2,T_a] :
% 155.39/155.48 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.39/155.48 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)
% 155.39/155.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__0__right,axiom,
% 155.39/155.48 ! [V_a,T_a] :
% 155.39/155.48 ( class_Groups_Omonoid__add(T_a)
% 155.39/155.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 155.39/155.48 ! [V_a,T_a] :
% 155.39/155.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.39/155.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add_Ocomm__neutral,axiom,
% 155.39/155.48 ! [V_a,T_a] :
% 155.39/155.48 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.39/155.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__0__iff,axiom,
% 155.39/155.48 ! [V_a_2,V_b_2,T_a] :
% 155.39/155.48 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 155.39/155.48 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)
% 155.39/155.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_double__eq__0__iff,axiom,
% 155.39/155.48 ! [V_a_2,T_a] :
% 155.39/155.48 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.39/155.48 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.39/155.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_zero__reorient,axiom,
% 155.39/155.48 ! [V_x_2,T_a] :
% 155.39/155.48 ( class_Groups_Ozero(T_a)
% 155.39/155.48 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 155.39/155.48 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__right__imp__eq,axiom,
% 155.39/155.48 ! [V_c,V_a,V_b,T_a] :
% 155.39/155.48 ( class_Groups_Ocancel__semigroup__add(T_a)
% 155.39/155.48 => ( 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)
% 155.39/155.48 => V_b = V_c ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__imp__eq,axiom,
% 155.39/155.48 ! [V_c,V_b,V_a,T_a] :
% 155.39/155.48 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 155.39/155.48 => ( 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)
% 155.39/155.48 => V_b = V_c ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__left__imp__eq,axiom,
% 155.39/155.48 ! [V_c,V_b,V_a,T_a] :
% 155.39/155.48 ( class_Groups_Ocancel__semigroup__add(T_a)
% 155.39/155.48 => ( 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)
% 155.39/155.48 => V_b = V_c ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 155.39/155.48 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.39/155.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.39/155.48 => 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)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__right__cancel,axiom,
% 155.39/155.48 ! [V_ca_2,V_a_2,V_b_2,T_a] :
% 155.39/155.48 ( class_Groups_Ocancel__semigroup__add(T_a)
% 155.39/155.48 => ( 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)
% 155.39/155.48 <=> V_b_2 = V_ca_2 ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_add__left__cancel,axiom,
% 155.39/155.48 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 155.39/155.48 ( class_Groups_Ocancel__semigroup__add(T_a)
% 155.39/155.48 => ( 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)
% 155.39/155.48 <=> V_b_2 = V_ca_2 ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 155.39/155.48 ! [V_c,V_b,V_a,T_a] :
% 155.39/155.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.39/155.48 => 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) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 155.39/155.48 ! [V_c,V_b,V_a,T_a] :
% 155.39/155.48 ( class_Groups_Oab__semigroup__add(T_a)
% 155.39/155.48 => 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)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 155.39/155.48 ! [V_c,V_b,V_a,T_a] :
% 155.39/155.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.39/155.48 => 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)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 155.39/155.48 ! [V_d,V_c,V_a,T_a] :
% 155.39/155.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.39/155.48 => 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) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 155.39/155.48 ! [V_d,V_c,V_a,T_a] :
% 155.39/155.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.39/155.48 => 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)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 155.39/155.48 ! [V_c,V_a,T_a] :
% 155.39/155.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.39/155.48 => 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) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_option_Osize_I1_J,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_nat_Osize_I2_J,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_nat_Osize_I4_J,axiom,
% 155.39/155.48 ! [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))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_option_Osize_I4_J,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_option_Osize_I3_J,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_dom__eq__singleton__conv,axiom,
% 155.39/155.48 ! [V_x_2,V_f_2,T_b,T_a] :
% 155.39/155.48 ( 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)))
% 155.39/155.48 <=> ? [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)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_the__eq__trivial,axiom,
% 155.39/155.48 ! [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 ).
% 155.39/155.48
% 155.39/155.48 fof(fact_the__sym__eq__trivial,axiom,
% 155.39/155.48 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 155.39/155.48
% 155.39/155.48 fof(fact_bool_Osize_I2_J,axiom,
% 155.39/155.48 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_bool_Osize_I1_J,axiom,
% 155.39/155.48 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_option__map__o__sum__case,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_nat__size,axiom,
% 155.39/155.48 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 155.39/155.48
% 155.39/155.48 fof(fact_dom__option__map,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_insert__dom,axiom,
% 155.39/155.48 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] :
% 155.39/155.48 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 155.39/155.48 => 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) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_dom__eq__empty__conv,axiom,
% 155.39/155.48 ! [V_f_2,T_b,T_a] :
% 155.39/155.48 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.39/155.48 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_dom__empty,axiom,
% 155.39/155.48 ! [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)) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_nat_Osize_I3_J,axiom,
% 155.39/155.48 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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_nat_Osize_I1_J,axiom,
% 155.39/155.48 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_sum__case__KK,axiom,
% 155.39/155.48 ! [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 ).
% 155.39/155.48
% 155.39/155.48 fof(fact_dom__fun__upd,axiom,
% 155.39/155.48 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] :
% 155.39/155.48 ( ( V_y_2 = c_Option_Ooption_ONone(T_a)
% 155.39/155.48 => 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)))) )
% 155.39/155.48 & ( V_y_2 != c_Option_Ooption_ONone(T_a)
% 155.39/155.48 => 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)) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_map__add__upd__left,axiom,
% 155.39/155.48 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] :
% 155.39/155.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2)))
% 155.39/155.48 => 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)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_sum__case__weak__cong,axiom,
% 155.39/155.48 ! [V_g_2,V_f_2,T_b,T_c,T_a,V_t_2,V_s_2] :
% 155.39/155.48 ( V_s_2 = V_t_2
% 155.39/155.48 => 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) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_sum__case__inject,axiom,
% 155.39/155.48 ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_b,T_c,T_a] :
% 155.39/155.48 ( 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)
% 155.39/155.48 => ~ ( V_f1_2 = V_g1_2
% 155.39/155.48 => V_f2_2 != V_g2_2 ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_map__le__imp__upd__le,axiom,
% 155.39/155.48 ! [V_y_2,V_x_2,V_m2_2,V_m1_2,T_b,T_a] :
% 155.39/155.48 ( c_Map_Omap__le(T_a,T_b,V_m1_2,V_m2_2)
% 155.39/155.48 => 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))) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_bool_Osize_I3_J,axiom,
% 155.39/155.48 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_bool_Osize_I4_J,axiom,
% 155.39/155.48 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_comp__cong,axiom,
% 155.39/155.48 ! [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] :
% 155.39/155.48 ( 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))
% 155.39/155.48 => 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) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_ospec,axiom,
% 155.39/155.48 ! [V_x_2,V_P_2,V_A_2,T_a] :
% 155.39/155.48 ( ! [B_x] :
% 155.39/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Option_Oset(T_a,V_A_2)))
% 155.39/155.48 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.39/155.48 => ( V_A_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 155.39/155.48 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_equalityCE,axiom,
% 155.39/155.48 ! [V_ca_2,T_a,V_B_2,V_A_2] :
% 155.39/155.48 ( V_A_2 = V_B_2
% 155.39/155.48 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.39/155.48 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) )
% 155.39/155.48 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.39/155.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_emptyE,axiom,
% 155.39/155.48 ! [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)))) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_insertCI,axiom,
% 155.39/155.48 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 155.39/155.48 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 155.39/155.48 => V_a_2 = V_b_2 )
% 155.39/155.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_insertE,axiom,
% 155.39/155.48 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 155.39/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 155.39/155.48 => ( V_a_2 != V_b_2
% 155.39/155.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_DiffI,axiom,
% 155.39/155.48 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.39/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.39/155.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 155.39/155.48 => 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))) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_DiffE,axiom,
% 155.39/155.48 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.39/155.48 ( 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)))
% 155.39/155.48 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.39/155.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_mem__def,axiom,
% 155.39/155.48 ! [V_A_2,V_x_2,T_a] :
% 155.39/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.39/155.48 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_Diff__iff,axiom,
% 155.39/155.48 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.39/155.48 ( 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)))
% 155.39/155.48 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.39/155.48 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_Diff__idemp,axiom,
% 155.39/155.48 ! [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) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_eqset__imp__iff,axiom,
% 155.39/155.48 ! [V_x_2,T_a,V_B_2,V_A_2] :
% 155.39/155.48 ( V_A_2 = V_B_2
% 155.39/155.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.39/155.48 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_eqelem__imp__iff,axiom,
% 155.39/155.48 ! [V_A_2,T_a,V_y_2,V_x_2] :
% 155.39/155.48 ( V_x_2 = V_y_2
% 155.39/155.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.39/155.48 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 155.39/155.48
% 155.39/155.48 fof(fact_eq__mem__trans,axiom,
% 155.39/155.48 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 155.55/155.48 ( V_a_2 = V_b_2
% 155.55/155.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 155.55/155.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_DiffD1,axiom,
% 155.55/155.48 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.55/155.48 ( 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)))
% 155.55/155.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_DiffD2,axiom,
% 155.55/155.48 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.55/155.48 ( 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)))
% 155.55/155.48 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__le__refl,axiom,
% 155.55/155.48 ! [V_f_2,T_b,T_a] : c_Map_Omap__le(T_a,T_b,V_f_2,V_f_2) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__le__antisym,axiom,
% 155.55/155.48 ! [V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.48 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2)
% 155.55/155.48 => ( c_Map_Omap__le(T_a,T_b,V_g_2,V_f_2)
% 155.55/155.48 => V_f_2 = V_g_2 ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__le__trans,axiom,
% 155.55/155.48 ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] :
% 155.55/155.48 ( c_Map_Omap__le(T_a,T_b,V_m1_2,V_m2_2)
% 155.55/155.48 => ( c_Map_Omap__le(T_a,T_b,V_m2_2,V_m3_2)
% 155.55/155.48 => c_Map_Omap__le(T_a,T_b,V_m1_2,V_m3_2) ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_insert__Diff1,axiom,
% 155.55/155.48 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 155.55/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 155.55/155.48 => 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) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_insert__Diff__if,axiom,
% 155.55/155.48 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 155.55/155.48 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 155.55/155.48 => 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) )
% 155.55/155.48 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 155.55/155.48 => 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)) ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_diff__eq__diff__eq,axiom,
% 155.55/155.48 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.48 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.48 => ( 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)
% 155.55/155.48 => ( V_a_2 = V_b_2
% 155.55/155.48 <=> V_ca_2 = V_d_2 ) ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_insert__Diff,axiom,
% 155.55/155.48 ! [V_A_2,V_a_2,T_a] :
% 155.55/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.48 => 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 ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_Diff__insert__absorb,axiom,
% 155.55/155.48 ! [V_A_2,V_x_2,T_a] :
% 155.55/155.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.48 => 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 ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_right__minus__eq,axiom,
% 155.55/155.48 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.48 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.48 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.48 <=> V_a_2 = V_b_2 ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_eq__iff__diff__eq__0,axiom,
% 155.55/155.48 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.48 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.48 => ( V_a_2 = V_b_2
% 155.55/155.48 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_diff__self,axiom,
% 155.55/155.48 ! [V_a,T_a] :
% 155.55/155.48 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.48 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_diff__0__right,axiom,
% 155.55/155.48 ! [V_a,T_a] :
% 155.55/155.48 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.48 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_add__diff__cancel,axiom,
% 155.55/155.48 ! [V_b,V_a,T_a] :
% 155.55/155.48 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.48 => 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 ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_diff__add__cancel,axiom,
% 155.55/155.48 ! [V_b,V_a,T_a] :
% 155.55/155.48 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.48 => 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 ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_Diff__cancel,axiom,
% 155.55/155.48 ! [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)) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_Diff__empty,axiom,
% 155.55/155.48 ! [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 ).
% 155.55/155.48
% 155.55/155.48 fof(fact_empty__Diff,axiom,
% 155.55/155.48 ! [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)) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_equals0D,axiom,
% 155.55/155.48 ! [V_a_2,T_a,V_A_2] :
% 155.55/155.48 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.48 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_empty__iff,axiom,
% 155.55/155.48 ! [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)))) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_ex__in__conv,axiom,
% 155.55/155.48 ! [V_A_2,T_a] :
% 155.55/155.48 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.48 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_all__not__in__conv,axiom,
% 155.55/155.48 ! [V_A_2,T_a] :
% 155.55/155.48 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.48 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_insert__absorb,axiom,
% 155.55/155.48 ! [V_A_2,V_a_2,T_a] :
% 155.55/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.48 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_insertI2,axiom,
% 155.55/155.48 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 155.55/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 155.55/155.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_insert__ident,axiom,
% 155.55/155.48 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 155.55/155.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 155.55/155.48 => ( 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)
% 155.55/155.48 <=> V_A_2 = V_B_2 ) ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_insert__iff,axiom,
% 155.55/155.48 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 155.55/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 155.55/155.48 <=> ( V_a_2 = V_b_2
% 155.55/155.48 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_insertI1,axiom,
% 155.55/155.48 ! [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))) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__le__def,axiom,
% 155.55/155.48 ! [V_m_092_060_094isub_0622_2,V_m_092_060_094isub_0621_2,T_b,T_a] :
% 155.55/155.48 ( c_Map_Omap__le(T_a,T_b,V_m_092_060_094isub_0621_2,V_m_092_060_094isub_0622_2)
% 155.55/155.48 <=> ! [B_x] :
% 155.55/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Map_Odom(T_a,T_b,V_m_092_060_094isub_0621_2)))
% 155.55/155.48 => hAPP(V_m_092_060_094isub_0621_2,B_x) = hAPP(V_m_092_060_094isub_0622_2,B_x) ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__le__upd,axiom,
% 155.55/155.48 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.48 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2)
% 155.55/155.48 => 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)) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__le__map__add,axiom,
% 155.55/155.48 ! [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)) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__le__iff__map__add__commute,axiom,
% 155.55/155.48 ! [V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.48 ( 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))
% 155.55/155.48 <=> 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) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__add__le__mapI,axiom,
% 155.55/155.48 ! [V_g_2,V_h_2,V_f_2,T_b,T_a] :
% 155.55/155.48 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_h_2)
% 155.55/155.48 => ( c_Map_Omap__le(T_a,T_b,V_g_2,V_h_2)
% 155.55/155.48 => ( 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))
% 155.55/155.48 => 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) ) ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__add__le__mapE,axiom,
% 155.55/155.48 ! [V_h_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.48 ( 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)
% 155.55/155.48 => c_Map_Omap__le(T_a,T_b,V_g_2,V_h_2) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__le__empty,axiom,
% 155.55/155.48 ! [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) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_insert__Diff__single,axiom,
% 155.55/155.48 ! [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) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_Diff__insert2,axiom,
% 155.55/155.48 ! [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) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_Diff__insert,axiom,
% 155.55/155.48 ! [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)))) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_singletonE,axiom,
% 155.55/155.48 ! [V_a_2,V_b_2,T_a] :
% 155.55/155.48 ( 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)))))
% 155.55/155.48 => V_b_2 = V_a_2 ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_singleton__iff,axiom,
% 155.55/155.48 ! [V_a_2,V_b_2,T_a] :
% 155.55/155.48 ( 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)))))
% 155.55/155.48 <=> V_b_2 = V_a_2 ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_domIff,axiom,
% 155.55/155.48 ! [V_m_2,T_b,V_a_2,T_a] :
% 155.55/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2)))
% 155.55/155.48 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_domI,axiom,
% 155.55/155.48 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 155.55/155.48 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 155.55/155.48 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 155.55/155.48 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] :
% 155.55/155.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2)))
% 155.55/155.48 => 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) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 155.55/155.48 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 155.55/155.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 155.55/155.48 => 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) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 155.55/155.48 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 155.55/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 155.55/155.48 => 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) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_ranI,axiom,
% 155.55/155.48 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 155.55/155.48 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 155.55/155.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_elem__set,axiom,
% 155.55/155.48 ! [V_xo_2,V_x_2,T_a] :
% 155.55/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2)))
% 155.55/155.48 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_upd__None__map__le,axiom,
% 155.55/155.48 ! [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) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_dom__minus,axiom,
% 155.55/155.48 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] :
% 155.55/155.48 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a)
% 155.55/155.48 => 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) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_fun__diff__def,axiom,
% 155.55/155.48 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.48 ( class_Groups_Ominus(T_a)
% 155.55/155.48 => 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)) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_bot__empty__eq,axiom,
% 155.55/155.48 ! [V_x_2,T_a] :
% 155.55/155.48 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2))
% 155.55/155.48 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_fun__upd__None__restrict,axiom,
% 155.55/155.48 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 155.55/155.48 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 155.55/155.48 => 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))))) )
% 155.55/155.48 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 155.55/155.48 => 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) ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_minus__apply,axiom,
% 155.55/155.48 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.48 ( class_Groups_Ominus(T_a)
% 155.55/155.48 => 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)) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_fun__upd__restrict__conv,axiom,
% 155.55/155.48 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 155.55/155.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 155.55/155.48 => 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) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_restrict__fun__upd,axiom,
% 155.55/155.48 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 155.55/155.48 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 155.55/155.48 => 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) )
% 155.55/155.48 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 155.55/155.48 => 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) ) ) ).
% 155.55/155.48
% 155.55/155.48 fof(fact_fun__upd__restrict,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 155.55/155.49 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => ( 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)
% 155.55/155.49 => 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)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_fun__upd__image,axiom,
% 155.55/155.49 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 155.55/155.49 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => 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)))))) )
% 155.55/155.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => 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) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_pred__equals__eq,axiom,
% 155.55/155.49 ! [V_S_2,V_R_2,T_a] :
% 155.55/155.49 ( 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)
% 155.55/155.49 <=> V_R_2 = V_S_2 ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__eqI,axiom,
% 155.55/155.49 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] :
% 155.55/155.49 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 155.55/155.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__image,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__ident,axiom,
% 155.55/155.49 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 155.55/155.49
% 155.55/155.49 fof(fact_rev__image__eqI,axiom,
% 155.55/155.49 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 155.55/155.49 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_imageI,axiom,
% 155.55/155.49 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => 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))) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__iff,axiom,
% 155.55/155.49 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 155.55/155.49 <=> ? [B_x] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.55/155.49 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_empty__is__image,axiom,
% 155.55/155.49 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( 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)
% 155.55/155.49 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__empty,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__is__empty,axiom,
% 155.55/155.49 ! [V_A_2,V_f_2,T_a,T_b] :
% 155.55/155.49 ( 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))
% 155.55/155.49 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__insert,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__compose,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diffs0__imp__equal,axiom,
% 155.55/155.49 ! [V_n,V_m] :
% 155.55/155.49 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.49 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.49 => V_m = V_n ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__self__eq__0,axiom,
% 155.55/155.49 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_minus__nat_Odiff__0,axiom,
% 155.55/155.49 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__0__eq__0,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__Suc__Suc,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Suc__diff__diff,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__cancel2,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__cancel,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__diff__left,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__add__inverse,axiom,
% 155.55/155.49 ! [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 ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__add__inverse2,axiom,
% 155.55/155.49 ! [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 ).
% 155.55/155.49
% 155.55/155.49 fof(fact_restrict__in,axiom,
% 155.55/155.49 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_insert__image,axiom,
% 155.55/155.49 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_restrict__map__empty,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__add__0,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__constant__conv,axiom,
% 155.55/155.49 ! [V_ca_2,T_b,T_a,V_A_2] :
% 155.55/155.49 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.49 => 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)) )
% 155.55/155.49 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.49 => 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))) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__Suc,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_restrict__out,axiom,
% 155.55/155.49 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 155.55/155.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_restrict__map__insert,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__map__upd,axiom,
% 155.55/155.49 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 155.55/155.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_restrict__map__def,axiom,
% 155.55/155.49 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 155.55/155.49 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => 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) )
% 155.55/155.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_restrict__map__to__empty,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__constant,axiom,
% 155.55/155.49 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => 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))) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_eq__mem,axiom,
% 155.55/155.49 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))
% 155.55/155.49 <=> V_x_2 = V_y_2 ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Body1,axiom,
% 155.55/155.49 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2))
% 155.55/155.49 => 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)))) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 155.55/155.49 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.49 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 155.55/155.49 | ? [B_x,B_y] :
% 155.55/155.49 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 155.55/155.49 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2))
% 155.55/155.49 & 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) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Body__sound__lemma,axiom,
% 155.55/155.49 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_hoare__derivs_OBody,axiom,
% 155.55/155.49 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_ran__restrictD,axiom,
% 155.55/155.49 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] :
% 155.55/155.49 ( 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))))
% 155.55/155.49 => ? [B_x] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.55/155.49 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_restrict__upd__same,axiom,
% 155.55/155.49 ! [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))))) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_restrict__complement__singleton__eq,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_pair__box_Osize_I1_J,axiom,
% 155.55/155.49 ! [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))) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__insert,axiom,
% 155.55/155.49 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))
% 155.55/155.49 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 & ~ 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))))))) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Powp__def,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2))
% 155.55/155.49 <=> ! [B_x] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 155.55/155.49 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup1E,axiom,
% 155.55/155.49 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 155.55/155.49 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup1CI,axiom,
% 155.55/155.49 ! [T_a,V_A_2,V_x_2,V_B_2] :
% 155.55/155.49 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 155.55/155.49 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_UnE,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( 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)))
% 155.55/155.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_UnCI,axiom,
% 155.55/155.49 ! [V_A_2,V_B_2,V_ca_2,T_a] :
% 155.55/155.49 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 155.55/155.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) )
% 155.55/155.49 => 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))) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__empty,axiom,
% 155.55/155.49 ! [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))) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__uminus,axiom,
% 155.55/155.49 ! [V_A_2,T_a] :
% 155.55/155.49 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.49 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_ComplI,axiom,
% 155.55/155.49 ! [V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.49 => 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))) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Compl__Diff__eq,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__commute,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_fun__Compl__def,axiom,
% 155.55/155.49 ! [V_x_2,V_A_2,T_b,T_a] :
% 155.55/155.49 ( class_Groups_Ouminus(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__fun__def,axiom,
% 155.55/155.49 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_double__compl,axiom,
% 155.55/155.49 ! [V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup_Oidem,axiom,
% 155.55/155.49 ! [V_a,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.49 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__idem,axiom,
% 155.55/155.49 ! [V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.49 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_uminus__apply,axiom,
% 155.55/155.49 ! [V_x_2,V_A_2,T_b,T_a] :
% 155.55/155.49 ( class_Groups_Ouminus(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup_Ocommute,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__sup__aci_I5_J,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__commute,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup_Oleft__idem,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__sup__aci_I8_J,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__left__idem,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup_Oleft__commute,axiom,
% 155.55/155.49 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__sup__aci_I7_J,axiom,
% 155.55/155.49 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__left__commute,axiom,
% 155.55/155.49 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_compl__eq__compl__iff,axiom,
% 155.55/155.49 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.49 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)
% 155.55/155.49 <=> V_x_2 = V_y_2 ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup_Oassoc,axiom,
% 155.55/155.49 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__sup__aci_I6_J,axiom,
% 155.55/155.49 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__assoc,axiom,
% 155.55/155.49 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__apply,axiom,
% 155.55/155.49 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup1I1,axiom,
% 155.55/155.49 ! [V_B_2,T_a,V_x_2,V_A_2] :
% 155.55/155.49 ( hBOOL(hAPP(V_A_2,V_x_2))
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup1I2,axiom,
% 155.55/155.49 ! [V_A_2,T_a,V_x_2,V_B_2] :
% 155.55/155.49 ( hBOOL(hAPP(V_B_2,V_x_2))
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 => ( 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)
% 155.55/155.49 <=> V_A_2 = V_B_2 ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__def,axiom,
% 155.55/155.49 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 <=> ! [B_x] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.49 => ! [B_xa] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 155.55/155.49 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 155.55/155.49 => B_x = B_xa ) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_double__complement,axiom,
% 155.55/155.49 ! [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 ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__absorb,axiom,
% 155.55/155.49 ! [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 ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__commute,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__left__absorb,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__left__commute,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Compl__eq__Compl__iff,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.49 ( 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)
% 155.55/155.49 <=> V_A_2 = V_B_2 ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__assoc,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_bex__Un,axiom,
% 155.55/155.49 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 155.55/155.49 ( ? [B_x] :
% 155.55/155.49 ( 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)))
% 155.55/155.49 & hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.49 <=> ( ? [B_x] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.49 & hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.49 | ? [B_x] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 155.55/155.49 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_ball__Un,axiom,
% 155.55/155.49 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 155.55/155.49 ( ! [B_x] :
% 155.55/155.49 ( 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)))
% 155.55/155.49 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.49 <=> ( ! [B_x] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.49 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.49 & ! [B_x] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 155.55/155.49 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__id2,axiom,
% 155.55/155.49 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_minus__minus,axiom,
% 155.55/155.49 ! [V_a,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_equation__minus__iff,axiom,
% 155.55/155.49 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 155.55/155.49 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_minus__equation__iff,axiom,
% 155.55/155.49 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2
% 155.55/155.49 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_neg__equal__iff__equal,axiom,
% 155.55/155.49 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 155.55/155.49 <=> V_a_2 = V_b_2 ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_pair__box_Oinject,axiom,
% 155.55/155.49 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.49 ( 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)
% 155.55/155.49 <=> ( V_a_2 = V_a_H_2
% 155.55/155.49 & V_b_2 = V_b_H_2 ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__contraD,axiom,
% 155.55/155.49 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => ( V_x_2 != V_y_2
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 155.55/155.49 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__iff,axiom,
% 155.55/155.49 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 155.55/155.49 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 155.55/155.49 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__onD,axiom,
% 155.55/155.49 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 155.55/155.49 => V_x_2 = V_y_2 ) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__Suc,axiom,
% 155.55/155.49 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__imageI2,axiom,
% 155.55/155.49 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] :
% 155.55/155.49 ( 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)
% 155.55/155.49 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__diff,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_neg__equal__zero,axiom,
% 155.55/155.49 ! [V_a_2,T_a] :
% 155.55/155.49 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2
% 155.55/155.49 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_neg__equal__0__iff__equal,axiom,
% 155.55/155.49 ! [V_a_2,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.49 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_equal__neg__zero,axiom,
% 155.55/155.49 ! [V_a_2,T_a] :
% 155.55/155.49 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.49 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 155.55/155.49 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_neg__0__equal__iff__equal,axiom,
% 155.55/155.49 ! [V_a_2,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 155.55/155.49 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_minus__zero,axiom,
% 155.55/155.49 ! [T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__eq__bot__iff,axiom,
% 155.55/155.49 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.49 ( class_Lattices_Obounded__lattice__bot(T_a)
% 155.55/155.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a)
% 155.55/155.49 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a)
% 155.55/155.49 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__bot__right,axiom,
% 155.55/155.49 ! [V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Obounded__lattice__bot(T_a)
% 155.55/155.49 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__bot__left,axiom,
% 155.55/155.49 ! [V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Obounded__lattice__bot(T_a)
% 155.55/155.49 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_minus__add__cancel,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => 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 ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_add__minus__cancel,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => 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 ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_minus__add,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_minus__add__distrib,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Compl__iff,axiom,
% 155.55/155.49 ! [V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( 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)))
% 155.55/155.49 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_ComplD,axiom,
% 155.55/155.49 ! [V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( 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)))
% 155.55/155.49 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_ComplE,axiom,
% 155.55/155.49 ! [V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( 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)))
% 155.55/155.49 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_minus__diff__eq,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__Some,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__iff,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( 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)))
% 155.55/155.49 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.49 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_UnI1,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.49 => 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))) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_UnI2,axiom,
% 155.55/155.49 ! [V_A_2,V_B_2,V_ca_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 155.55/155.49 => 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))) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__empty,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.49 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__empty__right,axiom,
% 155.55/155.49 ! [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 ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__empty__left,axiom,
% 155.55/155.49 ! [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 ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__insert__left,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__insert__right,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_image__Un,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__Diff__cancel,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__Diff__cancel2,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__Diff,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__add__nat,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__Un__eq,axiom,
% 155.55/155.49 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 <=> 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))) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__imageI,axiom,
% 155.55/155.49 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] :
% 155.55/155.49 ( 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)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_comp__inj__on,axiom,
% 155.55/155.49 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => ( 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))
% 155.55/155.49 => 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) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_comp__inj__on__iff,axiom,
% 155.55/155.49 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => ( 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))
% 155.55/155.49 <=> 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) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_right__minus,axiom,
% 155.55/155.49 ! [V_a,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 155.55/155.49 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 155.55/155.49 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_left__minus,axiom,
% 155.55/155.49 ! [V_a,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_ab__left__minus,axiom,
% 155.55/155.49 ! [V_a,T_a] :
% 155.55/155.49 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_minus__unique,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__0,axiom,
% 155.55/155.49 ! [V_a,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__minus__eq__add,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Rings_Ocomm__ring__1(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_ab__diff__minus,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__def,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Groups_Ogroup__add(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_insert__is__Un,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__map__add__dom,axiom,
% 155.55/155.49 ! [V_m_H_2,V_m_2,T_b,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 <=> 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_dom__map__add,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__fun__updI,axiom,
% 155.55/155.49 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 155.55/155.49 => 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) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_pair__box_Osize_I2_J,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_pair__box_Orecs,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_pair__box_Osimps_I2_J,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_the__inv__into__comp,axiom,
% 155.55/155.49 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2)
% 155.55/155.49 => ( 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))))
% 155.55/155.49 => 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) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__Un,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 155.55/155.49 & 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)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_f__the__inv__into__f,axiom,
% 155.55/155.49 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 155.55/155.49 => 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 ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_the__inv__into__def,axiom,
% 155.55/155.49 ! [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))) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Ints__double__eq__0__iff,axiom,
% 155.55/155.49 ! [V_a_2,T_a] :
% 155.55/155.49 ( class_Int_Oring__char__0(T_a)
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 155.55/155.49 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.49 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_add__eq__if,axiom,
% 155.55/155.49 ! [V_n,V_m] :
% 155.55/155.49 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 155.55/155.49 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.49 => 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)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf1E,axiom,
% 155.55/155.49 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 155.55/155.49 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf1I,axiom,
% 155.55/155.49 ! [T_a,V_B_2,V_x_2,V_A_2] :
% 155.55/155.49 ( hBOOL(hAPP(V_A_2,V_x_2))
% 155.55/155.49 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 155.55/155.49 => 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)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_IntE,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( 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)))
% 155.55/155.49 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.49 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_IntI,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 155.55/155.49 => 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))) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_one__reorient,axiom,
% 155.55/155.49 ! [V_x_2,T_a] :
% 155.55/155.49 ( class_Groups_Oone(T_a)
% 155.55/155.49 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 155.55/155.49 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__assoc,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__left__commute,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__left__absorb,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__commute,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__absorb,axiom,
% 155.55/155.49 ! [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 ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf1D2,axiom,
% 155.55/155.49 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf1D1,axiom,
% 155.55/155.49 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__apply,axiom,
% 155.55/155.49 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__assoc,axiom,
% 155.55/155.49 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__sup__aci_I2_J,axiom,
% 155.55/155.49 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf_Oassoc,axiom,
% 155.55/155.49 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__left__commute,axiom,
% 155.55/155.49 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__sup__aci_I3_J,axiom,
% 155.55/155.49 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf_Oleft__commute,axiom,
% 155.55/155.49 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__left__idem,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__sup__aci_I4_J,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf_Oleft__idem,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__commute,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__sup__aci_I1_J,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf_Ocommute,axiom,
% 155.55/155.49 ! [V_b,V_a,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__idem,axiom,
% 155.55/155.49 ! [V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf_Oidem,axiom,
% 155.55/155.49 ! [V_a,T_a] :
% 155.55/155.49 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__fun__def,axiom,
% 155.55/155.49 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Ints__1,axiom,
% 155.55/155.49 ! [T_a] :
% 155.55/155.49 ( class_Rings_Oring__1(T_a)
% 155.55/155.49 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__bot__left,axiom,
% 155.55/155.49 ! [V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Obounded__lattice__bot(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__bot__right,axiom,
% 155.55/155.49 ! [V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Obounded__lattice__bot(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__inf__distrib2,axiom,
% 155.55/155.49 ! [V_x,V_z,V_y,T_a] :
% 155.55/155.49 ( class_Lattices_Odistrib__lattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__sup__distrib2,axiom,
% 155.55/155.49 ! [V_x,V_z,V_y,T_a] :
% 155.55/155.49 ( class_Lattices_Odistrib__lattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__inf__distrib1,axiom,
% 155.55/155.49 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Odistrib__lattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__sup__distrib1,axiom,
% 155.55/155.49 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Odistrib__lattice(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_sup__inf__absorb,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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 ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__sup__absorb,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Olattice(T_a)
% 155.55/155.49 => 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 ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_IntD2,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( 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)))
% 155.55/155.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_IntD1,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( 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)))
% 155.55/155.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__iff,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 155.55/155.49 ( 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)))
% 155.55/155.49 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.49 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__empty__left,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__empty__right,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_disjoint__iff__not__equal,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 <=> ! [B_x] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.49 => ! [B_xa] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2))
% 155.55/155.49 => B_x != B_xa ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_insert__inter__insert,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__Int__crazy,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__Int__distrib2,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__Un__distrib2,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__Int__distrib,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__Un__distrib,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Diff__Int2,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Diff__Int__distrib2,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__Diff,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Diff__Int__distrib,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__Int,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 155.55/155.49 => 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)) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_restrict__restrict,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__Int__eq,axiom,
% 155.55/155.49 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 <=> 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))) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Ints__odd__nonzero,axiom,
% 155.55/155.49 ! [V_a_2,T_a] :
% 155.55/155.49 ( class_Int_Oring__char__0(T_a)
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 155.55/155.49 => 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) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_compl__inf__bot,axiom,
% 155.55/155.49 ! [V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inf__compl__bot,axiom,
% 155.55/155.49 ! [V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__eq,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_compl__sup,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_compl__inf,axiom,
% 155.55/155.49 ! [V_y,V_x,T_a] :
% 155.55/155.49 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__insert__right,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 155.55/155.49 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.49 => 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)) )
% 155.55/155.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.49 => 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) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__insert__left,axiom,
% 155.55/155.49 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 155.55/155.49 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 155.55/155.49 => 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)) )
% 155.55/155.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 155.55/155.49 => 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) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__insert__right__if0,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 155.55/155.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__insert__left__if0,axiom,
% 155.55/155.49 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 155.55/155.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__insert__right__if1,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Int__insert__left__if1,axiom,
% 155.55/155.49 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 155.55/155.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Diff__disjoint,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Diff__triv,axiom,
% 155.55/155.49 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Un__Diff__Int,axiom,
% 155.55/155.49 ! [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 ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Diff__Un,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Diff__Int,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_One__nat__def,axiom,
% 155.55/155.49 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Compl__disjoint,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Compl__disjoint2,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Suc__eq__plus1,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Suc__eq__plus1__left,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_diff__Suc__1,axiom,
% 155.55/155.49 ! [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 ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Compl__Un,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Compl__Int,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Diff__Compl,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Diff__eq,axiom,
% 155.55/155.49 ! [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)) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_dom__restrict,axiom,
% 155.55/155.49 ! [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) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Ints__0,axiom,
% 155.55/155.49 ! [T_a] :
% 155.55/155.49 ( class_Rings_Oring__1(T_a)
% 155.55/155.49 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Ints__add,axiom,
% 155.55/155.49 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.49 ( class_Rings_Oring__1(T_a)
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 155.55/155.49 => 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))) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Ints__diff,axiom,
% 155.55/155.49 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.49 ( class_Rings_Oring__1(T_a)
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 155.55/155.49 => 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))) ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_Ints__minus,axiom,
% 155.55/155.49 ! [V_a_2,T_a] :
% 155.55/155.49 ( class_Rings_Oring__1(T_a)
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 155.55/155.49 => 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))) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_map__add__comm,axiom,
% 155.55/155.49 ! [V_m2_2,V_m1_2,T_b,T_a] :
% 155.55/155.49 ( 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))
% 155.55/155.49 => 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) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_the__inv__into__f__eq,axiom,
% 155.55/155.49 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_the__inv__into__f__f,axiom,
% 155.55/155.49 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.49 => 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 ) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_the__inv__into__onto,axiom,
% 155.55/155.49 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => 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 ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_inj__on__the__inv__into,axiom,
% 155.55/155.49 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.49 => 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)) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_one__neq__zero,axiom,
% 155.55/155.49 ! [T_a] :
% 155.55/155.49 ( class_Rings_Ozero__neq__one(T_a)
% 155.55/155.49 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_zero__neq__one,axiom,
% 155.55/155.49 ! [T_a] :
% 155.55/155.49 ( class_Rings_Ozero__neq__one(T_a)
% 155.55/155.49 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 155.55/155.49
% 155.55/155.49 fof(fact_compl__unique,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.50 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 155.55/155.50 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 155.55/155.50 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_Ints__odd__less__0,axiom,
% 155.55/155.50 ! [V_a_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 155.55/155.50 ! [V_n_2,T_a] :
% 155.55/155.50 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_the__inv__into__into,axiom,
% 155.55/155.50 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.50 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => 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)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_Suc__diff__1,axiom,
% 155.55/155.50 ! [V_n] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.50 => 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 ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_Suc__pred_H,axiom,
% 155.55/155.50 ! [V_n] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.50 => 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__eq__if,axiom,
% 155.55/155.50 ! [V_n,V_m] :
% 155.55/155.50 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 155.55/155.50 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.50 => 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)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__refl,axiom,
% 155.55/155.50 ! [V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_UNIV__I,axiom,
% 155.55/155.50 ! [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)))) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_negative__zless,axiom,
% 155.55/155.50 ! [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))) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_equalityI,axiom,
% 155.55/155.50 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.50 => V_A_2 = V_B_2 ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_subsetD,axiom,
% 155.55/155.50 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_empty__subsetI,axiom,
% 155.55/155.50 ! [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)) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__zeroE,axiom,
% 155.55/155.50 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_Suc__mono,axiom,
% 155.55/155.50 ! [V_n,V_m] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_lessI,axiom,
% 155.55/155.50 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_zero__less__Suc,axiom,
% 155.55/155.50 ! [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))) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_negative__zless__0,axiom,
% 155.55/155.50 ! [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))) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_int__Suc,axiom,
% 155.55/155.50 ! [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)) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_int__1,axiom,
% 155.55/155.50 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) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__1__mult,axiom,
% 155.55/155.50 ! [V_n,V_m,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__class_Odistrib,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_combine__common__factor,axiom,
% 155.55/155.50 ! [V_c,V_b,V_e,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Osemiring(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_of__nat__0__less__iff,axiom,
% 155.55/155.50 ! [V_n_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_minus__mult__right,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oring(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_minus__mult__left,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oring(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_minus__mult__commute,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oring(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_minus__mult__minus,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oring(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_square__eq__iff,axiom,
% 155.55/155.50 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Rings_Oidom(T_a)
% 155.55/155.50 => ( 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)
% 155.55/155.50 <=> ( V_a_2 = V_b_2
% 155.55/155.50 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_times_Oidem,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 155.55/155.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__idem,axiom,
% 155.55/155.50 ! [V_x,T_a] :
% 155.55/155.50 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 155.55/155.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__left__idem,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_rev__predicate1D,axiom,
% 155.55/155.50 ! [V_Q_2,T_a,V_x_2,V_P_2] :
% 155.55/155.50 ( hBOOL(hAPP(V_P_2,V_x_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 155.55/155.50 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_predicate1D,axiom,
% 155.55/155.50 ! [V_x_2,V_Q_2,V_P_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 155.55/155.50 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 155.55/155.50 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__less__mono2,axiom,
% 155.55/155.50 ! [V_k,V_j,V_i] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__less__mono1,axiom,
% 155.55/155.50 ! [V_k,V_j,V_i] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__less__cancel2,axiom,
% 155.55/155.50 ! [V_n_2,V_k_2,V_m_2] :
% 155.55/155.50 ( 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)))
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__less__cancel1,axiom,
% 155.55/155.50 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.50 ( 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)))
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_nat__0__less__mult__iff,axiom,
% 155.55/155.50 ! [V_n_2,V_m_2] :
% 155.55/155.50 ( 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)))
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_Suc__mult__less__cancel1,axiom,
% 155.55/155.50 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.50 ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__less__irrefl,axiom,
% 155.55/155.50 ! [V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_subset__UNIV,axiom,
% 155.55/155.50 ! [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)))) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_top__greatest,axiom,
% 155.55/155.50 ! [V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Otop(T_a)
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_subset__refl,axiom,
% 155.55/155.50 ! [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)) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_top__apply,axiom,
% 155.55/155.50 ! [V_x_2,T_b,T_a] :
% 155.55/155.50 ( class_Orderings_Otop(T_a)
% 155.55/155.50 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__not__less,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__not__le,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__neq__iff,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( V_x_2 != V_y_2
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 155.55/155.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_not__less__iff__gr__or__eq,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 155.55/155.50 | V_x_2 = V_y_2 ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_le__fun__def,axiom,
% 155.55/155.50 ! [V_g_2,V_f_2,T_a,T_b] :
% 155.55/155.50 ( class_Orderings_Oord(T_b)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 155.55/155.50 <=> ! [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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__le__less__linear,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__linear,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_psubset__eq,axiom,
% 155.55/155.50 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 & V_A_2 != V_B_2 ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__fun__def,axiom,
% 155.55/155.50 ! [V_g_2,V_f_2,T_a,T_b] :
% 155.55/155.50 ( class_Orderings_Oord(T_b)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 155.55/155.50 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__less__le,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.50 & V_x_2 != V_y_2 ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__le__not__le,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.50 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_set__eq__subset,axiom,
% 155.55/155.50 ! [T_a,V_B_2,V_A_2] :
% 155.55/155.50 ( V_A_2 = V_B_2
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__eq__iff,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( V_x_2 = V_y_2
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_subset__iff__psubset__eq,axiom,
% 155.55/155.50 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 | V_A_2 = V_B_2 ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__le__less,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 155.55/155.50 | V_x_2 = V_y_2 ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__less__linear,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 | V_x = V_y
% 155.55/155.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_leI,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_not__leE,axiom,
% 155.55/155.50 ! [V_x,V_y,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__antisym__conv3,axiom,
% 155.55/155.50 ! [V_x_2,V_y_2,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 155.55/155.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__antisym__conv1,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__neq__le__trans,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( V_a != V_b
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I12_J,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( V_a != V_b
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__neqE,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( V_x != V_y
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__imp__neq,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => V_x != V_y ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__less__not__sym,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_leD,axiom,
% 155.55/155.50 ! [V_x,V_y,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_equalityD1,axiom,
% 155.55/155.50 ! [T_a,V_B_2,V_A_2] :
% 155.55/155.50 ( V_A_2 = V_B_2
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_equalityD2,axiom,
% 155.55/155.50 ! [T_a,V_B_2,V_A_2] :
% 155.55/155.50 ( V_A_2 = V_B_2
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__eq__refl,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ( V_x = V_y
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_psubset__imp__subset,axiom,
% 155.55/155.50 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__less__imp__le,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__less__imp__not__less,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__antisym__conv2,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 155.55/155.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_le__funD,axiom,
% 155.55/155.50 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 155.55/155.50 ( class_Orderings_Oord(T_b)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__less__imp__not__eq,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => V_x != V_y ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__less__imp__not__eq2,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => V_y != V_x ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__le__imp__less__or__eq,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 | V_x = V_y ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__antisym__conv,axiom,
% 155.55/155.50 ! [V_x_2,V_y_2,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__le__neq__trans,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => ( V_a != V_b
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I11_J,axiom,
% 155.55/155.50 ! [V_a,V_b,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 155.55/155.50 => ( V_a != V_b
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__less__asym_H,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I9_J,axiom,
% 155.55/155.50 ! [V_a,V_b,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 155.55/155.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_ord__eq__less__trans,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Orderings_Oord(T_a)
% 155.55/155.50 => ( V_a = V_b
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I1_J,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( V_a = V_b
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_ord__eq__le__trans,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Orderings_Oord(T_a)
% 155.55/155.50 => ( V_a = V_b
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I3_J,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( V_a = V_b
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_psubset__subset__trans,axiom,
% 155.55/155.50 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_ord__less__eq__trans,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Orderings_Oord(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => ( V_b = V_c
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I2_J,axiom,
% 155.55/155.50 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 155.55/155.50 => ( V_b = V_c
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__less__trans,axiom,
% 155.55/155.50 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__less__le__trans,axiom,
% 155.55/155.50 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I10_J,axiom,
% 155.55/155.50 ! [V_z,V_x,V_y,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I7_J,axiom,
% 155.55/155.50 ! [V_z,V_x,V_y,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_subset__psubset__trans,axiom,
% 155.55/155.50 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_subset__trans,axiom,
% 155.55/155.50 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_ord__le__eq__trans,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Orderings_Oord(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => ( V_b = V_c
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I4_J,axiom,
% 155.55/155.50 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 155.55/155.50 => ( V_b = V_c
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__le__less__trans,axiom,
% 155.55/155.50 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__antisym,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.50 => V_x = V_y ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__trans,axiom,
% 155.55/155.50 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I8_J,axiom,
% 155.55/155.50 ! [V_z,V_x,V_y,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I5_J,axiom,
% 155.55/155.50 ! [V_x,V_y,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.50 => V_x = V_y ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_xt1_I6_J,axiom,
% 155.55/155.50 ! [V_z,V_x,V_y,T_a] :
% 155.55/155.50 ( class_Orderings_Oorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_order__less__asym,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Opreorder(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_equalityE,axiom,
% 155.55/155.50 ! [T_a,V_B_2,V_A_2] :
% 155.55/155.50 ( V_A_2 = V_B_2
% 155.55/155.50 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_le__funE,axiom,
% 155.55/155.50 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 155.55/155.50 ( class_Orderings_Oord(T_b)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__le__cases,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__cases,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Olinorder(T_a)
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => ( V_x != V_y
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__neqE__linordered__idom,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.50 => ( V_x != V_y
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__not__refl,axiom,
% 155.55/155.50 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_of__nat__mult,axiom,
% 155.55/155.50 ! [V_n,V_m,T_a] :
% 155.55/155.50 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_nat__neq__iff,axiom,
% 155.55/155.50 ! [V_n_2,V_m_2] :
% 155.55/155.50 ( V_m_2 != V_n_2
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_nat__mult__commute,axiom,
% 155.55/155.50 ! [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) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_of__nat__eq__iff,axiom,
% 155.55/155.50 ! [V_n_2,V_m_2,T_a] :
% 155.55/155.50 ( class_Nat_Osemiring__char__0(T_a)
% 155.55/155.50 => ( 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)
% 155.55/155.50 <=> V_m_2 = V_n_2 ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_of__nat__less__iff,axiom,
% 155.55/155.50 ! [V_n_2,V_m_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_of__nat__le__iff,axiom,
% 155.55/155.50 ! [V_n_2,V_m_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_nat__mult__assoc,axiom,
% 155.55/155.50 ! [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)) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_linorder__neqE__nat,axiom,
% 155.55/155.50 ! [V_y,V_x] :
% 155.55/155.50 ( V_x != V_y
% 155.55/155.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__irrefl__nat,axiom,
% 155.55/155.50 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__not__refl2,axiom,
% 155.55/155.50 ! [V_m,V_n] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 155.55/155.50 => V_m != V_n ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__not__refl3,axiom,
% 155.55/155.50 ! [V_t,V_s] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 155.55/155.50 => V_s != V_t ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__imp__of__nat__less,axiom,
% 155.55/155.50 ! [V_n,V_m,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_of__nat__less__imp__less,axiom,
% 155.55/155.50 ! [V_n,V_m,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_nat__less__cases,axiom,
% 155.55/155.50 ! [V_P_2,V_n_2,V_m_2] :
% 155.55/155.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 155.55/155.50 => ( ( V_m_2 = V_n_2
% 155.55/155.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 155.55/155.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 155.55/155.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 155.55/155.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_of__nat__0__le__iff,axiom,
% 155.55/155.50 ! [V_n,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.50 => 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_zero__le__imp__of__nat,axiom,
% 155.55/155.50 ! [V_m,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.50 => 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_of__nat__less__0__iff,axiom,
% 155.55/155.50 ! [V_m,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.50 => ~ 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_split__mult__neg__le,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__cancel__semiring(T_a)
% 155.55/155.50 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 155.55/155.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_split__mult__pos__le,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__ring(T_a)
% 155.55/155.50 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 155.55/155.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__left__le__imp__le,axiom,
% 155.55/155.50 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__right__le__imp__le,axiom,
% 155.55/155.50 ! [V_b,V_c,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__less__imp__less__left,axiom,
% 155.55/155.50 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__left__less__imp__less,axiom,
% 155.55/155.50 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__less__imp__less__right,axiom,
% 155.55/155.50 ! [V_b,V_c,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__right__less__imp__less,axiom,
% 155.55/155.50 ! [V_b,V_c,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__mono,axiom,
% 155.55/155.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__semiring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__mono_H,axiom,
% 155.55/155.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__semiring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__le__less__imp__less,axiom,
% 155.55/155.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__less__le__imp__less,axiom,
% 155.55/155.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__strict__mono_H,axiom,
% 155.55/155.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__strict__mono,axiom,
% 155.55/155.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__left__mono__neg,axiom,
% 155.55/155.50 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__ring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__right__mono__neg,axiom,
% 155.55/155.50 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__ring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__strict__left__mono__neg,axiom,
% 155.55/155.50 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__strict__right__mono__neg,axiom,
% 155.55/155.50 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__mult__left__mono,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__comm__semiring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__left__mono,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__semiring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__right__mono,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__semiring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__mult__strict__left__mono,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__strict__left__mono,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__strict__right__mono,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__nonpos__nonpos,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__ring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__neg__neg,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__nonpos__nonneg,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__cancel__semiring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__neg__pos,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__le__cancel__left__neg,axiom,
% 155.55/155.50 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__less__cancel__left__neg,axiom,
% 155.55/155.50 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_zero__less__mult__pos2,axiom,
% 155.55/155.50 ! [V_a,V_b,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_zero__less__mult__pos,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__nonneg__nonpos2,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__cancel__semiring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__nonneg__nonpos,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__cancel__semiring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__pos__neg2,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__pos__neg,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__nonneg__nonneg,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__cancel__semiring(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__pos__pos,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__le__cancel__left__pos,axiom,
% 155.55/155.50 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__less__cancel__left__pos,axiom,
% 155.55/155.50 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__less__cancel__left__disj,axiom,
% 155.55/155.50 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 155.55/155.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__less__cancel__right__disj,axiom,
% 155.55/155.50 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 155.55/155.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__le__0__iff,axiom,
% 155.55/155.50 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 155.55/155.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_zero__le__mult__iff,axiom,
% 155.55/155.50 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 155.55/155.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_zero__less__int__conv,axiom,
% 155.55/155.50 ! [V_n_2] :
% 155.55/155.50 ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_zero__le__square,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring(T_a)
% 155.55/155.50 => 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_not__square__less__zero,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring(T_a)
% 155.55/155.50 => ~ 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 155.55/155.50 ! [V_ry,V_rx,V_lx,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 155.55/155.50 ! [V_ry,V_rx,V_lx,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_zless__int,axiom,
% 155.55/155.50 ! [V_n_2,V_m_2] :
% 155.55/155.50 ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oab__semigroup__mult(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 155.55/155.50 ! [V_rx,V_ly,V_lx,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 155.55/155.50 ! [V_rx,V_ly,V_lx,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 155.55/155.50 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 155.55/155.50 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 155.55/155.50 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__le__less__mono,axiom,
% 155.55/155.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__less__le__mono,axiom,
% 155.55/155.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_zless__iff__Suc__zadd,axiom,
% 155.55/155.50 ! [V_z_2,V_w_2] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 155.55/155.50 <=> ? [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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__zero__left,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Rings_Omult__zero(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__zero__right,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Rings_Omult__zero(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__eq__0__iff,axiom,
% 155.55/155.50 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Rings_Oring__no__zero__divisors(T_a)
% 155.55/155.50 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.50 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.50 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_no__zero__divisors,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Ono__zero__divisors(T_a)
% 155.55/155.50 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_divisors__zero,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Ono__zero__divisors(T_a)
% 155.55/155.50 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.50 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.50 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__left__le__one__le,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 155.55/155.50 => 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)) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__right__le__one__le,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 155.55/155.50 => 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)) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__add__iff1,axiom,
% 155.55/155.50 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__ring(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> 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)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__add__iff2,axiom,
% 155.55/155.50 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__ring(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_le__add__iff1,axiom,
% 155.55/155.50 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__ring(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> 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)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_le__add__iff2,axiom,
% 155.55/155.50 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Rings_Oordered__ring(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_convex__bound__lt,axiom,
% 155.55/155.50 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 155.55/155.50 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 155.55/155.50 => 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)) ) ) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_inj__of__nat,axiom,
% 155.55/155.50 ! [T_a] :
% 155.55/155.50 ( class_Nat_Osemiring__char__0(T_a)
% 155.55/155.50 => 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_Powp__mono,axiom,
% 155.55/155.50 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_sum__squares__gt__zero__iff,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( 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))))
% 155.55/155.50 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.50 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_not__sum__squares__lt__zero,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring(T_a)
% 155.55/155.50 => ~ 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_sum__squares__le__zero__iff,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.50 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_sum__squares__ge__zero,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__ring(T_a)
% 155.55/155.50 => 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)))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__pos__nonneg,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__nonneg__pos,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__strict__increasing,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__strict__increasing2,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__neg__nonpos,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__nonpos__neg,axiom,
% 155.55/155.50 ! [V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_int__Suc0__eq__1,axiom,
% 155.55/155.50 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) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_one__less__mult,axiom,
% 155.55/155.50 ! [V_m,V_n] :
% 155.55/155.50 ( 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))
% 155.55/155.50 => ( 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))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_n__less__n__mult__m,axiom,
% 155.55/155.50 ! [V_m,V_n] :
% 155.55/155.50 ( 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))
% 155.55/155.50 => ( 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))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_n__less__m__mult__n,axiom,
% 155.55/155.50 ! [V_m,V_n] :
% 155.55/155.50 ( 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))
% 155.55/155.50 => ( 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))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_inj__image__subset__iff,axiom,
% 155.55/155.50 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.50 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_surj__Compl__image__subset,axiom,
% 155.55/155.50 ! [V_A_2,V_f_2,T_a,T_b] :
% 155.55/155.50 ( 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))
% 155.55/155.50 => 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)))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_convex__bound__le,axiom,
% 155.55/155.50 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 155.55/155.50 ( class_Rings_Olinordered__semiring__1(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 155.55/155.50 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 155.55/155.50 => 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)) ) ) ) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_int__0,axiom,
% 155.55/155.50 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) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_int__eq__0__conv,axiom,
% 155.55/155.50 ! [V_n_2] :
% 155.55/155.50 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.50 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_negative__eq__positive,axiom,
% 155.55/155.50 ! [V_m_2,V_n_2] :
% 155.55/155.50 ( 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)
% 155.55/155.50 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.50 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_zadd__int,axiom,
% 155.55/155.50 ! [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)) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_zadd__int__left,axiom,
% 155.55/155.50 ! [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) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_psubsetD,axiom,
% 155.55/155.50 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_crossproduct__eq,axiom,
% 155.55/155.50 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 155.55/155.50 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 155.55/155.50 => ( 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))
% 155.55/155.50 <=> ( V_w_2 = V_x_2
% 155.55/155.50 | V_y_2 = V_z_2 ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 155.55/155.50 ! [V_b,V_m,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_crossproduct__noteq,axiom,
% 155.55/155.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 155.55/155.50 => ( ( V_a_2 != V_b_2
% 155.55/155.50 & V_ca_2 != V_d_2 )
% 155.55/155.50 <=> 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)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 155.55/155.50 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => 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)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__less__imp__less__left,axiom,
% 155.55/155.50 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__less__imp__less__right,axiom,
% 155.55/155.50 ! [V_b,V_c,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__strict__mono,axiom,
% 155.55/155.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__strict__left__mono,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__strict__right__mono,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__less__cancel__left,axiom,
% 155.55/155.50 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__less__cancel__right,axiom,
% 155.55/155.50 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_in__mono,axiom,
% 155.55/155.50 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_set__rev__mp,axiom,
% 155.55/155.50 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_set__mp,axiom,
% 155.55/155.50 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 155.55/155.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_iso__tuple__UNIV__I,axiom,
% 155.55/155.50 ! [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)))) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_not__psubset__empty,axiom,
% 155.55/155.50 ! [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)))) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__le__imp__le__left,axiom,
% 155.55/155.50 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__le__imp__le__right,axiom,
% 155.55/155.50 ! [V_b,V_c,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__mono,axiom,
% 155.55/155.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 155.55/155.50 => 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))) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__left__mono,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__right__mono,axiom,
% 155.55/155.50 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__le__cancel__left,axiom,
% 155.55/155.50 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_add__le__cancel__right,axiom,
% 155.55/155.50 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 155.55/155.50 => ( 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)))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_diff__eq__diff__less,axiom,
% 155.55/155.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.50 => ( 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)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__1__left,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__1,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Groups_Ocomm__monoid__mult(T_a)
% 155.55/155.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__1__right,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult_Ocomm__neutral,axiom,
% 155.55/155.50 ! [V_a,T_a] :
% 155.55/155.50 ( class_Groups_Ocomm__monoid__mult(T_a)
% 155.55/155.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_bot__least,axiom,
% 155.55/155.50 ! [V_x,T_a] :
% 155.55/155.50 ( class_Orderings_Obot(T_a)
% 155.55/155.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_diff__eq__diff__less__eq,axiom,
% 155.55/155.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.50 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.50 => ( 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)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 155.55/155.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__supI1,axiom,
% 155.55/155.50 ! [V_b,V_a,V_x,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__supI2,axiom,
% 155.55/155.50 ! [V_a,V_b,V_x,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__0,axiom,
% 155.55/155.50 ! [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) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__0__right,axiom,
% 155.55/155.50 ! [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) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__is__0,axiom,
% 155.55/155.50 ! [V_n_2,V_m_2] :
% 155.55/155.50 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.50 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.50 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__cancel1,axiom,
% 155.55/155.50 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.50 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 155.55/155.50 <=> ( V_m_2 = V_n_2
% 155.55/155.50 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_mult__cancel2,axiom,
% 155.55/155.50 ! [V_n_2,V_k_2,V_m_2] :
% 155.55/155.50 ( 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)
% 155.55/155.50 <=> ( V_m_2 = V_n_2
% 155.55/155.50 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__infI1,axiom,
% 155.55/155.50 ! [V_b,V_x,V_a,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 155.55/155.50 => 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)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_less__infI2,axiom,
% 155.55/155.50 ! [V_a,V_x,V_b,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 155.55/155.50 => 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)) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_Suc__mult__cancel1,axiom,
% 155.55/155.50 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.50 ( 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)
% 155.55/155.50 <=> V_m_2 = V_n_2 ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_subset__empty,axiom,
% 155.55/155.50 ! [V_A_2,T_a] :
% 155.55/155.50 ( 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))))
% 155.55/155.50 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_inf__sup__ord_I3_J,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Lattices_Olattice(T_a)
% 155.55/155.50 => 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_sup__ge1,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.50 => 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_inf__sup__ord_I4_J,axiom,
% 155.55/155.50 ! [V_x,V_y,T_a] :
% 155.55/155.50 ( class_Lattices_Olattice(T_a)
% 155.55/155.50 => 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_sup__ge2,axiom,
% 155.55/155.50 ! [V_x,V_y,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.50 => 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))) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_le__iff__sup,axiom,
% 155.55/155.50 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.50 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_le__sup__iff,axiom,
% 155.55/155.50 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.50 => ( 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))
% 155.55/155.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 155.55/155.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_le__supI1,axiom,
% 155.55/155.50 ! [V_b,V_a,V_x,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_le__supI2,axiom,
% 155.55/155.50 ! [V_a,V_b,V_x,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 155.55/155.50 => 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))) ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_sup__absorb2,axiom,
% 155.55/155.50 ! [V_y,V_x,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.50 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 155.55/155.50
% 155.55/155.50 fof(fact_sup__absorb1,axiom,
% 155.55/155.50 ! [V_x,V_y,T_a] :
% 155.55/155.50 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.51 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__supI,axiom,
% 155.55/155.51 ! [V_b,V_x,V_a,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 155.55/155.51 => 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)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_sup__least,axiom,
% 155.55/155.51 ! [V_z,V_x,V_y,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 155.55/155.51 => 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)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_sup__mono,axiom,
% 155.55/155.51 ! [V_d,V_b,V_c,V_a,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__supE,axiom,
% 155.55/155.51 ! [V_x,V_b,V_a,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.51 => ( 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))
% 155.55/155.51 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 155.55/155.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__minus__iff,axiom,
% 155.55/155.51 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_minus__less__iff,axiom,
% 155.55/155.51 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_neg__less__iff__less,axiom,
% 155.55/155.51 ! [V_a_2,V_b_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inf__sup__ord_I1_J,axiom,
% 155.55/155.51 ! [V_y,V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Olattice(T_a)
% 155.55/155.51 => 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inf__le1,axiom,
% 155.55/155.51 ! [V_y,V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inf__sup__ord_I2_J,axiom,
% 155.55/155.51 ! [V_y,V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Olattice(T_a)
% 155.55/155.51 => 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inf__le2,axiom,
% 155.55/155.51 ! [V_y,V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__iff__inf,axiom,
% 155.55/155.51 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.51 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__inf__iff,axiom,
% 155.55/155.51 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__infI1,axiom,
% 155.55/155.51 ! [V_b,V_x,V_a,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 155.55/155.51 => 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)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__infI2,axiom,
% 155.55/155.51 ! [V_a,V_x,V_b,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 155.55/155.51 => 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)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inf__absorb1,axiom,
% 155.55/155.51 ! [V_y,V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.51 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inf__absorb2,axiom,
% 155.55/155.51 ! [V_x,V_y,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.51 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__infI,axiom,
% 155.55/155.51 ! [V_b,V_a,V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inf__greatest,axiom,
% 155.55/155.51 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inf__mono,axiom,
% 155.55/155.51 ! [V_d,V_b,V_c,V_a,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__infE,axiom,
% 155.55/155.51 ! [V_b,V_a,V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 155.55/155.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_UNIV__not__empty,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_not__less0,axiom,
% 155.55/155.51 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_neq0__conv,axiom,
% 155.55/155.51 ! [V_n_2] :
% 155.55/155.51 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__nat__zero__code,axiom,
% 155.55/155.51 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_gr__implies__not0,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_gr0I,axiom,
% 155.55/155.51 ! [V_n] :
% 155.55/155.51 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_insert__mono,axiom,
% 155.55/155.51 ! [V_a_2,V_D_2,V_C_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_subset__insertI2,axiom,
% 155.55/155.51 ! [V_b_2,V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_subset__insertI,axiom,
% 155.55/155.51 ! [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))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_compl__le__compl__iff,axiom,
% 155.55/155.51 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.51 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_compl__mono,axiom,
% 155.55/155.51 ! [V_y,V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__minus__iff,axiom,
% 155.55/155.51 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_minus__le__iff,axiom,
% 155.55/155.51 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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))
% 155.55/155.51 <=> 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)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_neg__le__iff__le,axiom,
% 155.55/155.51 ! [V_a_2,V_b_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__imp__neg__le,axiom,
% 155.55/155.51 ! [V_b,V_a,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__mult__distrib2,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__mult__distrib,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Suc__less__SucD,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Suc__lessD,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__SucE,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 155.55/155.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 => V_m = V_n ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__trans__Suc,axiom,
% 155.55/155.51 ! [V_k,V_j,V_i] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Suc__lessI,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__SucI,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__antisym,axiom,
% 155.55/155.51 ! [V_m,V_n] :
% 155.55/155.51 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 155.55/155.51 => V_m = V_n ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_not__less__less__Suc__eq,axiom,
% 155.55/155.51 ! [V_m_2,V_n_2] :
% 155.55/155.51 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 155.55/155.51 <=> V_n_2 = V_m_2 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Suc__less__eq,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__Suc__eq,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 155.55/155.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.51 | V_m_2 = V_n_2 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_not__less__eq,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_subset__image__iff,axiom,
% 155.55/155.51 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> ? [B_AA] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2))
% 155.55/155.51 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_image__mono,axiom,
% 155.55/155.51 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_termination__basic__simps_I2_J,axiom,
% 155.55/155.51 ! [V_y,V_z,V_x] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_termination__basic__simps_I1_J,axiom,
% 155.55/155.51 ! [V_z,V_y,V_x] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_not__add__less1,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_not__add__less2,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_nat__add__left__cancel__less,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_trans__less__add1,axiom,
% 155.55/155.51 ! [V_m,V_j,V_i] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_trans__less__add2,axiom,
% 155.55/155.51 ! [V_m,V_j,V_i] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__less__mono1,axiom,
% 155.55/155.51 ! [V_k,V_j,V_i] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__less__mono,axiom,
% 155.55/155.51 ! [V_l,V_k,V_j,V_i] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__add__eq__less,axiom,
% 155.55/155.51 ! [V_n,V_m,V_l,V_k] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 155.55/155.51 => ( 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)
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__lessD1,axiom,
% 155.55/155.51 ! [V_k,V_j,V_i] :
% 155.55/155.51 ( 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))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Un__upper1,axiom,
% 155.55/155.51 ! [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))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Un__upper2,axiom,
% 155.55/155.51 ! [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))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_subset__Un__eq,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.51 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Un__absorb1,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.51 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Un__absorb2,axiom,
% 155.55/155.51 ! [V_A_2,V_B_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.51 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Un__least,axiom,
% 155.55/155.51 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 155.55/155.51 => 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)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Un__mono,axiom,
% 155.55/155.51 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Int__lower1,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Int__lower2,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Int__absorb2,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.51 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Int__absorb1,axiom,
% 155.55/155.51 ! [V_A_2,V_B_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.51 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Int__greatest,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,V_C_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Int__mono,axiom,
% 155.55/155.51 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_diff__mult__distrib2,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_diff__mult__distrib,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Un__UNIV__left,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Un__UNIV__right,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Int__UNIV__left,axiom,
% 155.55/155.51 ! [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 ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Int__UNIV__right,axiom,
% 155.55/155.51 ! [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 ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Diff__subset,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Diff__mono,axiom,
% 155.55/155.51 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_double__diff,axiom,
% 155.55/155.51 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 155.55/155.51 => 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 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__imp__diff__less,axiom,
% 155.55/155.51 ! [V_n,V_k,V_j] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 155.55/155.51 => 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_diff__less__mono2,axiom,
% 155.55/155.51 ! [V_l,V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_subset__inj__on,axiom,
% 155.55/155.51 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.51 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__eq,axiom,
% 155.55/155.51 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.51 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 155.55/155.51 <=> V_x_2 = V_y_2 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_injD,axiom,
% 155.55/155.51 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.51 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 155.55/155.51 => V_x_2 = V_y_2 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_nat__mult__1,axiom,
% 155.55/155.51 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 155.55/155.51
% 155.55/155.51 fof(fact_nat__1__eq__mult__iff,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 155.55/155.51 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 155.55/155.51 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_nat__mult__1__right,axiom,
% 155.55/155.51 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 155.55/155.51
% 155.55/155.51 fof(fact_nat__mult__eq__1__iff,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 155.55/155.51 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 155.55/155.51 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_pos__add__strict,axiom,
% 155.55/155.51 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Compl__subset__Compl__iff,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Compl__anti__mono,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_thin,axiom,
% 155.55/155.51 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] :
% 155.55/155.51 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 155.55/155.51 => ( 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))
% 155.55/155.51 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_weaken,axiom,
% 155.55/155.51 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_a] :
% 155.55/155.51 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_H_2)
% 155.55/155.51 => ( 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))
% 155.55/155.51 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_asm,axiom,
% 155.55/155.51 ! [V_Ga_2,V_ts_2,T_a] :
% 155.55/155.51 ( 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))
% 155.55/155.51 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_eq__add__iff1,axiom,
% 155.55/155.51 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 155.55/155.51 ( class_Rings_Oring(T_a)
% 155.55/155.51 => ( 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)
% 155.55/155.51 <=> 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 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_eq__add__iff2,axiom,
% 155.55/155.51 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 155.55/155.51 ( class_Rings_Oring(T_a)
% 155.55/155.51 => ( 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)
% 155.55/155.51 <=> 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) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zero__less__one,axiom,
% 155.55/155.51 ! [T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_not__one__less__zero,axiom,
% 155.55/155.51 ! [T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zero__le__one,axiom,
% 155.55/155.51 ! [T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_not__one__le__zero,axiom,
% 155.55/155.51 ! [T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.51 => ~ 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__minus__self__iff,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__add__one,axiom,
% 155.55/155.51 ! [V_a,T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.51 => 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)))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_square__eq__1__iff,axiom,
% 155.55/155.51 ! [V_x_2,T_a] :
% 155.55/155.51 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 155.55/155.51 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 155.55/155.51 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 155.55/155.51 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_pred__subset__eq,axiom,
% 155.55/155.51 ! [V_S_2,V_R_2,T_a] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_range__composition,axiom,
% 155.55/155.51 ! [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)))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__image__Compl__subset,axiom,
% 155.55/155.51 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.51 => 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)))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__fun,axiom,
% 155.55/155.51 ! [T_c,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_sup__top__left,axiom,
% 155.55/155.51 ! [V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Obounded__lattice__top(T_a)
% 155.55/155.51 => 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) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_sup__top__right,axiom,
% 155.55/155.51 ! [V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Obounded__lattice__top(T_a)
% 155.55/155.51 => 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) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inf__top__left,axiom,
% 155.55/155.51 ! [V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Obounded__lattice__top(T_a)
% 155.55/155.51 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inf__top__right,axiom,
% 155.55/155.51 ! [V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Obounded__lattice__top(T_a)
% 155.55/155.51 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inf__eq__top__iff,axiom,
% 155.55/155.51 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.51 ( class_Lattices_Obounded__lattice__top(T_a)
% 155.55/155.51 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a)
% 155.55/155.51 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a)
% 155.55/155.51 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_UNIV__option__conv,axiom,
% 155.55/155.51 ! [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)))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_not__less__Least,axiom,
% 155.55/155.51 ! [V_P_2,V_k_2,T_a] :
% 155.55/155.51 ( class_Orderings_Owellorder(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),c_Orderings_Oord__class_OLeast(T_a,V_P_2)))
% 155.55/155.51 => ~ hBOOL(hAPP(V_P_2,V_k_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Least__le,axiom,
% 155.55/155.51 ! [V_k_2,V_P_2,T_a] :
% 155.55/155.51 ( class_Orderings_Owellorder(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Oord__class_OLeast(T_a,V_P_2)),V_k_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_psubset__insert__iff,axiom,
% 155.55/155.51 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 155.55/155.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 155.55/155.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.51 => 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)) )
% 155.55/155.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__scale__eq__noteq,axiom,
% 155.55/155.51 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 155.55/155.51 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 155.55/155.51 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.51 => ( ( V_a = V_b
% 155.55/155.51 & V_c != V_d )
% 155.55/155.51 => 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)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_sum__squares__eq__zero__iff,axiom,
% 155.55/155.51 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__ring__strict(T_a)
% 155.55/155.51 => ( 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)
% 155.55/155.51 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.51 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zero__less__two,axiom,
% 155.55/155.51 ! [T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.51 => 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)))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_even__less__0__iff,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__pos__pos,axiom,
% 155.55/155.51 ! [V_b,V_a,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__neg__neg,axiom,
% 155.55/155.51 ! [V_b,V_a,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__iff__diff__less__0,axiom,
% 155.55/155.51 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 155.55/155.51 <=> 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__nonneg__nonneg,axiom,
% 155.55/155.51 ! [V_b,V_a,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__nonneg__eq__0__iff,axiom,
% 155.55/155.51 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
% 155.55/155.51 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.51 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.51 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__increasing,axiom,
% 155.55/155.51 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__increasing2,axiom,
% 155.55/155.51 ! [V_a,V_b,V_c,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__nonpos__nonpos,axiom,
% 155.55/155.51 ! [V_b,V_a,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 155.55/155.51 ! [V_m,V_a,T_a] :
% 155.55/155.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.51 => 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) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 155.55/155.51 ! [V_a,V_m,T_a] :
% 155.55/155.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.51 => 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) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 155.55/155.51 ! [V_m,T_a] :
% 155.55/155.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.51 => 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) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__iff__diff__le__0,axiom,
% 155.55/155.51 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 155.55/155.51 <=> 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_neg__less__nonneg,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_neg__less__0__iff__less,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_neg__0__less__iff__less,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_minus__le__self__iff,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_neg__le__0__iff__le,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__minus__self__iff,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_neg__0__le__iff__le,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_of__nat__0,axiom,
% 155.55/155.51 ! [T_a] :
% 155.55/155.51 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.51 => 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) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 155.55/155.51 ! [V_x,T_a] :
% 155.55/155.51 ( class_Rings_Ocomm__ring__1(T_a)
% 155.55/155.51 => 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) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_subset__insert,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 155.55/155.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_insert__subset,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 155.55/155.51 ( 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))
% 155.55/155.51 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 155.55/155.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_mult__eq__1__iff,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( 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))
% 155.55/155.51 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 155.55/155.51 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_range__eqI,axiom,
% 155.55/155.51 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] :
% 155.55/155.51 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 155.55/155.51 => 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))))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_rangeI,axiom,
% 155.55/155.51 ! [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))))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_distrib__inf__le,axiom,
% 155.55/155.51 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Olattice(T_a)
% 155.55/155.51 => 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)))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_distrib__sup__le,axiom,
% 155.55/155.51 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Olattice(T_a)
% 155.55/155.51 => 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)))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_subset__singletonD,axiom,
% 155.55/155.51 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.51 ( 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)))))
% 155.55/155.51 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.51 | 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_mult__Suc__right,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_mult__Suc,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_of__nat__add,axiom,
% 155.55/155.51 ! [V_n,V_m,T_a] :
% 155.55/155.51 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.51 => 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_gr0__conv__Suc,axiom,
% 155.55/155.51 ! [V_n_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 155.55/155.51 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__Suc0,axiom,
% 155.55/155.51 ! [V_n_2] :
% 155.55/155.51 ( 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))))
% 155.55/155.51 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__Suc__eq__0__disj,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 155.55/155.51 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.51 | ? [B_j] :
% 155.55/155.51 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 155.55/155.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__gr__0,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 155.55/155.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__add__Suc1,axiom,
% 155.55/155.51 ! [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)))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__add__Suc2,axiom,
% 155.55/155.51 ! [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)))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__iff__Suc__add,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.51 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__on__strict__subset,axiom,
% 155.55/155.51 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Diff__UNIV,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_image__Int__subset,axiom,
% 155.55/155.51 ! [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)))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_ball__UNIV,axiom,
% 155.55/155.51 ! [V_P_2,T_a] :
% 155.55/155.51 ( ! [B_x] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 155.55/155.51 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.51 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zero__less__diff,axiom,
% 155.55/155.51 ! [V_m_2,V_n_2] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_diff__less,axiom,
% 155.55/155.51 ! [V_m,V_n] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 155.55/155.51 => 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)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Un__Int__assoc__eq,axiom,
% 155.55/155.51 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( 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))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_diff__less__Suc,axiom,
% 155.55/155.51 ! [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))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_comp__surj,axiom,
% 155.55/155.51 ! [V_g_2,T_c,V_f_2,T_a,T_b] :
% 155.55/155.51 ( 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))
% 155.55/155.51 => ( 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))
% 155.55/155.51 => 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)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_mult__eq__self__implies__10,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 155.55/155.51 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 155.55/155.51 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_image__diff__subset,axiom,
% 155.55/155.51 ! [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)))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__diff__conv,axiom,
% 155.55/155.51 ! [V_k_2,V_j_2,V_i_2] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add__diff__inverse,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 => 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 ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Diff__partition,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.51 => 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 ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Diff__subset__conv,axiom,
% 155.55/155.51 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( 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))
% 155.55/155.51 <=> 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__image__eq__iff,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.51 => ( 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)
% 155.55/155.51 <=> V_A_2 = V_B_2 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__comp,axiom,
% 155.55/155.51 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.51 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_of__nat__1,axiom,
% 155.55/155.51 ! [T_a] :
% 155.55/155.51 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.51 => 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) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_subset__Compl__self__eq,axiom,
% 155.55/155.51 ! [V_A_2,T_a] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Compl__UNIV__eq,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Compl__empty__eq,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Ints__mult,axiom,
% 155.55/155.51 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.51 ( class_Rings_Oring__1(T_a)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Compl__partition,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Compl__partition2,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 155.55/155.51 ! [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) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Ints__of__nat,axiom,
% 155.55/155.51 ! [V_n_2,T_a] :
% 155.55/155.51 ( class_Rings_Oring__1(T_a)
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__singleton,axiom,
% 155.55/155.51 ! [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))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_map__le__implies__dom__le,axiom,
% 155.55/155.51 ! [V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2)
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_the__inv__f__f,axiom,
% 155.55/155.51 ! [V_x_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.51 => 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 ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_dom__const,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_compl__top__eq,axiom,
% 155.55/155.51 ! [T_a] :
% 155.55/155.51 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.51 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_compl__bot__eq,axiom,
% 155.55/155.51 ! [T_a] :
% 155.55/155.51 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.51 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_sup__compl__top,axiom,
% 155.55/155.51 ! [V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.51 => 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) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_compl__sup__top,axiom,
% 155.55/155.51 ! [V_x,T_a] :
% 155.55/155.51 ( class_Lattices_Oboolean__algebra(T_a)
% 155.55/155.51 => 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) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_of__nat__Suc,axiom,
% 155.55/155.51 ! [V_m,T_a] :
% 155.55/155.51 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.51 => 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__image__mem__iff,axiom,
% 155.55/155.51 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_range__ex1__eq,axiom,
% 155.55/155.51 ! [V_b_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.51 => ( 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)))))
% 155.55/155.51 <=> ? [B_x] :
% 155.55/155.51 ( V_b_2 = hAPP(V_f_2,B_x)
% 155.55/155.51 & ! [B_y] :
% 155.55/155.51 ( V_b_2 = hAPP(V_f_2,B_y)
% 155.55/155.51 => B_y = B_x ) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_diff__Suc__less,axiom,
% 155.55/155.51 ! [V_i,V_n] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.51 => 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Suc__pred,axiom,
% 155.55/155.51 ! [V_n] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.51 => 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 ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_nat__diff__split,axiom,
% 155.55/155.51 ! [V_b_2,V_a_2,V_P_2] :
% 155.55/155.51 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 155.55/155.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 155.55/155.51 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 155.55/155.51 & ! [B_d] :
% 155.55/155.51 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 155.55/155.51 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_nat__diff__split__asm,axiom,
% 155.55/155.51 ! [V_b_2,V_a_2,V_P_2] :
% 155.55/155.51 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 155.55/155.51 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 155.55/155.51 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 155.55/155.51 | ? [B_d] :
% 155.55/155.51 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 155.55/155.51 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__on__image__Int,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 155.55/155.51 => 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)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_image__Int,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.51 => 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__on__image__set__diff,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 155.55/155.51 => 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)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_image__set__diff,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.51 => 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_disjoint__eq__subset__Compl,axiom,
% 155.55/155.51 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( 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))
% 155.55/155.51 <=> 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_subset__insert__iff,axiom,
% 155.55/155.51 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.51 => 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)) )
% 155.55/155.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_diff__single__insert,axiom,
% 155.55/155.51 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 155.55/155.51 ( 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))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__on__iff__surj,axiom,
% 155.55/155.51 ! [V_A_H_2,T_b,T_a,V_A_2] :
% 155.55/155.51 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.51 => ( ? [B_f] :
% 155.55/155.51 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 155.55/155.51 & 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)) )
% 155.55/155.51 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_nat__mult__less__cancel1,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 155.55/155.51 => ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_nat__mult__eq__cancel1,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 155.55/155.51 => ( 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)
% 155.55/155.51 <=> V_m_2 = V_n_2 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_flat__lub__def,axiom,
% 155.55/155.51 ! [V_b_2,V_A_2,T_a] :
% 155.55/155.51 ( ( 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)))))
% 155.55/155.51 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 )
% 155.55/155.51 & ( ~ 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)))))
% 155.55/155.51 => 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)))))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_left__add__mult__distrib,axiom,
% 155.55/155.51 ! [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) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.51 ( 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)
% 155.55/155.51 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.51 | V_m_2 = V_n_2 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Least__mono,axiom,
% 155.55/155.51 ! [V_S_2,V_f_2,T_a,T_b] :
% 155.55/155.51 ( ( class_Orderings_Oorder(T_b)
% 155.55/155.51 & class_Orderings_Oorder(T_a) )
% 155.55/155.51 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 155.55/155.51 => ( ? [B_x] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 155.55/155.51 & ! [B_xa] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_S_2))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) )
% 155.55/155.51 => 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))) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_sgn__1__neg,axiom,
% 155.55/155.51 ! [V_a_2,T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.51 => ( 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))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_top1I,axiom,
% 155.55/155.51 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le0,axiom,
% 155.55/155.51 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_negative__zle,axiom,
% 155.55/155.51 ! [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))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zle__diff1__eq,axiom,
% 155.55/155.51 ! [V_z_2,V_w_2] :
% 155.55/155.51 ( 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))))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_negative__zle__0,axiom,
% 155.55/155.51 ! [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))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zsgn__def,axiom,
% 155.55/155.51 ! [V_i] :
% 155.55/155.51 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.51 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 155.55/155.51 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 155.55/155.51 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 155.55/155.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 155.55/155.51 => 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)) ) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_not__int__zless__negative,axiom,
% 155.55/155.51 ! [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)))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_inj__int,axiom,
% 155.55/155.51 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))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zmult__zminus,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__imp__0__less,axiom,
% 155.55/155.51 ! [V_z] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_odd__less__0,axiom,
% 155.55/155.51 ! [V_z_2] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_odd__nonzero,axiom,
% 155.55/155.51 ! [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) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zle__add1__eq__le,axiom,
% 155.55/155.51 ! [V_z_2,V_w_2] :
% 155.55/155.51 ( 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))))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zless__add1__eq,axiom,
% 155.55/155.51 ! [V_z_2,V_w_2] :
% 155.55/155.51 ( 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))))
% 155.55/155.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 155.55/155.51 | V_w_2 = V_z_2 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_add1__zle__eq,axiom,
% 155.55/155.51 ! [V_z_2,V_w_2] :
% 155.55/155.51 ( 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))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zless__imp__add1__zle,axiom,
% 155.55/155.51 ! [V_z,V_w] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 155.55/155.51 => 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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zmult__1__right,axiom,
% 155.55/155.51 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zmult__1,axiom,
% 155.55/155.51 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 155.55/155.51
% 155.55/155.51 fof(fact_int__0__neq__1,axiom,
% 155.55/155.51 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_int__0__less__1,axiom,
% 155.55/155.51 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))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_int__one__le__iff__zero__less,axiom,
% 155.55/155.51 ! [V_z_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_pos__zmult__eq__1__iff,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 155.55/155.51 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 155.55/155.51 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 155.55/155.51 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_psubset__trans,axiom,
% 155.55/155.51 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_sgn__sgn,axiom,
% 155.55/155.51 ! [V_a,T_a] :
% 155.55/155.51 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.51 => 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) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__refl,axiom,
% 155.55/155.51 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_nat__le__linear,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_eq__imp__le,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( V_m = V_n
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__trans,axiom,
% 155.55/155.51 ! [V_k,V_j,V_i] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__antisym,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 155.55/155.51 => V_m = V_n ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zmult__zless__mono2,axiom,
% 155.55/155.51 ! [V_k,V_j,V_i] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zero__zle__int,axiom,
% 155.55/155.51 ! [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))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_int__less__0__conv,axiom,
% 155.55/155.51 ! [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))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zless__le,axiom,
% 155.55/155.51 ! [V_w_2,V_z_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 155.55/155.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 155.55/155.51 & V_z_2 != V_w_2 ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zless__linear,axiom,
% 155.55/155.51 ! [V_y,V_x] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 155.55/155.51 | V_x = V_y
% 155.55/155.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_int__int__eq,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( 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)
% 155.55/155.51 <=> V_m_2 = V_n_2 ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zle__int,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zadd__zless__mono,axiom,
% 155.55/155.51 ! [V_z,V_z_H,V_w,V_w_H] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 155.55/155.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 155.55/155.51 => 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))) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zadd__left__mono,axiom,
% 155.55/155.51 ! [V_k,V_j,V_i] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zadd__strict__right__mono,axiom,
% 155.55/155.51 ! [V_k,V_j,V_i] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 155.55/155.51 => 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zadd__zmult__distrib,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zadd__zmult__distrib2,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zle__iff__zadd,axiom,
% 155.55/155.51 ! [V_z_2,V_w_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 155.55/155.51 <=> ? [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)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__bin__lemma,axiom,
% 155.55/155.51 ! [V_l_2,V_k_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 155.55/155.51 <=> 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))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zadd__0__right,axiom,
% 155.55/155.51 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zadd__0,axiom,
% 155.55/155.51 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zadd__commute,axiom,
% 155.55/155.51 ! [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) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zadd__left__commute,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zadd__assoc,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zadd__zminus__inverse2,axiom,
% 155.55/155.51 ! [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) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zminus__zadd__distrib,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zminus__zminus,axiom,
% 155.55/155.51 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 155.55/155.51
% 155.55/155.51 fof(fact_zminus__0,axiom,
% 155.55/155.51 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) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_diff__int__def,axiom,
% 155.55/155.51 ! [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)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_diff__int__def__symmetric,axiom,
% 155.55/155.51 ! [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) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__0__eq,axiom,
% 155.55/155.51 ! [V_n_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 155.55/155.51 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 155.55/155.51 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_int__le__0__conv,axiom,
% 155.55/155.51 ! [V_n_2] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_int__zle__neg,axiom,
% 155.55/155.51 ! [V_m_2,V_n_2] :
% 155.55/155.51 ( 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))))
% 155.55/155.51 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.51 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Suc__n__not__le__n,axiom,
% 155.55/155.51 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_not__less__eq__eq,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__Suc__eq,axiom,
% 155.55/155.51 ! [V_n_2,V_m_2] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 155.55/155.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.51 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Suc__le__mono,axiom,
% 155.55/155.51 ! [V_m_2,V_n_2] :
% 155.55/155.51 ( 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)))
% 155.55/155.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__SucI,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__SucE,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 155.55/155.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_Suc__leD,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_not__zle__0__negative,axiom,
% 155.55/155.51 ! [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))))) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_termination__basic__simps_I5_J,axiom,
% 155.55/155.51 ! [V_y,V_x] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__or__eq__imp__le,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 | V_m = V_n )
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_le__neq__implies__less,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.51 => ( V_m != V_n
% 155.55/155.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 155.55/155.51
% 155.55/155.51 fof(fact_less__imp__le__nat,axiom,
% 155.55/155.51 ! [V_n,V_m] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__eq__less__or__eq,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.52 | V_m_2 = V_n_2 ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__less__le,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.52 & V_m_2 != V_n_2 ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__leE,axiom,
% 155.55/155.52 ! [V_n,V_k,V_m] :
% 155.55/155.52 ( 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))
% 155.55/155.52 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.52 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__leD1,axiom,
% 155.55/155.52 ! [V_n,V_k,V_m] :
% 155.55/155.52 ( 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))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__leD2,axiom,
% 155.55/155.52 ! [V_n,V_k,V_m] :
% 155.55/155.52 ( 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))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__le__mono,axiom,
% 155.55/155.52 ! [V_l,V_k,V_j,V_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__le__mono1,axiom,
% 155.55/155.52 ! [V_k,V_j,V_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_trans__le__add2,axiom,
% 155.55/155.52 ! [V_m,V_j,V_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_trans__le__add1,axiom,
% 155.55/155.52 ! [V_m,V_j,V_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__add__left__cancel__le,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__iff__add,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.52 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__add1,axiom,
% 155.55/155.52 ! [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))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__add2,axiom,
% 155.55/155.52 ! [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))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_termination__basic__simps_I3_J,axiom,
% 155.55/155.52 ! [V_z,V_y,V_x] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_termination__basic__simps_I4_J,axiom,
% 155.55/155.52 ! [V_y,V_z,V_x] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zmult__int,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_int__mult,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__diff__iff,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat_Odiff__diff__eq,axiom,
% 155.55/155.52 ! [V_n,V_m,V_k] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 155.55/155.52 => 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) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_eq__diff__iff,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 155.55/155.52 => ( 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)
% 155.55/155.52 <=> V_m_2 = V_n_2 ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__diff__cancel,axiom,
% 155.55/155.52 ! [V_n,V_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 155.55/155.52 => 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 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__le__mono,axiom,
% 155.55/155.52 ! [V_l,V_n,V_m] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__le__mono2,axiom,
% 155.55/155.52 ! [V_l,V_n,V_m] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__le__self,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zdiff__int,axiom,
% 155.55/155.52 ! [V_m,V_n] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mult__le__mono,axiom,
% 155.55/155.52 ! [V_l,V_k,V_j,V_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mult__le__mono2,axiom,
% 155.55/155.52 ! [V_k,V_j,V_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mult__le__mono1,axiom,
% 155.55/155.52 ! [V_k,V_j,V_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__cube,axiom,
% 155.55/155.52 ! [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)))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__square,axiom,
% 155.55/155.52 ! [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))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_evaln__nonstrict,axiom,
% 155.55/155.52 ! [V_m,V_t,V_n,V_s,V_c] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 155.55/155.52 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_monoD,axiom,
% 155.55/155.52 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] :
% 155.55/155.52 ( ( class_Orderings_Oorder(T_b)
% 155.55/155.52 & class_Orderings_Oorder(T_a) )
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.52 => 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))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mono__Suc,axiom,
% 155.55/155.52 c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 155.55/155.52 <=> 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_sgn0,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Groups_Osgn__if(T_a)
% 155.55/155.52 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_sgn__0__0,axiom,
% 155.55/155.52 ! [V_a_2,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_sgn__times,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zmult__zless__mono2__lemma,axiom,
% 155.55/155.52 ! [V_k,V_j,V_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__mult__le__cancel1,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__eq__Suc__le,axiom,
% 155.55/155.52 ! [V_m_2,V_n_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__Suc__eq__le,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Suc__le__eq,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__imp__less__Suc,axiom,
% 155.55/155.52 ! [V_n,V_m] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Suc__leI,axiom,
% 155.55/155.52 ! [V_n,V_m] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__less__Suc__eq,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 155.55/155.52 <=> V_n_2 = V_m_2 ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Suc__le__lessD,axiom,
% 155.55/155.52 ! [V_n,V_m] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__is__0__eq_H,axiom,
% 155.55/155.52 ! [V_n,V_m] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__is__0__eq,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2] :
% 155.55/155.52 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Suc__diff__le,axiom,
% 155.55/155.52 ! [V_m,V_n] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Suc__mult__le__cancel1,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__eq__add__iff2,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 155.55/155.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 155.55/155.52 <=> 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) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__diff__add__eq2,axiom,
% 155.55/155.52 ! [V_n,V_m,V_u,V_j,V_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__le__add__iff2,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__eq__add__iff1,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 155.55/155.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 155.55/155.52 <=> 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 ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__diff__add__eq1,axiom,
% 155.55/155.52 ! [V_n,V_m,V_u,V_i,V_j] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__le__add__iff1,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__less__mono,axiom,
% 155.55/155.52 ! [V_c,V_b,V_a] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__diff__iff,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__add__assoc2,axiom,
% 155.55/155.52 ! [V_i,V_j,V_k] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__diff__assoc2,axiom,
% 155.55/155.52 ! [V_i,V_j,V_k] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__add__assoc,axiom,
% 155.55/155.52 ! [V_i,V_j,V_k] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__imp__diff__is__add,axiom,
% 155.55/155.52 ! [V_k_2,V_j_2,V_i_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 155.55/155.52 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 155.55/155.52 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__add__diff__inverse2,axiom,
% 155.55/155.52 ! [V_m,V_n] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 155.55/155.52 => 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 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__diff__conv2,axiom,
% 155.55/155.52 ! [V_i_2,V_j_2,V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__diff__assoc,axiom,
% 155.55/155.52 ! [V_i,V_j,V_k] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__add__diff__inverse,axiom,
% 155.55/155.52 ! [V_m,V_n] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 155.55/155.52 => 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 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__add__diff,axiom,
% 155.55/155.52 ! [V_m,V_n,V_k] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__diff__conv,axiom,
% 155.55/155.52 ! [V_i_2,V_k_2,V_j_2] :
% 155.55/155.52 ( 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))
% 155.55/155.52 <=> 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__diff__right,axiom,
% 155.55/155.52 ! [V_i,V_j,V_k] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mono__Un,axiom,
% 155.55/155.52 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.52 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 155.55/155.52 => 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)))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mono__Int,axiom,
% 155.55/155.52 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.52 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 155.55/155.52 => 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)))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__eq__Suc__le__raw,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mono__iff__le__Suc,axiom,
% 155.55/155.52 ! [V_f_2,T_a] :
% 155.55/155.52 ( class_Orderings_Oorder(T_a)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_a,V_f_2)
% 155.55/155.52 <=> ! [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)))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mono__sup,axiom,
% 155.55/155.52 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 155.55/155.52 ( ( class_Lattices_Osemilattice__sup(T_b)
% 155.55/155.52 & class_Lattices_Osemilattice__sup(T_a) )
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 155.55/155.52 => 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)))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mono__inf,axiom,
% 155.55/155.52 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 155.55/155.52 ( ( class_Lattices_Osemilattice__inf(T_b)
% 155.55/155.52 & class_Lattices_Osemilattice__inf(T_a) )
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 155.55/155.52 => 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)))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__less__add__iff1,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__less__add__iff2,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_sgn__greater,axiom,
% 155.55/155.52 ! [V_a_2,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_sgn__less,axiom,
% 155.55/155.52 ! [V_a_2,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_one__le__mult__iff,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> ( 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))
% 155.55/155.52 & 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mult__le__cancel2,axiom,
% 155.55/155.52 ! [V_n_2,V_k_2,V_m_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mult__le__cancel1,axiom,
% 155.55/155.52 ! [V_n_2,V_m_2,V_k_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__Suc__diff__eq1,axiom,
% 155.55/155.52 ! [V_m,V_j,V_k] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__Suc__diff__eq2,axiom,
% 155.55/155.52 ! [V_m,V_j,V_k] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_of__nat__diff,axiom,
% 155.55/155.52 ! [V_m,V_n,T_a] :
% 155.55/155.52 ( class_Rings_Oring__1(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_sgn__1__pos,axiom,
% 155.55/155.52 ! [V_a_2,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_sgn__pos,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.52 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_sgn__if,axiom,
% 155.55/155.52 ! [V_x,T_a] :
% 155.55/155.52 ( class_Groups_Osgn__if(T_a)
% 155.55/155.52 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.52 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 155.55/155.52 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.52 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.52 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_sgn__neg,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.52 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zdiff__int__split,axiom,
% 155.55/155.52 ! [V_y_2,V_x_2,V_P_2] :
% 155.55/155.52 ( 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))))
% 155.55/155.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 155.55/155.52 => 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)))) )
% 155.55/155.52 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 155.55/155.52 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_self__quotient__aux1,axiom,
% 155.55/155.52 ! [V_q,V_r,V_a] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.52 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_self__quotient__aux2,axiom,
% 155.55/155.52 ! [V_q,V_r,V_a] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.52 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 155.55/155.52 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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 155.55/155.52 ! [V_y_2,V_x_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_q__pos__lemma,axiom,
% 155.55/155.52 ! [V_r_H,V_q_H,V_b_H] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zle__refl,axiom,
% 155.55/155.52 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zmult__commute,axiom,
% 155.55/155.52 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zle__linear,axiom,
% 155.55/155.52 ! [V_w,V_z] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 155.55/155.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zmult__assoc,axiom,
% 155.55/155.52 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zle__trans,axiom,
% 155.55/155.52 ! [V_k,V_j,V_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zle__antisym,axiom,
% 155.55/155.52 ! [V_w,V_z] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 155.55/155.52 => V_z = V_w ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zdiff__zmult__distrib,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zdiff__zmult__distrib2,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 155.55/155.52 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))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 155.55/155.52 ! [V_y,V_x] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 155.55/155.52 ! [V_A_2,V_x_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 155.55/155.52 <=> 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 155.55/155.52 ! [V_B_2,V_A_2] :
% 155.55/155.52 ( V_A_2 = V_B_2
% 155.55/155.52 <=> 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 155.55/155.52 ! [V_B_2,V_A_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.52 <=> 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 155.55/155.52 ! [V_B_2,V_A_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.52 <=> 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 155.55/155.52 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))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 155.55/155.52 ! [V_y_2,V_x_2] :
% 155.55/155.52 ( 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)
% 155.55/155.52 <=> V_x_2 = V_y_2 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 155.55/155.52 ! [V_y,V_x] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 155.55/155.52 ! [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))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 155.55/155.52 ! [V_P_2] :
% 155.55/155.52 ( ? [B_x] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 155.55/155.52 & hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.52 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 155.55/155.52 ! [V_P_2] :
% 155.55/155.52 ( ! [B_x] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 155.55/155.52 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.52 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 155.55/155.52 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))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 155.55/155.52 ! [V_y_2,V_x_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 155.55/155.52 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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 155.55/155.52 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 155.55/155.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
% 155.55/155.52 => ( 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)))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_unique__quotient__lemma__neg,axiom,
% 155.55/155.52 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zdiv__mono2__lemma,axiom,
% 155.55/155.52 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 155.55/155.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
% 155.55/155.52 => ( 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)))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_unique__quotient__lemma,axiom,
% 155.55/155.52 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_q__neg__lemma,axiom,
% 155.55/155.52 ! [V_r_H,V_q_H,V_b_H] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_coinduct3__mono__lemma,axiom,
% 155.55/155.52 ! [V_B_2,V_X_2,V_f_2,T_b,T_a] :
% 155.55/155.52 ( class_Orderings_Oorder(T_a)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_small_H_Osimps,axiom,
% 155.55/155.52 ! [V_f_2,V_i_2,V_d_2] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 155.55/155.52 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_tsub__def,axiom,
% 155.55/155.52 ! [V_x,V_y] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 155.55/155.52 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 155.55/155.52 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_inj__vimage__singleton,axiom,
% 155.55/155.52 ! [V_a_2,V_f_2,T_b,T_a] :
% 155.55/155.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.52 => 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))))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_decr__mult__lemma,axiom,
% 155.55/155.52 ! [V_k_2,V_P_2,V_d_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 155.55/155.52 => ( ! [B_x] :
% 155.55/155.52 ( hBOOL(hAPP(V_P_2,B_x))
% 155.55/155.52 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 155.55/155.52 => ! [B_x] :
% 155.55/155.52 ( hBOOL(hAPP(V_P_2,B_x))
% 155.55/155.52 => 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)))) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_negD,axiom,
% 155.55/155.52 ! [V_x] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.52 => ? [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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimageI,axiom,
% 155.55/155.52 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] :
% 155.55/155.52 ( hAPP(V_f_2,V_a_2) = V_b_2
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__ident,axiom,
% 155.55/155.52 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__code,axiom,
% 155.55/155.52 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2))
% 155.55/155.52 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimageI2,axiom,
% 155.55/155.52 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimageD,axiom,
% 155.55/155.52 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__eq,axiom,
% 155.55/155.52 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__empty,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__mono,axiom,
% 155.55/155.52 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__UNIV,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__Un,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__Int,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__compose,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__Diff,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__Compl,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_image__vimage__subset,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_surj__image__vimage__eq,axiom,
% 155.55/155.52 ! [V_A_2,V_f_2,T_a,T_b] :
% 155.55/155.52 ( 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))
% 155.55/155.52 => 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 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__singleton__eq,axiom,
% 155.55/155.52 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] :
% 155.55/155.52 ( 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))))))
% 155.55/155.52 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__insert,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__subsetD,axiom,
% 155.55/155.52 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] :
% 155.55/155.52 ( 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))
% 155.55/155.52 => ( 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))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_image__vimage__eq,axiom,
% 155.55/155.52 ! [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)))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_inj__vimage__image__eq,axiom,
% 155.55/155.52 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.52 => 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 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__const,axiom,
% 155.55/155.52 ! [T_b,V_A_2,V_ca_2,T_a] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.52 => 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)) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__subsetI,axiom,
% 155.55/155.52 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 155.55/155.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.52 => ( 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)))
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_vimage__if,axiom,
% 155.55/155.52 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.52 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 155.55/155.52 => 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)) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 155.55/155.52 => 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 ) ) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 155.55/155.52 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 155.55/155.52 => 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) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 155.55/155.52 => 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)) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 155.55/155.52 ! [V_y,V_x] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_tsub__eq,axiom,
% 155.55/155.52 ! [V_x,V_y] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 155.55/155.52 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_incr__mult__lemma,axiom,
% 155.55/155.52 ! [V_k_2,V_P_2,V_d_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 155.55/155.52 => ( ! [B_x] :
% 155.55/155.52 ( hBOOL(hAPP(V_P_2,B_x))
% 155.55/155.52 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 155.55/155.52 => ! [B_x] :
% 155.55/155.52 ( hBOOL(hAPP(V_P_2,B_x))
% 155.55/155.52 => 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)))) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_ex__least__nat__less,axiom,
% 155.55/155.52 ! [V_n_2,V_P_2] :
% 155.55/155.52 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 155.55/155.52 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 155.55/155.52 => ? [B_k] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 155.55/155.52 & ! [B_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 155.55/155.52 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 155.55/155.52 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zero__less__imp__eq__int,axiom,
% 155.55/155.52 ! [V_k] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 155.55/155.52 => ? [B_n] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 155.55/155.52 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_incr__lemma,axiom,
% 155.55/155.52 ! [V_x,V_z,V_d] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 155.55/155.52 => 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)))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_decr__lemma,axiom,
% 155.55/155.52 ! [V_z,V_x,V_d] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_inj__on__diff__nat,axiom,
% 155.55/155.52 ! [V_k_2,V_N_2] :
% 155.55/155.52 ( ! [B_x] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__idempotent,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__ge__self,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__le__D1,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__eq__0,axiom,
% 155.55/155.52 ! [V_a_2,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__zero,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__add__abs,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__mult__self,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__mult,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__minus__commute,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__one,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__minus__cancel,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__of__nat,axiom,
% 155.55/155.52 ! [V_n,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__int__eq,axiom,
% 155.55/155.52 ! [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) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__of__nonneg,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__le__zero__iff,axiom,
% 155.55/155.52 ! [V_a_2,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__ge__zero,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__of__pos,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zero__less__abs__iff,axiom,
% 155.55/155.52 ! [V_a_2,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__not__less__zero,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ~ 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__triangle__ineq,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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)))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__mult__less,axiom,
% 155.55/155.52 ! [V_d,V_b,V_c,V_a,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 155.55/155.52 => 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))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__triangle__ineq2__sym,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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)))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__triangle__ineq2,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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)))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__triangle__ineq3,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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)))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__ge__minus__self,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__le__iff,axiom,
% 155.55/155.52 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ( 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))
% 155.55/155.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 155.55/155.52 & 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)) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__leI,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__le__D2,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__less__iff,axiom,
% 155.55/155.52 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2))
% 155.55/155.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 155.55/155.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__zmult__eq__1,axiom,
% 155.55/155.52 ! [V_n,V_m] :
% 155.55/155.52 ( 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)
% 155.55/155.52 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__sgn,axiom,
% 155.55/155.52 ! [V_k,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mult__sgn__abs,axiom,
% 155.55/155.52 ! [V_x,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => 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 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__eq__mult,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Rings_Oordered__ring__abs(T_a)
% 155.55/155.52 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 155.55/155.52 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__mult__pos,axiom,
% 155.55/155.52 ! [V_y,V_x,T_a] :
% 155.55/155.52 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__diff__triangle__ineq,axiom,
% 155.55/155.52 ! [V_d,V_c,V_b,V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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))))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__triangle__ineq4,axiom,
% 155.55/155.52 ! [V_b,V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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)))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__of__nonpos,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__minus__le__zero,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__of__neg,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__if,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Groups_Oabs__if(T_a)
% 155.55/155.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zabs__less__one__iff,axiom,
% 155.55/155.52 ! [V_z_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zabs__def,axiom,
% 155.55/155.52 ! [V_i] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.52 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.52 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_int__val__lemma,axiom,
% 155.55/155.52 ! [V_k_2,V_f_2,V_n_2] :
% 155.55/155.52 ( ! [B_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 155.55/155.52 => 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))) )
% 155.55/155.52 => ( 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))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 155.55/155.52 => ? [B_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 155.55/155.52 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat0__intermed__int__val,axiom,
% 155.55/155.52 ! [V_k_2,V_f_2,V_n_2] :
% 155.55/155.52 ( ! [B_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 155.55/155.52 => 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))) )
% 155.55/155.52 => ( 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))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 155.55/155.52 => ? [B_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 155.55/155.52 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_coinduct__set,axiom,
% 155.55/155.52 ! [V_X_2,V_a_2,V_f_2,T_a] :
% 155.55/155.52 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 155.55/155.52 => ( 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)))))
% 155.55/155.52 => 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))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_def__coinduct__set,axiom,
% 155.55/155.52 ! [V_X_2,V_a_2,V_f_2,T_a,V_A_2] :
% 155.55/155.52 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 155.55/155.52 => ( 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))))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_expand__Suc,axiom,
% 155.55/155.52 ! [V_v] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__intermed__int__val,axiom,
% 155.55/155.52 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 155.55/155.52 ( ! [B_i] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 155.55/155.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 155.55/155.52 => 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))) )
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 155.55/155.52 => ? [B_i] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 155.55/155.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 155.55/155.52 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_eq__number__of,axiom,
% 155.55/155.52 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Int_Oring__char__0(T_a) )
% 155.55/155.52 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 155.55/155.52 <=> V_x_2 = V_y_2 ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_number__of__reorient,axiom,
% 155.55/155.52 ! [V_x_2,V_w_2,T_a] :
% 155.55/155.52 ( class_Int_Onumber(T_a)
% 155.55/155.52 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2
% 155.55/155.52 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_of__nat__number__of__lemma,axiom,
% 155.55/155.52 ! [V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => ( ( 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)))
% 155.55/155.52 => 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) )
% 155.55/155.52 & ( ~ 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)))
% 155.55/155.52 => 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) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_gfp__upperbound,axiom,
% 155.55/155.52 ! [V_f_2,V_X_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),hAPP(V_f_2,V_X_2)))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_gfp__unfold,axiom,
% 155.55/155.52 ! [V_f_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_def__gfp__unfold,axiom,
% 155.55/155.52 ! [V_f_2,V_A_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => V_A_2 = hAPP(V_f_2,V_A_2) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__number__of__eq__not__less,axiom,
% 155.55/155.52 ! [V_w_2,V_v_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber(T_a)
% 155.55/155.52 & class_Orderings_Olinorder(T_a) )
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> ~ 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_right__distrib__number__of,axiom,
% 155.55/155.52 ! [V_c,V_b,V_v,T_b] :
% 155.55/155.52 ( ( class_Int_Onumber(T_b)
% 155.55/155.52 & class_Rings_Osemiring(T_b) )
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_left__distrib__number__of,axiom,
% 155.55/155.52 ! [V_v,V_b,V_a,T_b] :
% 155.55/155.52 ( ( class_Int_Onumber(T_b)
% 155.55/155.52 & class_Rings_Osemiring(T_b) )
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_right__diff__distrib__number__of,axiom,
% 155.55/155.52 ! [V_c,V_b,V_v,T_b] :
% 155.55/155.52 ( ( class_Int_Onumber(T_b)
% 155.55/155.52 & class_Rings_Oring(T_b) )
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_left__diff__distrib__number__of,axiom,
% 155.55/155.52 ! [V_v,V_b,V_a,T_b] :
% 155.55/155.52 ( ( class_Int_Onumber(T_b)
% 155.55/155.52 & class_Rings_Oring(T_b) )
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__number__of,axiom,
% 155.55/155.52 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__number__of,axiom,
% 155.55/155.52 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_number__of__add,axiom,
% 155.55/155.52 ! [V_w,V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__number__of__eq,axiom,
% 155.55/155.52 ! [V_w,V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__number__of__left,axiom,
% 155.55/155.52 ! [V_z,V_w,V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mult__number__of__left,axiom,
% 155.55/155.52 ! [V_z,V_w,V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_arith__simps_I32_J,axiom,
% 155.55/155.52 ! [V_w,V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_number__of__mult,axiom,
% 155.55/155.52 ! [V_w,V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_number__of__diff,axiom,
% 155.55/155.52 ! [V_w,V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_number__of__minus,axiom,
% 155.55/155.52 ! [V_w,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_arith__simps_I30_J,axiom,
% 155.55/155.52 ! [V_w,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Ints__number__of,axiom,
% 155.55/155.52 ! [V_w_2,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_weak__coinduct,axiom,
% 155.55/155.52 ! [V_f_2,V_X_2,V_a_2,T_a] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 155.55/155.52 => ( 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)))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__number__of__diff1,axiom,
% 155.55/155.52 ! [V_c,V_w,V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_minus__number__of__mult,axiom,
% 155.55/155.52 ! [V_z,V_w,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__number__of__eq,axiom,
% 155.55/155.52 ! [V_w,V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_gfp__lemma3,axiom,
% 155.55/155.52 ! [V_f_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_gfp__lemma2,axiom,
% 155.55/155.52 ! [V_f_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => 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)))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_weak__coinduct__image,axiom,
% 155.55/155.52 ! [V_f_2,V_g_2,T_b,V_X_2,V_a_2,T_a] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 155.55/155.52 => ( 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))))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_abs__number__of,axiom,
% 155.55/155.52 ! [V_x,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.52 => ( ( 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)))
% 155.55/155.52 => 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)) )
% 155.55/155.52 & ( ~ 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)))
% 155.55/155.52 => 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) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__number__of__diff2,axiom,
% 155.55/155.52 ! [V_w,V_c,V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_gfp__fun__UnI2,axiom,
% 155.55/155.52 ! [V_X_2,V_a_2,V_f_2,T_a] :
% 155.55/155.52 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 155.55/155.52 => ( 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)))
% 155.55/155.52 => 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))))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_coinduct,axiom,
% 155.55/155.52 ! [V_X_2,V_f_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => ( 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)))))
% 155.55/155.52 => 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))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_coinduct__lemma,axiom,
% 155.55/155.52 ! [V_f_2,V_X_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( 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)))))
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => 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))))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_def__coinduct,axiom,
% 155.55/155.52 ! [V_X_2,V_f_2,V_A_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => ( 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))))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),V_A_2)) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_def__coinduct3,axiom,
% 155.55/155.52 ! [V_X_2,V_a_2,V_f_2,T_a,V_A_2] :
% 155.55/155.52 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 155.55/155.52 => ( 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)))))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_coinduct3,axiom,
% 155.55/155.52 ! [V_X_2,V_a_2,V_f_2,T_a] :
% 155.55/155.52 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 155.55/155.52 => ( 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))))))
% 155.55/155.52 => 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))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_coinduct3__lemma,axiom,
% 155.55/155.52 ! [V_f_2,V_X_2,T_a] :
% 155.55/155.52 ( 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))))))
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 155.55/155.52 => 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)))))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_eq__number__of__eq,axiom,
% 155.55/155.52 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 155.55/155.52 <=> 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)))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mult__nat__number__of,axiom,
% 155.55/155.52 ! [V_v_H,V_v] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => 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) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__number__of__mult__left,axiom,
% 155.55/155.52 ! [V_k,V_v_H,V_v] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => 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) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => 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) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_number__of__is__id,axiom,
% 155.55/155.52 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 155.55/155.52
% 155.55/155.52 fof(fact_iszero__Numeral0,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zero__is__num__zero,axiom,
% 155.55/155.52 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_lfp__const,axiom,
% 155.55/155.52 ! [V_t_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => c_Inductive_Ocomplete__lattice__class_Olfp(T_a,hAPP(c_COMBK(T_a,T_a),V_t_2)) = V_t_2 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_number__of2,axiom,
% 155.55/155.52 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))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__eq__number__of__int__code,axiom,
% 155.55/155.52 ! [V_l_2,V_k_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__number__of__int__code,axiom,
% 155.55/155.52 ! [V_l_2,V_k_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_plus__numeral__code_I9_J,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Pls__def,axiom,
% 155.55/155.52 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_times__numeral__code_I5_J,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_rel__simps_I19_J,axiom,
% 155.55/155.52 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_rel__simps_I2_J,axiom,
% 155.55/155.52 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__Pls__right,axiom,
% 155.55/155.52 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__Pls,axiom,
% 155.55/155.52 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 155.55/155.52
% 155.55/155.52 fof(fact_minus__numeral__code_I5_J,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mult__Pls,axiom,
% 155.55/155.52 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__bin__simps_I1_J,axiom,
% 155.55/155.52 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 155.55/155.52
% 155.55/155.52 fof(fact_minus__Pls,axiom,
% 155.55/155.52 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 155.55/155.52
% 155.55/155.52 fof(fact_lfp__lowerbound,axiom,
% 155.55/155.52 ! [V_A_2,V_f_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_A_2)),V_A_2))
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_def__lfp__unfold,axiom,
% 155.55/155.52 ! [V_f_2,V_h_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( V_h_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => V_h_2 = hAPP(V_f_2,V_h_2) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_lfp__unfold,axiom,
% 155.55/155.52 ! [V_f_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_iszero__def,axiom,
% 155.55/155.52 ! [V_z_2,T_a] :
% 155.55/155.52 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.52 => ( c_Int_Oiszero(T_a,V_z_2)
% 155.55/155.52 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_iszero__0,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.52 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_not__iszero__1,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.52 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_number__of__Pls,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_semiring__norm_I112_J,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__numeral__0__right,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__numeral__0,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_bin__less__0__simps_I1_J,axiom,
% 155.55/155.52 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_semiring__norm_I113_J,axiom,
% 155.55/155.52 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__number__of__Pls,axiom,
% 155.55/155.52 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_eq__special_I1_J,axiom,
% 155.55/155.52 ! [V_y_2,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 155.55/155.52 <=> 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)))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_eq__special_I3_J,axiom,
% 155.55/155.52 ! [V_x_2,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.52 <=> 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)))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_eq__0__number__of,axiom,
% 155.55/155.52 ! [V_v_2] :
% 155.55/155.52 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_eq__number__of__0,axiom,
% 155.55/155.52 ! [V_v_2] :
% 155.55/155.52 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__nat__number__of,axiom,
% 155.55/155.52 ! [V_v_H_2,V_v_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 155.55/155.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__nat__number__of,axiom,
% 155.55/155.52 ! [V_v_H_2,V_v_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_minus__numeral__code_I6_J,axiom,
% 155.55/155.52 ! [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))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_lfp__lemma3,axiom,
% 155.55/155.52 ! [V_f_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => 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)))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_lfp__lemma2,axiom,
% 155.55/155.52 ! [V_f_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__special_I3_J,axiom,
% 155.55/155.52 ! [V_x_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__special_I1_J,axiom,
% 155.55/155.52 ! [V_y_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__special_I3_J,axiom,
% 155.55/155.52 ! [V_x_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__special_I1_J,axiom,
% 155.55/155.52 ! [V_y_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__0__number__of,axiom,
% 155.55/155.52 ! [V_v_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__nat__number__of,axiom,
% 155.55/155.52 ! [V_v_H,V_v] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => 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) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 155.55/155.52 => 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) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 155.55/155.52 => 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)) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_lfp__induct,axiom,
% 155.55/155.52 ! [V_P_2,V_f_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => ( 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))
% 155.55/155.52 => 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)) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_def__lfp__induct,axiom,
% 155.55/155.52 ! [V_P_2,V_f_2,V_A_2,T_a] :
% 155.55/155.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.52 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)
% 155.55/155.52 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2)
% 155.55/155.52 => ( 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))
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_A_2),V_P_2)) ) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__number__of__add__1,axiom,
% 155.55/155.52 ! [V_v] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => 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) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__1__add__number__of,axiom,
% 155.55/155.52 ! [V_v] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => 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) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__number__of__diff__1,axiom,
% 155.55/155.52 ! [V_v] :
% 155.55/155.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => 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) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 155.55/155.52 => 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)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nats__number__of,axiom,
% 155.55/155.52 ! [V_w_2,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 155.55/155.52 => 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))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Suc__diff__number__of,axiom,
% 155.55/155.52 ! [V_m,V_v] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_eq__special_I4_J,axiom,
% 155.55/155.52 ! [V_x_2,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 155.55/155.52 <=> 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))))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_succ__Pls,axiom,
% 155.55/155.52 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_rel__simps_I51_J,axiom,
% 155.55/155.52 ! [V_l_2,V_k_2] :
% 155.55/155.52 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 155.55/155.52 <=> V_k_2 = V_l_2 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_succ__pred,axiom,
% 155.55/155.52 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 155.55/155.52
% 155.55/155.52 fof(fact_minus__Bit1,axiom,
% 155.55/155.52 ! [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))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__eq__int__code_I16_J,axiom,
% 155.55/155.52 ! [V_k2_2,V_k1_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_rel__simps_I34_J,axiom,
% 155.55/155.52 ! [V_l_2,V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_rel__simps_I17_J,axiom,
% 155.55/155.52 ! [V_l_2,V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__int__code_I16_J,axiom,
% 155.55/155.52 ! [V_k2_2,V_k1_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_rel__simps_I46_J,axiom,
% 155.55/155.52 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 155.55/155.52
% 155.55/155.52 fof(fact_rel__simps_I39_J,axiom,
% 155.55/155.52 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_bin__less__0__simps_I4_J,axiom,
% 155.55/155.52 ! [V_w_2] :
% 155.55/155.52 ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_rel__simps_I22_J,axiom,
% 155.55/155.52 ! [V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_rel__simps_I12_J,axiom,
% 155.55/155.52 ! [V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Bit1__def,axiom,
% 155.55/155.52 ! [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) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_iszero__number__of__Bit1,axiom,
% 155.55/155.52 ! [V_w,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Int_Oring__char__0(T_a) )
% 155.55/155.52 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__iff__pred__less,axiom,
% 155.55/155.52 ! [V_l_2,V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_pred__def,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_number__of__Bit1,axiom,
% 155.55/155.52 ! [V_w,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mult__numeral__1,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_mult__numeral__1__right,axiom,
% 155.55/155.52 ! [V_a,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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 ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_numeral__1__eq__1,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_semiring__norm_I110_J,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_rel__simps_I29_J,axiom,
% 155.55/155.52 ! [V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_rel__simps_I5_J,axiom,
% 155.55/155.52 ! [V_k_2] :
% 155.55/155.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_one__is__num__one,axiom,
% 155.55/155.52 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Numeral1__eq1__nat,axiom,
% 155.55/155.52 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__numeral__1__eq__1,axiom,
% 155.55/155.52 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_not__iszero__Numeral1,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_succ__def,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nats__0,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nats__add,axiom,
% 155.55/155.52 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.52 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 155.55/155.52 => 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))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nats__mult,axiom,
% 155.55/155.52 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.52 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 155.55/155.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 155.55/155.52 => 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))) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nats__1,axiom,
% 155.55/155.52 ! [T_a] :
% 155.55/155.52 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.52 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_of__nat__in__Nats,axiom,
% 155.55/155.52 ! [V_n_2,T_a] :
% 155.55/155.52 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_numeral__1__eq__Suc__0,axiom,
% 155.55/155.52 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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_numeral__3__eq__3,axiom,
% 155.55/155.52 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)))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 155.55/155.52 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))))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Suc3__eq__add__3,axiom,
% 155.55/155.52 ! [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) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 155.55/155.52 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)))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__special_I2_J,axiom,
% 155.55/155.52 ! [V_y_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_le__special_I4_J,axiom,
% 155.55/155.52 ! [V_x_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__special_I4_J,axiom,
% 155.55/155.52 ! [V_x_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_less__special_I2_J,axiom,
% 155.55/155.52 ! [V_y_2,T_a] :
% 155.55/155.52 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.52 => ( 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)))
% 155.55/155.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_number__of__succ,axiom,
% 155.55/155.52 ! [V_k,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__special_I3_J,axiom,
% 155.55/155.52 ! [V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_add__special_I2_J,axiom,
% 155.55/155.52 ! [V_w,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 155.55/155.52 ! [V_m,V_n] :
% 155.55/155.52 ( 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))
% 155.55/155.52 => 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)))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_number__of__pred,axiom,
% 155.55/155.52 ! [V_w,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__special_I2_J,axiom,
% 155.55/155.52 ! [V_v,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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)))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_diff__special_I1_J,axiom,
% 155.55/155.52 ! [V_w,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => 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))) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_eq__special_I2_J,axiom,
% 155.55/155.52 ! [V_y_2,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 155.55/155.52 <=> 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)))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_power__number__of__odd__number__of,axiom,
% 155.55/155.52 ! [V_v_2,V_w_2,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => ( ( 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)))
% 155.55/155.52 => 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))) )
% 155.55/155.52 & ( ~ 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)))
% 155.55/155.52 => 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) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_nat__number__of__Bit1,axiom,
% 155.55/155.52 ! [V_w_2] :
% 155.55/155.52 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 155.55/155.52 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 155.55/155.52 => 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)))) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Suc__nat__number__of__add,axiom,
% 155.55/155.52 ! [V_n,V_v] :
% 155.55/155.52 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.52 => 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) )
% 155.55/155.52 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.52 => 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) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zpower__number__of__odd,axiom,
% 155.55/155.52 ! [V_z_2,V_w_2] :
% 155.55/155.52 ( ( 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)))
% 155.55/155.52 => 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))) )
% 155.55/155.52 & ( ~ 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)))
% 155.55/155.52 => 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) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_one__code__numeral__code,axiom,
% 155.55/155.52 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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_power__number__of__odd,axiom,
% 155.55/155.52 ! [V_z_2,V_w_2,T_a] :
% 155.55/155.52 ( class_Int_Onumber__ring(T_a)
% 155.55/155.52 => ( ( 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)))
% 155.55/155.52 => 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))) )
% 155.55/155.52 & ( ~ 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)))
% 155.55/155.52 => 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) ) ) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_int__power,axiom,
% 155.55/155.52 ! [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) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zpower__int,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 155.55/155.52 ! [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)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_code__numeral__zero__minus__one,axiom,
% 155.55/155.52 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) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 155.55/155.52 ! [V_q,V_y,V_x,T_a] :
% 155.55/155.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 155.55/155.52 ! [V_q,V_p,V_x,T_a] :
% 155.55/155.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_zpower__zpower,axiom,
% 155.55/155.52 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 155.55/155.52 ! [V_x,T_a] :
% 155.55/155.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.52 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_not__neg__0,axiom,
% 155.55/155.52 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_not__neg__int,axiom,
% 155.55/155.52 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_not__neg__1,axiom,
% 155.55/155.52 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 155.55/155.52 ! [V_q,V_x,T_a] :
% 155.55/155.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.52
% 155.55/155.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 155.55/155.52 ! [V_q,V_x,T_a] :
% 155.55/155.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.52 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 155.55/155.53 ! [V_q,V_x,T_a] :
% 155.55/155.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 155.55/155.53 ! [V_x,T_a] :
% 155.55/155.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 155.55/155.53 ! [V_q,V_p,V_x,T_a] :
% 155.55/155.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 155.55/155.53 ! [V_n,V_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zpower__zadd__distrib,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Ints__power,axiom,
% 155.55/155.53 ! [V_n_2,V_a_2,T_a] :
% 155.55/155.53 ( class_Rings_Oring__1(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_not__neg__eq__ge__0,axiom,
% 155.55/155.53 ! [V_x_2] :
% 155.55/155.53 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__def,axiom,
% 155.55/155.53 ! [V_Z_2] :
% 155.55/155.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_not__neg__number__of__Pls,axiom,
% 155.55/155.53 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__number__of__Bit1,axiom,
% 155.55/155.53 ! [V_w_2] :
% 155.55/155.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 155.55/155.53 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__le__zpower__abs,axiom,
% 155.55/155.53 ! [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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__code__numeral__code,axiom,
% 155.55/155.53 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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__imp__number__of__eq__0,axiom,
% 155.55/155.53 ! [V_v] :
% 155.55/155.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__zminus__int,axiom,
% 155.55/155.53 ! [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))))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power3__eq__cube,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__eq__if,axiom,
% 155.55/155.53 ! [V_p,V_m] :
% 155.55/155.53 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.53 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 155.55/155.53 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.53 => 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)))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__less__zpower__abs__iff,axiom,
% 155.55/155.53 ! [V_n_2,V_x_2] :
% 155.55/155.53 ( 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)))
% 155.55/155.53 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_eq__nat__number__of,axiom,
% 155.55/155.53 ! [V_v_H_2,V_v_2] :
% 155.55/155.53 ( 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)
% 155.55/155.53 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 155.55/155.53 => 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))) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 155.55/155.53 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 155.55/155.53 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 155.55/155.53 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__number__of__add__left,axiom,
% 155.55/155.53 ! [V_k,V_v_H,V_v] :
% 155.55/155.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 155.55/155.53 => 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) ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_int__nat__number__of,axiom,
% 155.55/155.53 ! [V_v] :
% 155.55/155.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => 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) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__number__of__pred__iff__0,axiom,
% 155.55/155.53 ! [V_v_2] :
% 155.55/155.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 155.55/155.53 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_of__nat__number__of__eq,axiom,
% 155.55/155.53 ! [V_v,T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => 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) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Suc__nat__number__of,axiom,
% 155.55/155.53 ! [V_v] :
% 155.55/155.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__strict__mono,axiom,
% 155.55/155.53 ! [V_n,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.53 => 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))) ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_one__less__power,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__increasing__iff,axiom,
% 155.55/155.53 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__le__imp__le__exp,axiom,
% 155.55/155.53 ! [V_n,V_m,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__decreasing,axiom,
% 155.55/155.53 ! [V_a,V_N,V_n,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 155.55/155.53 => 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))) ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__strict__decreasing,axiom,
% 155.55/155.53 ! [V_a,V_N,V_n,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 155.55/155.53 => 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))) ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_field__power__not__zero,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 155.55/155.53 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 155.55/155.53 ! [V_m_2,V_x_2] :
% 155.55/155.53 ( 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))
% 155.55/155.53 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.53 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__Suc__0,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__zero__less__power__iff,axiom,
% 155.55/155.53 ! [V_n_2,V_x_2] :
% 155.55/155.53 ( 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)))
% 155.55/155.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 155.55/155.53 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__power__less__imp__less,axiom,
% 155.55/155.53 ! [V_n,V_m,V_i] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__mult__distrib,axiom,
% 155.55/155.53 ! [V_n,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Groups_Ocomm__monoid__mult(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__commutes,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__one,axiom,
% 155.55/155.53 ! [V_n,T_a] :
% 155.55/155.53 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_of__nat__power,axiom,
% 155.55/155.53 ! [V_n,V_m,T_a] :
% 155.55/155.53 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__mult,axiom,
% 155.55/155.53 ! [V_n,V_m,V_a,T_a] :
% 155.55/155.53 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__abs,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__one__right,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.53 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__le__power,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__mono,axiom,
% 155.55/155.53 ! [V_n,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__less__power,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__eq__0__iff,axiom,
% 155.55/155.53 ! [V_n_2,V_a_2,T_a] :
% 155.55/155.53 ( ( class_Power_Opower(T_a)
% 155.55/155.53 & class_Rings_Omult__zero(T_a)
% 155.55/155.53 & class_Rings_Ono__zero__divisors(T_a)
% 155.55/155.53 & class_Rings_Ozero__neq__one(T_a) )
% 155.55/155.53 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_one__le__power,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__0__Suc,axiom,
% 155.55/155.53 ! [V_n,T_a] :
% 155.55/155.53 ( ( class_Power_Opower(T_a)
% 155.55/155.53 & class_Rings_Osemiring__0(T_a) )
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__inject__exp,axiom,
% 155.55/155.53 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2))
% 155.55/155.53 => ( 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)
% 155.55/155.53 <=> V_m_2 = V_n_2 ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__Suc2,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__Suc,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Power_Opower(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__one__le__power,axiom,
% 155.55/155.53 ! [V_n,V_i] :
% 155.55/155.53 ( 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))
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__0,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Power_Opower(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__add,axiom,
% 155.55/155.53 ! [V_n,V_m,V_a,T_a] :
% 155.55/155.53 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_abs__power__minus,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__less__imp__less__base,axiom,
% 155.55/155.53 ! [V_b,V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( 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)))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__inject__base,axiom,
% 155.55/155.53 ! [V_b,V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( 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))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.53 => V_a = V_b ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__le__imp__le__base,axiom,
% 155.55/155.53 ! [V_b,V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( 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))))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__less__power__Suc,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 155.55/155.53 => 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)))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__gt1__lemma,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 155.55/155.53 => 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)))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__0__left,axiom,
% 155.55/155.53 ! [V_n,T_a] :
% 155.55/155.53 ( ( class_Power_Opower(T_a)
% 155.55/155.53 & class_Rings_Osemiring__0(T_a) )
% 155.55/155.53 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.53 => 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) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__gt1,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 155.55/155.53 => 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)))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__strict__increasing,axiom,
% 155.55/155.53 ! [V_a,V_N,V_n,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__less__imp__less__exp,axiom,
% 155.55/155.53 ! [V_n,V_m,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__strict__increasing__iff,axiom,
% 155.55/155.53 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__le__power__abs,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__increasing,axiom,
% 155.55/155.53 ! [V_a,V_N,V_n,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__minus,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Oring__1(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__Suc__less,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__eq__imp__eq__base,axiom,
% 155.55/155.53 ! [V_b,V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( 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)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.53 => V_a = V_b ) ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__Suc__less__one,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__of__aux__code,axiom,
% 155.55/155.53 ! [V_n,V_i] :
% 155.55/155.53 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 155.55/155.53 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 155.55/155.53 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_diff__nat__number__of,axiom,
% 155.55/155.53 ! [V_v_2,V_v_H_2] :
% 155.55/155.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__power__power,axiom,
% 155.55/155.53 ! [T_a] :
% 155.55/155.53 ( class_Power_Opower(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__minus1__odd,axiom,
% 155.55/155.53 ! [V_n,T_a] :
% 155.55/155.53 ( class_Rings_Oring__1(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_odd__power__less__zero,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I48_J,axiom,
% 155.55/155.53 ! [V_l_2,V_k_2] :
% 155.55/155.53 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 155.55/155.53 <=> V_k_2 = V_l_2 ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I31_J,axiom,
% 155.55/155.53 ! [V_l_2,V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_less__eq__int__code_I13_J,axiom,
% 155.55/155.53 ! [V_k2_2,V_k1_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_less__int__code_I13_J,axiom,
% 155.55/155.53 ! [V_k2_2,V_k1_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I14_J,axiom,
% 155.55/155.53 ! [V_l_2,V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Bit0__Pls,axiom,
% 155.55/155.53 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I38_J,axiom,
% 155.55/155.53 ! [V_l_2] :
% 155.55/155.53 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 155.55/155.53 <=> c_Int_OPls = V_l_2 ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I44_J,axiom,
% 155.55/155.53 ! [V_k_2] :
% 155.55/155.53 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 155.55/155.53 <=> V_k_2 = c_Int_OPls ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I49_J,axiom,
% 155.55/155.53 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I50_J,axiom,
% 155.55/155.53 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_add__Bit0__Bit0,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Bit0__def,axiom,
% 155.55/155.53 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__int,axiom,
% 155.55/155.53 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mult__Bit0,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_diff__bin__simps_I7_J,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_minus__Bit0,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 155.55/155.53 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)))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 155.55/155.53 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__0,axiom,
% 155.55/155.53 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 155.55/155.53 ! [V_y_2,V_x_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 155.55/155.53 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 155.55/155.53 <=> V_x_2 = V_y_2 ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_all__nat,axiom,
% 155.55/155.53 ! [V_P_2] :
% 155.55/155.53 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 155.55/155.53 <=> ! [B_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 155.55/155.53 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_ex__nat,axiom,
% 155.55/155.53 ! [V_P_2] :
% 155.55/155.53 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 155.55/155.53 <=> ? [B_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 155.55/155.53 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_eq__nat__nat__iff,axiom,
% 155.55/155.53 ! [V_z_H_2,V_z_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 155.55/155.53 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 155.55/155.53 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_bin__less__0__simps_I3_J,axiom,
% 155.55/155.53 ! [V_w_2] :
% 155.55/155.53 ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I21_J,axiom,
% 155.55/155.53 ! [V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I27_J,axiom,
% 155.55/155.53 ! [V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I32_J,axiom,
% 155.55/155.53 ! [V_l_2,V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_less__eq__int__code_I14_J,axiom,
% 155.55/155.53 ! [V_k2_2,V_k1_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I10_J,axiom,
% 155.55/155.53 ! [V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I4_J,axiom,
% 155.55/155.53 ! [V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_less__int__code_I15_J,axiom,
% 155.55/155.53 ! [V_k2_2,V_k1_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I16_J,axiom,
% 155.55/155.53 ! [V_l_2,V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__number__of,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__number__of__def,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_add__Bit0__Bit1,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_add__Bit1__Bit0,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_diff__bin__simps_I3_J,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_diff__bin__simps_I9_J,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_diff__bin__simps_I10_J,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 155.55/155.53 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__nat,axiom,
% 155.55/155.53 ! [V_z] :
% 155.55/155.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 155.55/155.53 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_not__neg__nat,axiom,
% 155.55/155.53 ! [V_z] :
% 155.55/155.53 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 155.55/155.53 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__number__of__Bit0,axiom,
% 155.55/155.53 ! [V_w_2] :
% 155.55/155.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 155.55/155.53 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_pred__Bit1,axiom,
% 155.55/155.53 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_pred__Bit0,axiom,
% 155.55/155.53 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 155.55/155.53 ! [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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 155.55/155.53 ! [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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 155.55/155.53 ! [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 ).
% 155.55/155.53
% 155.55/155.53 fof(fact_iszero__number__of__Bit0,axiom,
% 155.55/155.53 ! [V_w_2,T_a] :
% 155.55/155.53 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 & class_Int_Oring__char__0(T_a) )
% 155.55/155.53 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2)))
% 155.55/155.53 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__2,axiom,
% 155.55/155.53 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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_succ__Bit0,axiom,
% 155.55/155.53 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_succ__Bit1,axiom,
% 155.55/155.53 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__number__of__Bit0,axiom,
% 155.55/155.53 ! [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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 155.55/155.53 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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_number__of__Bit0,axiom,
% 155.55/155.53 ! [V_w,T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__0__iff,axiom,
% 155.55/155.53 ! [V_i_2] :
% 155.55/155.53 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__le__0,axiom,
% 155.55/155.53 ! [V_z] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__mono__iff,axiom,
% 155.55/155.53 ! [V_w_2,V_z_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zless__nat__conj,axiom,
% 155.55/155.53 ! [V_z_2,V_w_2] :
% 155.55/155.53 ( 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)))
% 155.55/155.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 155.55/155.53 ! [V_y_2,V_x_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__1,axiom,
% 155.55/155.53 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_int__nat__eq,axiom,
% 155.55/155.53 ! [V_z] :
% 155.55/155.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 155.55/155.53 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 155.55/155.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 155.55/155.53 => 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) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_int__eq__iff,axiom,
% 155.55/155.53 ! [V_z_2,V_m_2] :
% 155.55/155.53 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 155.55/155.53 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__0__le,axiom,
% 155.55/155.53 ! [V_z] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 155.55/155.53 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zless__nat__eq__int__zless,axiom,
% 155.55/155.53 ! [V_z_2,V_m_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 155.55/155.53 <=> 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_less__eq__int__code_I15_J,axiom,
% 155.55/155.53 ! [V_k2_2,V_k1_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I33_J,axiom,
% 155.55/155.53 ! [V_l_2,V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_less__int__code_I14_J,axiom,
% 155.55/155.53 ! [V_k2_2,V_k1_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I15_J,axiom,
% 155.55/155.53 ! [V_l_2,V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__zminus__int,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mult__Bit1,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power_Opower_Opower__0,axiom,
% 155.55/155.53 ! [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 ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__abs__mult__distrib,axiom,
% 155.55/155.53 ! [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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power_Opower_Opower__Suc,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_diff__bin__simps_I8_J,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_add__Bit1__Bit1,axiom,
% 155.55/155.53 ! [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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__number__of__even,axiom,
% 155.55/155.53 ! [V_w_2,V_z_2,T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zpower__number__of__even,axiom,
% 155.55/155.53 ! [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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_of__nat__double,axiom,
% 155.55/155.53 ! [V_x,T_a] :
% 155.55/155.53 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_double__number__of__Bit0,axiom,
% 155.55/155.53 ! [V_w,T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__less__nat__eq,axiom,
% 155.55/155.53 ! [V_z_2] :
% 155.55/155.53 ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 155.55/155.53 ! [V_y_2,V_x_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__less__eq__zless,axiom,
% 155.55/155.53 ! [V_z_2,V_w_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__eq__iff2,axiom,
% 155.55/155.53 ! [V_w_2,V_m_2] :
% 155.55/155.53 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 155.55/155.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 155.55/155.53 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 155.55/155.53 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__eq__iff,axiom,
% 155.55/155.53 ! [V_m_2,V_w_2] :
% 155.55/155.53 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 155.55/155.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 155.55/155.53 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 155.55/155.53 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__le__eq__zle,axiom,
% 155.55/155.53 ! [V_z_2,V_w_2] :
% 155.55/155.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 155.55/155.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_split__nat,axiom,
% 155.55/155.53 ! [V_i_2,V_P_2] :
% 155.55/155.53 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 155.55/155.53 <=> ( ! [B_n] :
% 155.55/155.53 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 155.55/155.53 => hBOOL(hAPP(V_P_2,B_n)) )
% 155.55/155.53 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 155.55/155.53 ! [V_y,V_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__add__distrib,axiom,
% 155.55/155.53 ! [V_z_H,V_z] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_int__eq__iff__number__of,axiom,
% 155.55/155.53 ! [V_v_2,V_m_2] :
% 155.55/155.53 ( 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)
% 155.55/155.53 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 155.55/155.53 & 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 155.55/155.53 ! [V_y,V_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__mult__distrib,axiom,
% 155.55/155.53 ! [V_z_H,V_z] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_number__of1,axiom,
% 155.55/155.53 ! [V_n] :
% 155.55/155.53 ( 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)))
% 155.55/155.53 => ( 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))))
% 155.55/155.53 & 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)))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__diff__distrib,axiom,
% 155.55/155.53 ! [V_z,V_z_H] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 155.55/155.53 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)))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__number__of__even__number__of,axiom,
% 155.55/155.53 ! [V_w_2,V_v_2,T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 155.55/155.53 ! [V_n,V_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__power__eq,axiom,
% 155.55/155.53 ! [V_n,V_z] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 155.55/155.53 ! [V_y,V_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_diff__nat__eq__if,axiom,
% 155.55/155.53 ! [V_z_2,V_z_H_2] :
% 155.55/155.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mult__2,axiom,
% 155.55/155.53 ! [V_z,T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mult__2__right,axiom,
% 155.55/155.53 ! [V_z,T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_one__less__nat__eq,axiom,
% 155.55/155.53 ! [V_z_2] :
% 155.55/155.53 ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_one__add__one__is__two,axiom,
% 155.55/155.53 ! [T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__less__iff,axiom,
% 155.55/155.53 ! [V_m_2,V_w_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 155.55/155.53 <=> 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 155.55/155.53 ! [V_z] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__eq__power2,axiom,
% 155.55/155.53 ! [V_a_2,T_a] :
% 155.55/155.53 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 155.55/155.53 => ( 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)
% 155.55/155.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__power2,axiom,
% 155.55/155.53 ! [T_a] :
% 155.55/155.53 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_numeral__2__eq__2,axiom,
% 155.55/155.53 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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_semiring__norm_I115_J,axiom,
% 155.55/155.53 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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 155.55/155.53 ! [V_x,T_a] :
% 155.55/155.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.53 => 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)))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power2__eq__square,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 155.55/155.53 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))))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_add__2__eq__Suc,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_add__2__eq__Suc_H,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_one__power2,axiom,
% 155.55/155.53 ! [T_a] :
% 155.55/155.53 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__mult__distrib__neg,axiom,
% 155.55/155.53 ! [V_z_H,V_z] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power2__minus,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Rings_Oring__1(T_a)
% 155.55/155.53 => 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)))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__mult__2__right,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__mult__2,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__even__eq,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.53 => 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)))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 155.55/155.53 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)))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power2__abs,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => 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)))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_abs__power2,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => 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)))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__1__add__1,axiom,
% 155.55/155.53 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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Suc__eq__number__of,axiom,
% 155.55/155.53 ! [V_v_2,V_n_2] :
% 155.55/155.53 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 155.55/155.53 <=> 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))))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_eq__number__of__Suc,axiom,
% 155.55/155.53 ! [V_n_2,V_v_2] :
% 155.55/155.53 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 155.55/155.53 <=> 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))))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__case__number__of,axiom,
% 155.55/155.53 ! [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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power2__eq__imp__eq,axiom,
% 155.55/155.53 ! [V_y,V_x,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( 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))))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.53 => V_x = V_y ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power2__le__imp__le,axiom,
% 155.55/155.53 ! [V_y,V_x,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( 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))))))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__le__power2,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => 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)))))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power2__less__0,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => ~ 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__less__power2,axiom,
% 155.55/155.53 ! [V_a_2,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => ( 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))))))
% 155.55/155.53 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_sum__power2__eq__zero__iff,axiom,
% 155.55/155.53 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => ( 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)
% 155.55/155.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power2__eq__square__number__of,axiom,
% 155.55/155.53 ! [V_w,T_b] :
% 155.55/155.53 ( ( class_Groups_Omonoid__mult(T_b)
% 155.55/155.53 & class_Int_Onumber(T_b) )
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_less__2__cases,axiom,
% 155.55/155.53 ! [V_n] :
% 155.55/155.53 ( 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)))))
% 155.55/155.53 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.53 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__rec__number__of,axiom,
% 155.55/155.53 ! [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)))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power2__eq__1__iff,axiom,
% 155.55/155.53 ! [V_a_2,T_a] :
% 155.55/155.53 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 155.55/155.53 => ( 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)
% 155.55/155.53 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a)
% 155.55/155.53 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 155.55/155.53 ! [V_n,V_x,T_a] :
% 155.55/155.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__minus__even,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Oring__1(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__nat__number__of__number__of,axiom,
% 155.55/155.53 ! [V_w,V_v] :
% 155.55/155.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => 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)) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__nat__number__of,axiom,
% 155.55/155.53 ! [V_n,V_v] :
% 155.55/155.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_less__number__of__Suc,axiom,
% 155.55/155.53 ! [V_n_2,V_v_2] :
% 155.55/155.53 ( 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)))
% 155.55/155.53 <=> 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)))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_less__Suc__number__of,axiom,
% 155.55/155.53 ! [V_v_2,V_n_2] :
% 155.55/155.53 ( 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)))
% 155.55/155.53 <=> 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))))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_le__Suc__number__of,axiom,
% 155.55/155.53 ! [V_v_2,V_n_2] :
% 155.55/155.53 ( 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)))
% 155.55/155.53 <=> 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))))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_le__number__of__Suc,axiom,
% 155.55/155.53 ! [V_n_2,V_v_2] :
% 155.55/155.53 ( 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)))
% 155.55/155.53 <=> 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)))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power2__less__imp__less,axiom,
% 155.55/155.53 ! [V_y,V_x,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__semidom(T_a)
% 155.55/155.53 => ( 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))))))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_sum__power2__ge__zero,axiom,
% 155.55/155.53 ! [V_y,V_x,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => 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))))))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_sum__power2__le__zero__iff,axiom,
% 155.55/155.53 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__case__add__eq__if,axiom,
% 155.55/155.53 ! [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)))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_sum__power2__gt__zero__iff,axiom,
% 155.55/155.53 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => ( 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)))))))
% 155.55/155.53 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_not__sum__power2__lt__zero,axiom,
% 155.55/155.53 ! [V_y,V_x,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => ~ 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power2__sum,axiom,
% 155.55/155.53 ! [V_y,V_x,T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zero__le__even__power_H,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => 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)))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__rec__add__eq__if,axiom,
% 155.55/155.53 ! [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))))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__odd__eq,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Groups_Omonoid__mult(T_a)
% 155.55/155.53 => 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))))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 155.55/155.53 ! [V_n,V_x,T_a] :
% 155.55/155.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__minus1__even,axiom,
% 155.55/155.53 ! [V_n,T_a] :
% 155.55/155.53 ( class_Rings_Oring__1(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power2__diff,axiom,
% 155.55/155.53 ! [V_y,V_x,T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 155.55/155.53 ! [V_n,V_a,T_a] :
% 155.55/155.53 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.53 => ( 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)))))
% 155.55/155.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__aux__def,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__number__of__Bit1,axiom,
% 155.55/155.53 ! [V_v,V_w] :
% 155.55/155.53 ( ( 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)))
% 155.55/155.53 => 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)) )
% 155.55/155.53 & ( ~ 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)))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__zmod__mult__2,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__morphism__nat__int,axiom,
% 155.55/155.53 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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_pos__zmod__mult__2,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__add__cong,axiom,
% 155.55/155.53 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 155.55/155.53 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 155.55/155.53 => 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) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__simps_I1_J,axiom,
% 155.55/155.53 ! [V_b,V_c,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__simps_I2_J,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__add__eq,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__add__left__eq,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__add__right__eq,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__add__self1,axiom,
% 155.55/155.53 ! [V_a,V_b,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__add__self2,axiom,
% 155.55/155.53 ! [V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__cong,axiom,
% 155.55/155.53 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 155.55/155.53 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 155.55/155.53 => 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) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__simps_I4_J,axiom,
% 155.55/155.53 ! [V_b,V_c,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__mult2,axiom,
% 155.55/155.53 ! [V_b,V_c,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__mult1,axiom,
% 155.55/155.53 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__eq,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__left__eq,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__right__eq,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mod__trivial,axiom,
% 155.55/155.53 ! [V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__minus__eq,axiom,
% 155.55/155.53 ! [V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Oring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__minus__cong,axiom,
% 155.55/155.53 ! [V_a_H,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Oring__div(T_a)
% 155.55/155.53 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 155.55/155.53 => 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) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__0,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__by__0,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__self,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__diff__right__eq,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Oring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__diff__left__eq,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Oring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__diff__eq,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Oring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__diff__cong,axiom,
% 155.55/155.53 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Oring__div(T_a)
% 155.55/155.53 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 155.55/155.53 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 155.55/155.53 => 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) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__self,axiom,
% 155.55/155.53 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zero,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zmult1__eq,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__simps_I3_J,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiff__zmod__left,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiff__zmod__right,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zminus__zmod,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zminus__zminus,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zminus2,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zpower__zmod,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__self2__is__0,axiom,
% 155.55/155.53 ! [V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__self1__is__0,axiom,
% 155.55/155.53 ! [V_a,V_b,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__self2,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__self1,axiom,
% 155.55/155.53 ! [V_b,V_c,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__by__1,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__le__nonneg__dividend,axiom,
% 155.55/155.53 ! [V_k,V_m] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 155.55/155.53 ! [V_y,V_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__mod__bound,axiom,
% 155.55/155.53 ! [V_a,V_b] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_pos__mod__bound,axiom,
% 155.55/155.53 ! [V_a,V_b] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__eq__0__iff,axiom,
% 155.55/155.53 ! [V_d_2,V_m_2] :
% 155.55/155.53 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zminus2__not__zero,axiom,
% 155.55/155.53 ! [V_l,V_k] :
% 155.55/155.53 ( 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)
% 155.55/155.53 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zminus1__not__zero,axiom,
% 155.55/155.53 ! [V_l,V_k] :
% 155.55/155.53 ( 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)
% 155.55/155.53 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__neg__neg__trivial,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 155.55/155.53 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__mod__conj,axiom,
% 155.55/155.53 ! [V_a,V_b] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 & 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__mod__sign,axiom,
% 155.55/155.53 ! [V_a,V_b] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__pos__pos__trivial,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 155.55/155.53 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_pos__mod__conj,axiom,
% 155.55/155.53 ! [V_a,V_b] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 & 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_pos__mod__sign,axiom,
% 155.55/155.53 ! [V_a,V_b] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zminus2__eq__if,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => 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) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zminus1__eq__if,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__pos__neg__trivial,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 => 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) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_split__zmod,axiom,
% 155.55/155.53 ! [V_k_2,V_n_2,V_P_2] :
% 155.55/155.53 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 155.55/155.53 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 155.55/155.53 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 155.55/155.53 => ! [B_i,B_j] :
% 155.55/155.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 155.55/155.53 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 155.55/155.53 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 155.55/155.53 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => ! [B_i,B_j] :
% 155.55/155.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 155.55/155.53 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmult2__lemma__aux3,axiom,
% 155.55/155.53 ! [V_q,V_b,V_r,V_c] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmult2__lemma__aux4,axiom,
% 155.55/155.53 ! [V_q,V_b,V_r,V_c] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmult2__lemma__aux1,axiom,
% 155.55/155.53 ! [V_q,V_r,V_b,V_c] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmult2__lemma__aux2,axiom,
% 155.55/155.53 ! [V_q,V_r,V_b,V_c] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_divmod__int__rel__mod__eq,axiom,
% 155.55/155.53 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 155.55/155.53 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y)
% 155.55/155.53 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 155.55/155.53 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__number__of__Bit0,axiom,
% 155.55/155.53 ! [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))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 155.55/155.53 ! [V_B_2,V_A_2] :
% 155.55/155.53 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.53 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 155.55/155.53 ! [V_B_2,V_A_2] :
% 155.55/155.53 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.53 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_z3mod__def,axiom,
% 155.55/155.53 ! [V_k,V_l] :
% 155.55/155.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 155.55/155.53 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__zdiv__mult__2,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_pos__zdiv__mult__2,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__less,axiom,
% 155.55/155.53 ! [V_n,V_m] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.53 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__less__eq__dividend,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__distrib2,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__distrib,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__zminus__zminus,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__zminus2,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__zero,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__by__0,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => hAPP(c_Divides_Odiv__class_Odiv(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__0,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => hAPP(c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__by__1,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => hAPP(c_Divides_Odiv__class_Odiv(T_a,V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__1,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__Suc,axiom,
% 155.55/155.53 ! [V_n,V_m] :
% 155.55/155.53 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 155.55/155.53 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 155.55/155.53 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 155.55/155.53 ! [V_y,V_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__less__divisor,axiom,
% 155.55/155.53 ! [V_m,V_n] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 155.55/155.53 ! [V_a_2,V_b_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 155.55/155.53 ! [V_a_2,V_b_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__neg__pos__less0,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__self,axiom,
% 155.55/155.53 ! [V_a] :
% 155.55/155.53 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__eq__0__iff,axiom,
% 155.55/155.53 ! [V_d_2,V_m_2] :
% 155.55/155.53 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.53 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__if,axiom,
% 155.55/155.53 ! [V_n,V_m] :
% 155.55/155.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.53 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 155.55/155.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.53 => 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) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__geq,axiom,
% 155.55/155.53 ! [V_n,V_m] :
% 155.55/155.53 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__number__of__Bit0,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_DIVISION__BY__ZERO,axiom,
% 155.55/155.53 ! [V_a] :
% 155.55/155.53 ( 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)
% 155.55/155.53 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zdiv__trivial,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__self3,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_le__mod__geq,axiom,
% 155.55/155.53 ! [V_m,V_n] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__zadd1__eq,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__int,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__mult__mult1,axiom,
% 155.55/155.53 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => 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) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__mult__mult2,axiom,
% 155.55/155.53 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => 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) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__mult__self1__is__id,axiom,
% 155.55/155.53 ! [V_a,V_b,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => 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 ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__mult__self2__is__id,axiom,
% 155.55/155.53 ! [V_a,V_b,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => 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 ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__mult__mult1__if,axiom,
% 155.55/155.53 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => 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) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__self,axiom,
% 155.55/155.53 ! [V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => hAPP(c_Divides_Odiv__class_Odiv(T_a,V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__div__trivial,axiom,
% 155.55/155.53 ! [V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 155.55/155.53 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 155.55/155.53 ! [V_B_2,V_A_2] :
% 155.55/155.53 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.53 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 155.55/155.53 ! [V_B_2,V_A_2] :
% 155.55/155.53 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.53 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__set__def,axiom,
% 155.55/155.53 ! [V_S_2] :
% 155.55/155.53 ( c_Nat__Transfer_Onat__set(V_S_2)
% 155.55/155.53 <=> ! [B_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 155.55/155.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__eq__0__iff,axiom,
% 155.55/155.53 ! [V_k_2,V_i_2] :
% 155.55/155.53 ( hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 155.55/155.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 155.55/155.53 ! [V_a_2,V_b_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 155.55/155.53 ! [V_i_2,V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 155.55/155.53 ! [V_b_2,V_a_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__mono2,axiom,
% 155.55/155.53 ! [V_b,V_b_H,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__nonneg__neg__le0,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__pos__pos__trivial,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 155.55/155.53 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 155.55/155.53 ! [V_a_2,V_b_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__nonpos__pos__le0,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__mono2__neg,axiom,
% 155.55/155.53 ! [V_b,V_b_H,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 155.55/155.53 => 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__neg__neg__trivial,axiom,
% 155.55/155.53 ! [V_b,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 155.55/155.53 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__mono1,axiom,
% 155.55/155.53 ! [V_b,V_a_H,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__mono1__neg,axiom,
% 155.55/155.53 ! [V_b,V_a_H,V_a] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__le__divisor,axiom,
% 155.55/155.53 ! [V_m,V_n] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_int__div__less__self,axiom,
% 155.55/155.53 ! [V_k,V_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__zmult2__eq,axiom,
% 155.55/155.53 ! [V_b,V_a,V_c] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__mult__self4,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 155.55/155.53 ! [V_B_2,V_A_2] :
% 155.55/155.53 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.53 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 155.55/155.53 => ( V_A_2 = V_B_2
% 155.55/155.53 <=> 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) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zdiv__equality,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__zmult1__eq,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__zmod__equality,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__zmod__equality2,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zdiv__equality_H,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmult__div__cancel,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__mult__self2,axiom,
% 155.55/155.53 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__mult__self1,axiom,
% 155.55/155.53 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__add__self2,axiom,
% 155.55/155.53 ! [V_a,V_b,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__add__self1,axiom,
% 155.55/155.53 ! [V_a,V_b,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__mod__equality,axiom,
% 155.55/155.53 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__mod__equality2,axiom,
% 155.55/155.53 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__div__equality,axiom,
% 155.55/155.53 ! [V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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 ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__div__equality2,axiom,
% 155.55/155.53 ! [V_a,V_b,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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 ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 155.55/155.53 ! [V_b,V_a,T_a] :
% 155.55/155.53 ( class_Divides_Osemiring__div(T_a)
% 155.55/155.53 => 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 ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_split__mod,axiom,
% 155.55/155.53 ! [V_k_2,V_n_2,V_P_2] :
% 155.55/155.53 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 155.55/155.53 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.53 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 155.55/155.53 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.53 => ! [B_i,B_j] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 155.55/155.53 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
% 155.55/155.53 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__lemma,axiom,
% 155.55/155.53 ! [V_q,V_b,V_r,V_c] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Suc__times__mod__eq,axiom,
% 155.55/155.53 ! [V_m,V_k] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_nat__mod__distrib,axiom,
% 155.55/155.53 ! [V_y,V_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 155.55/155.53 ! [V_y,V_x] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 155.55/155.53 ! [V_x_2,V_A_2] :
% 155.55/155.53 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 155.55/155.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_divmod__int__rel__div__eq,axiom,
% 155.55/155.53 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 155.55/155.53 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
% 155.55/155.53 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 155.55/155.53 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1),V_b_1) = V_y ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_split__zdiv,axiom,
% 155.55/155.53 ! [V_k_2,V_n_2,V_P_2] :
% 155.55/155.53 ( hBOOL(hAPP(V_P_2,hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2),V_k_2)))
% 155.55/155.53 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 155.55/155.53 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 155.55/155.53 => ! [B_i] :
% 155.55/155.53 ( ? [B_j] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 155.55/155.53 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 155.55/155.53 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 155.55/155.53 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => ! [B_i] :
% 155.55/155.53 ( ? [B_j] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 155.55/155.53 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zmod__zmult2__eq,axiom,
% 155.55/155.53 ! [V_b,V_a,V_c] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 155.55/155.53 => 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)) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod2__Suc__Suc,axiom,
% 155.55/155.53 ! [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)))) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__zminus2__eq__if,axiom,
% 155.55/155.53 ! [V_a,V_b] :
% 155.55/155.53 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => 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)) )
% 155.55/155.53 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => 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)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__zminus1__eq__if,axiom,
% 155.55/155.53 ! [V_a,V_b] :
% 155.55/155.53 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => 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)) )
% 155.55/155.53 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.53 => 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)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 155.55/155.53 ! [V_A_2] :
% 155.55/155.53 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.53 => 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 ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_split__neg__lemma,axiom,
% 155.55/155.53 ! [V_n_2,V_P_2,V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> ! [B_i,B_j] :
% 155.55/155.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.53 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 155.55/155.53 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_split__pos__lemma,axiom,
% 155.55/155.53 ! [V_n_2,V_P_2,V_k_2] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 155.55/155.53 => ( 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)))
% 155.55/155.53 <=> ! [B_i,B_j] :
% 155.55/155.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 155.55/155.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 155.55/155.53 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 155.55/155.53 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod__nat__number__of,axiom,
% 155.55/155.53 ! [V_v_H,V_v] :
% 155.55/155.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.53 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 155.55/155.53 => 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) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 155.55/155.53 => 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))) ) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_zdiv__number__of__Bit1,axiom,
% 155.55/155.53 ! [V_v,V_w] :
% 155.55/155.53 ( ( 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)))
% 155.55/155.53 => 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)) )
% 155.55/155.53 & ( ~ 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)))
% 155.55/155.53 => 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)) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_int__power__div__base,axiom,
% 155.55/155.53 ! [V_k,V_m] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 155.55/155.53 => 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)))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_mod2__gr__0,axiom,
% 155.55/155.53 ! [V_m_2] :
% 155.55/155.53 ( 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))))))
% 155.55/155.53 <=> 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 155.55/155.53 ! [V_B_2,V_A_2] :
% 155.55/155.53 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.53 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.53 <=> 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 155.55/155.53 ! [V_B_2,V_A_2] :
% 155.55/155.53 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.53 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.53 <=> 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_one__mod__nat__number__of,axiom,
% 155.55/155.53 ! [V_v_H] :
% 155.55/155.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 155.55/155.53 => 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)) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_z3div__def,axiom,
% 155.55/155.53 ! [V_k,V_l] :
% 155.55/155.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 155.55/155.53 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k),V_l) )
% 155.55/155.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 155.55/155.53 => 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))) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__m1__odd,axiom,
% 155.55/155.53 ! [V_n,T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_power__m1__even,axiom,
% 155.55/155.53 ! [V_n,T_a] :
% 155.55/155.53 ( class_Int_Onumber__ring(T_a)
% 155.55/155.53 => 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) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 155.55/155.53 ! [V_A_2,V_x_2] :
% 155.55/155.53 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 155.55/155.53 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.53 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 155.55/155.53 <=> 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))) ) ) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 155.55/155.53 ! [V_n] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.53 => 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)))))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__add1__eq,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__mult2__eq,axiom,
% 155.55/155.53 ! [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) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__le__dividend,axiom,
% 155.55/155.53 ! [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)) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_div__le__mono,axiom,
% 155.55/155.53 ! [V_k,V_n,V_m] :
% 155.55/155.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.53 => 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))) ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I42_J,axiom,
% 155.55/155.53 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I45_J,axiom,
% 155.55/155.53 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 155.55/155.53
% 155.55/155.53 fof(fact_Bit1__Min,axiom,
% 155.55/155.53 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I43_J,axiom,
% 155.55/155.53 ! [V_l_2] :
% 155.55/155.53 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 155.55/155.53 <=> c_Int_OMin = V_l_2 ) ).
% 155.55/155.53
% 155.55/155.53 fof(fact_rel__simps_I47_J,axiom,
% 155.55/155.53 ! [V_k_2] :
% 155.55/155.54 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 155.55/155.54 <=> V_k_2 = c_Int_OMin ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I40_J,axiom,
% 155.55/155.54 c_Int_OMin != c_Int_OPls ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I37_J,axiom,
% 155.55/155.54 c_Int_OPls != c_Int_OMin ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I7_J,axiom,
% 155.55/155.54 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I24_J,axiom,
% 155.55/155.54 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 155.55/155.54 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 155.55/155.54 ! [V_y,V_x] :
% 155.55/155.54 ( c_Nat__Transfer_Ois__nat(V_x)
% 155.55/155.54 => ( c_Nat__Transfer_Ois__nat(V_y)
% 155.55/155.54 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 155.55/155.54 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 155.55/155.54 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 155.55/155.54 ! [V_y,V_x] :
% 155.55/155.54 ( c_Nat__Transfer_Ois__nat(V_x)
% 155.55/155.54 => ( c_Nat__Transfer_Ois__nat(V_y)
% 155.55/155.54 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 155.55/155.54 ! [V_y,V_x] :
% 155.55/155.54 ( c_Nat__Transfer_Ois__nat(V_x)
% 155.55/155.54 => ( c_Nat__Transfer_Ois__nat(V_y)
% 155.55/155.54 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 155.55/155.54 ! [V_y,V_x] :
% 155.55/155.54 ( c_Nat__Transfer_Ois__nat(V_x)
% 155.55/155.54 => ( c_Nat__Transfer_Ois__nat(V_y)
% 155.55/155.54 => c_Nat__Transfer_Ois__nat(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x),V_y)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 155.55/155.54 ! [V_n,V_x] :
% 155.55/155.54 ( c_Nat__Transfer_Ois__nat(V_x)
% 155.55/155.54 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__1,axiom,
% 155.55/155.54 ! [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 ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__less,axiom,
% 155.55/155.54 ! [V_n,V_m] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.54 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_nat__mult__div__cancel__disj,axiom,
% 155.55/155.54 ! [V_n,V_m,V_k] :
% 155.55/155.54 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 => 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) )
% 155.55/155.54 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 => 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) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__mult1__eq,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mod__mult2__eq,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__mod__equality_H,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mult__div__cancel,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Divides_Omod__div__equality_H,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_zdiv__int,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_bin__less__0__simps_I2_J,axiom,
% 155.55/155.54 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I20_J,axiom,
% 155.55/155.54 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I23_J,axiom,
% 155.55/155.54 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I30_J,axiom,
% 155.55/155.54 ! [V_k_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I26_J,axiom,
% 155.55/155.54 ! [V_k_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I6_J,axiom,
% 155.55/155.54 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I3_J,axiom,
% 155.55/155.54 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I9_J,axiom,
% 155.55/155.54 ! [V_k_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I13_J,axiom,
% 155.55/155.54 ! [V_k_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I28_J,axiom,
% 155.55/155.54 ! [V_k_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I8_J,axiom,
% 155.55/155.54 ! [V_k_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_eq__number__of__Pls__Min,axiom,
% 155.55/155.54 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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Int_OMin__def,axiom,
% 155.55/155.54 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mult__Min,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 155.55/155.54 ! [V_y,V_x] :
% 155.55/155.54 ( c_Nat__Transfer_Ois__nat(V_x)
% 155.55/155.54 => ( c_Nat__Transfer_Ois__nat(V_y)
% 155.55/155.54 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_neg__number__of__Min,axiom,
% 155.55/155.54 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pred__Pls,axiom,
% 155.55/155.54 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 155.55/155.54
% 155.55/155.54 fof(fact_add__Min__right,axiom,
% 155.55/155.54 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_add__Min,axiom,
% 155.55/155.54 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pred__Min,axiom,
% 155.55/155.54 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_nonzero__number__of__Min,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( class_Int_Onumber__ring(T_a)
% 155.55/155.54 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_succ__Min,axiom,
% 155.55/155.54 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 155.55/155.54
% 155.55/155.54 fof(fact_diff__bin__simps_I2_J,axiom,
% 155.55/155.54 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_is__nat__def,axiom,
% 155.55/155.54 ! [V_x_2] :
% 155.55/155.54 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__le__mono2,axiom,
% 155.55/155.54 ! [V_k,V_n,V_m] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_nat__mult__div__cancel1,axiom,
% 155.55/155.54 ! [V_n,V_m,V_k] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__mult__self__is__m,axiom,
% 155.55/155.54 ! [V_m,V_n] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.54 => 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 ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__mult__self1__is__m,axiom,
% 155.55/155.54 ! [V_m,V_n] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.54 => 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 ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__less__dividend,axiom,
% 155.55/155.54 ! [V_m,V_n] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mult__minus1__right,axiom,
% 155.55/155.54 ! [V_z,T_a] :
% 155.55/155.54 ( class_Int_Onumber__ring(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mult__minus1,axiom,
% 155.55/155.54 ! [V_z,T_a] :
% 155.55/155.54 ( class_Int_Onumber__ring(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_number__of__Min,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( class_Int_Onumber__ring(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_arith__simps_I31_J,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( class_Int_Onumber__ring(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_abs__minus__one,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.54 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I25_J,axiom,
% 155.55/155.54 ! [V_k_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rel__simps_I11_J,axiom,
% 155.55/155.54 ! [V_k_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_zmod__minus1__right,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_diff__bin__simps_I4_J,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_minus__Min,axiom,
% 155.55/155.54 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_zmult__eq__1__iff,axiom,
% 155.55/155.54 ! [V_n_2,V_m_2] :
% 155.55/155.54 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 155.55/155.54 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 155.55/155.54 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 155.55/155.54 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 155.55/155.54 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 155.55/155.54 ! [V_n,V_m] :
% 155.55/155.54 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 155.55/155.54 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 155.55/155.54 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_diff__bin__simps_I6_J,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_diff__bin__simps_I5_J,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_zdiv__minus1__right,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 155.55/155.54 ! [V_x_2,V_A_2] :
% 155.55/155.54 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 155.55/155.54 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__if,axiom,
% 155.55/155.54 ! [V_m,V_n] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.54 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.54 => 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)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__geq,axiom,
% 155.55/155.54 ! [V_m,V_n] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.54 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__div,axiom,
% 155.55/155.54 ! [V_k_2,V_n_2,V_P_2] :
% 155.55/155.54 ( hBOOL(hAPP(V_P_2,hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2),V_k_2)))
% 155.55/155.54 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 155.55/155.54 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 => ! [B_i,B_j] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 155.55/155.54 => ( 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)
% 155.55/155.54 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 155.55/155.54 ! [V_y,V_x] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_nat__div__distrib,axiom,
% 155.55/155.54 ! [V_y,V_x] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_abs__power__minus__one,axiom,
% 155.55/155.54 ! [V_n,T_a] :
% 155.55/155.54 ( ( class_Int_Onumber__ring(T_a)
% 155.55/155.54 & class_Rings_Olinordered__idom(T_a) )
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__eq__minus1,axiom,
% 155.55/155.54 ! [V_b] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 155.55/155.54 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_le__div__geq,axiom,
% 155.55/155.54 ! [V_m,V_n] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__div__lemma,axiom,
% 155.55/155.54 ! [V_m_2,V_q_2,V_n_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 155.55/155.54 => ( ( 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))
% 155.55/155.54 & 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)))) )
% 155.55/155.54 <=> V_q_2 = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2),V_n_2) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__div_H,axiom,
% 155.55/155.54 ! [V_n_2,V_m_2,V_P_2] :
% 155.55/155.54 ( hBOOL(hAPP(V_P_2,hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2),V_n_2)))
% 155.55/155.54 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 155.55/155.54 | ? [B_q] :
% 155.55/155.54 ( 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))
% 155.55/155.54 & 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))))
% 155.55/155.54 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__Suc__eq__div__add3,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Suc__div__eq__add3__div,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div2__Suc__Suc,axiom,
% 155.55/155.54 ! [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))))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_add__self__div__2,axiom,
% 155.55/155.54 ! [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 ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 155.55/155.54 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__nat__number__of,axiom,
% 155.55/155.54 ! [V_v_H,V_v] :
% 155.55/155.54 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.54 => 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) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__pos__neg__trivial,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.54 => ( 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)))
% 155.55/155.54 => 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) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_zmod__minus1,axiom,
% 155.55/155.54 ! [V_b] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__2__gt__zero,axiom,
% 155.55/155.54 ! [V_n] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 155.55/155.54 => 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)))))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_one__div__nat__number__of,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_int__of__code,axiom,
% 155.55/155.54 ! [V_k] :
% 155.55/155.54 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 155.55/155.54 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 155.55/155.54 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 155.55/155.54 => ( ( 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)
% 155.55/155.54 => 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)))))) )
% 155.55/155.54 & ( 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)
% 155.55/155.54 => 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)) ) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__Suc__number__of,axiom,
% 155.55/155.54 ! [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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__number__of__Suc,axiom,
% 155.55/155.54 ! [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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_code__numeral_Osize_I1_J,axiom,
% 155.55/155.54 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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__of__nat,axiom,
% 155.55/155.54 ! [V_k,T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => 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)))) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => 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)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__of__mono,axiom,
% 155.55/155.54 ! [V_n_2,V_m_2,V_f_2,T_a,T_b] :
% 155.55/155.54 ( ( class_Orderings_Olinorder(T_b)
% 155.55/155.54 & class_Orderings_Olinorder(T_a) )
% 155.55/155.54 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_inf__nat__def,axiom,
% 155.55/155.54 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_inf__min,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.54 & class_Orderings_Olinorder(T_a) )
% 155.55/155.54 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__0R,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__0L,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__Suc__Suc,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__diff,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__le__iff__disj,axiom,
% 155.55/155.54 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( 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))
% 155.55/155.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__infE,axiom,
% 155.55/155.54 ! [V_b,V_a,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( 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)))
% 155.55/155.54 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 155.55/155.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__mono,axiom,
% 155.55/155.54 ! [V_d,V_b,V_c,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 155.55/155.54 => 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))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__greatest,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 155.55/155.54 => 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))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__infI,axiom,
% 155.55/155.54 ! [V_b,V_a,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 155.55/155.54 => 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))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__absorb2,axiom,
% 155.55/155.54 ! [V_x,V_y,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.54 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__absorb1,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.54 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__infI2,axiom,
% 155.55/155.54 ! [V_a,V_x,V_b,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__infI1,axiom,
% 155.55/155.54 ! [V_b,V_x,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__inf__iff,axiom,
% 155.55/155.54 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( 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)))
% 155.55/155.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__iff__inf,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.54 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__le2,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__le1,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__less__iff__disj,axiom,
% 155.55/155.54 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( 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))
% 155.55/155.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__less__iff__conj,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( 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)))
% 155.55/155.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 155.55/155.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oless__infI2,axiom,
% 155.55/155.54 ! [V_a,V_x,V_b,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oless__infI1,axiom,
% 155.55/155.54 ! [V_b,V_x,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf_Oidem,axiom,
% 155.55/155.54 ! [V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf_Ocommute,axiom,
% 155.55/155.54 ! [V_b,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__commute,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 155.55/155.54 ! [V_b,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__left__idem,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 155.55/155.54 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__left__commute,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf_Oassoc,axiom,
% 155.55/155.54 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__assoc,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__eq__iff,axiom,
% 155.55/155.54 ! [V_z_2,V_w_2,T_a] :
% 155.55/155.54 ( class_Int_Oring__char__0(T_a)
% 155.55/155.54 => ( 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)
% 155.55/155.54 <=> V_w_2 = V_z_2 ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__diff__distrib__left,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__add__distrib__left,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_number__of__eq,axiom,
% 155.55/155.54 ! [V_k,T_a] :
% 155.55/155.54 ( class_Int_Onumber__ring(T_a)
% 155.55/155.54 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_int__number__of__def,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__int__eq,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__number__of,axiom,
% 155.55/155.54 ! [V_v,V_u,T_b] :
% 155.55/155.54 ( ( class_Int_Onumber(T_b)
% 155.55/155.54 & class_Orderings_Oord(T_b) )
% 155.55/155.54 => ( ( 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)))
% 155.55/155.54 => 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) )
% 155.55/155.54 & ( ~ 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)))
% 155.55/155.54 => 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) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__eq__0__iff,axiom,
% 155.55/155.54 ! [V_z_2,T_a] :
% 155.55/155.54 ( class_Int_Oring__char__0(T_a)
% 155.55/155.54 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.54 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__0__eq__iff,axiom,
% 155.55/155.54 ! [V_z_2,T_a] :
% 155.55/155.54 ( class_Int_Oring__char__0(T_a)
% 155.55/155.54 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)
% 155.55/155.54 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__0,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__le__iff,axiom,
% 155.55/155.54 ! [V_z_2,V_w_2,T_a] :
% 155.55/155.54 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.54 => ( 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)))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__less__iff,axiom,
% 155.55/155.54 ! [V_z_2,V_w_2,T_a] :
% 155.55/155.54 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.54 => ( 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)))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__add,axiom,
% 155.55/155.54 ! [V_z,V_w,T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__number__of__eq,axiom,
% 155.55/155.54 ! [V_v,T_a] :
% 155.55/155.54 ( class_Int_Onumber__ring(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__mult,axiom,
% 155.55/155.54 ! [V_z,V_w,T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__1,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__diff,axiom,
% 155.55/155.54 ! [V_z,V_w,T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__of__nat__eq,axiom,
% 155.55/155.54 ! [V_n,T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__minus,axiom,
% 155.55/155.54 ! [V_z,T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Ints__of__int,axiom,
% 155.55/155.54 ! [V_z_2,T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__power,axiom,
% 155.55/155.54 ! [V_n,V_z,T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Omono__inf,axiom,
% 155.55/155.54 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 155.55/155.54 ( ( class_Lattices_Osemilattice__inf(T_b)
% 155.55/155.54 & class_Orderings_Olinorder(T_a) )
% 155.55/155.54 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 155.55/155.54 => 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)))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__m1,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( class_Int_Onumber__ring(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__Suc2,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__Suc1,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__le__0__iff,axiom,
% 155.55/155.54 ! [V_z_2,T_a] :
% 155.55/155.54 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.54 => ( 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)))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__0__le__iff,axiom,
% 155.55/155.54 ! [V_z_2,T_a] :
% 155.55/155.54 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.54 => ( 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)))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__less__0__iff,axiom,
% 155.55/155.54 ! [V_z_2,T_a] :
% 155.55/155.54 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.54 => ( 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)))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__0__less__iff,axiom,
% 155.55/155.54 ! [V_z_2,T_a] :
% 155.55/155.54 ( class_Rings_Olinordered__idom(T_a)
% 155.55/155.54 => ( 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)))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__nat__nat,axiom,
% 155.55/155.54 ! [V_z,T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 155.55/155.54 => 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) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_small__int__def,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_of__int__num,axiom,
% 155.55/155.54 ! [V_k_2,T_a] :
% 155.55/155.54 ( class_Rings_Oring__1(T_a)
% 155.55/155.54 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) )
% 155.55/155.54 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => 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))) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => 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))))) ) ) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__ord__min,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( class_Orderings_Oord(T_a)
% 155.55/155.54 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_code__numeral_Osize_I2_J,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_code__numeral_Oinject,axiom,
% 155.55/155.54 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 155.55/155.54 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 155.55/155.54 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 155.55/155.54 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Suc__code__numeral__minus__one,axiom,
% 155.55/155.54 ! [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 ).
% 155.55/155.54
% 155.55/155.54 fof(fact_code__numeral_Osize_I4_J,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_full__small__int__def,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__rel__def,axiom,
% 155.55/155.54 ! [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))))))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nitpick_OFrac__def,axiom,
% 155.55/155.54 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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__correct,axiom,
% 155.55/155.54 ! [V_a,V_b] :
% 155.55/155.54 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_code__numeral_Osize_I3_J,axiom,
% 155.55/155.54 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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 155.55/155.54 ! [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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_zmult2__lemma,axiom,
% 155.55/155.54 ! [V_c,V_r,V_q,V_b,V_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 155.55/155.54 => 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)))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 155.55/155.54 ! [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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_adjust__eq,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_bot__empty__eq2,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,T_b,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 <=> 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)))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pred__equals__eq2,axiom,
% 155.55/155.54 ! [V_S_2,V_R_2,T_b,T_a] :
% 155.55/155.54 ( 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)
% 155.55/155.54 <=> V_R_2 = V_S_2 ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pred__subset__eq2,axiom,
% 155.55/155.54 ! [V_S_2,V_R_2,T_b,T_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 <=> 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_sup__Un__eq2,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 <=> 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_inf__Int__eq2,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 <=> 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_small__prod__def,axiom,
% 155.55/155.54 ! [V_d_2,V_f_2,T_a,T_b] :
% 155.55/155.54 ( ( class_Smallcheck_Osmall(T_b)
% 155.55/155.54 & class_Smallcheck_Osmall(T_a) )
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_unique__remainder,axiom,
% 155.55/155.54 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( 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)))
% 155.55/155.54 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => V_r = V_r_H ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_unique__quotient,axiom,
% 155.55/155.54 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( 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)))
% 155.55/155.54 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => V_q = V_q_H ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_self__remainder,axiom,
% 155.55/155.54 ! [V_r,V_q,V_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__rel__0,axiom,
% 155.55/155.54 ! [V_b] :
% 155.55/155.54 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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)))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_self__quotient,axiom,
% 155.55/155.54 ! [V_r,V_q,V_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__rel__mod,axiom,
% 155.55/155.54 ! [V_r,V_q,V_b,V_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__rel__div,axiom,
% 155.55/155.54 ! [V_r,V_q,V_b,V_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b) = V_q ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__mod__div,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__rel__div__mod,axiom,
% 155.55/155.54 ! [V_a,V_b] :
% 155.55/155.54 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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)))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_nat__gcd_Osimps,axiom,
% 155.55/155.54 ! [V_x,V_y] :
% 155.55/155.54 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 155.55/155.54 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_zadd1__lemma,axiom,
% 155.55/155.54 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( 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)))
% 155.55/155.54 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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)))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_zminus1__lemma,axiom,
% 155.55/155.54 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => 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))))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__relI,axiom,
% 155.55/155.54 ! [V_r,V_q,V_b,V_a] :
% 155.55/155.54 ( 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)
% 155.55/155.54 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 155.55/155.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 155.55/155.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_zmult1__lemma,axiom,
% 155.55/155.54 ! [V_a,V_r,V_q,V_c,V_b] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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)))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_adjust__def,axiom,
% 155.55/155.54 ! [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))))))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pair__imageI,axiom,
% 155.55/155.54 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 => 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_norm__frac_Osimps,axiom,
% 155.55/155.54 ! [V_a_2,V_b_2] :
% 155.55/155.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 155.55/155.54 => 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))) ) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 155.55/155.54 ! [V_w] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( 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))))
% 155.55/155.54 => 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))) )
% 155.55/155.54 & ( ~ 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))))
% 155.55/155.54 => 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)))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_splitI,axiom,
% 155.55/155.54 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 155.55/155.54 => 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_sup2CI,axiom,
% 155.55/155.54 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] :
% 155.55/155.54 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_sup2E,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_inf2I,axiom,
% 155.55/155.54 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_inf2E,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 155.55/155.54 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mem__splitI,axiom,
% 155.55/155.54 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2)))
% 155.55/155.54 => 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)))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_prod__caseI,axiom,
% 155.55/155.54 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 155.55/155.54 => 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_bot2E,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_swap__inj__on,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_splitD_H,axiom,
% 155.55/155.54 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_inf2D1,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_inf2D2,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_sup2I2,axiom,
% 155.55/155.54 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_sup2I1,axiom,
% 155.55/155.54 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_predicate2D,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rev__predicate2D,axiom,
% 155.55/155.54 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 155.55/155.54 => ( 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))
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_less__by__empty,axiom,
% 155.55/155.54 ! [V_B_2,T_a,V_A_2] :
% 155.55/155.54 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Pair__inject,axiom,
% 155.55/155.54 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 155.55/155.54 ( 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)
% 155.55/155.54 => ~ ( V_a = V_a_H
% 155.55/155.54 => V_b != V_b_H ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Pair__eq,axiom,
% 155.55/155.54 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.54 ( 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)
% 155.55/155.54 <=> ( V_a_2 = V_a_H_2
% 155.55/155.54 & V_b_2 = V_b_H_2 ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__paired__All,axiom,
% 155.55/155.54 ! [T_b,T_a,V_P_2] :
% 155.55/155.54 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 155.55/155.54 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__weak__cong,axiom,
% 155.55/155.54 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] :
% 155.55/155.54 ( V_p_2 = V_q_2
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_negDivAlg__correct,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__twice,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_prod_Osimps_I2_J,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__conv,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_splitD,axiom,
% 155.55/155.54 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_negDivAlg__div__mod,axiom,
% 155.55/155.54 ! [V_l,V_k] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_negDivAlg__minus1,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__eta,axiom,
% 155.55/155.54 ! [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 ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__paired__The,axiom,
% 155.55/155.54 ! [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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_The__split__eq,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_negDivAlg_Osimps,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( ( ( 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)))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( ~ ( 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)))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_negDivAlg__eqn__number__of,axiom,
% 155.55/155.54 ! [V_w,V_v] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( 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))))
% 155.55/155.54 => 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))) )
% 155.55/155.54 & ( ~ 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))))
% 155.55/155.54 => 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)))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_negDivAlg__eqn,axiom,
% 155.55/155.54 ! [V_a,V_b] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => ( ( 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)))
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( ~ 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)))
% 155.55/155.54 => 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))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_in__rel__def,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))
% 155.55/155.54 <=> 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__mod__code__numeral__def,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Nitpick_Orefl_H__def,axiom,
% 155.55/155.54 ! [V_r_2,T_a] :
% 155.55/155.54 ( c_Nitpick_Orefl_H(T_a,V_r_2)
% 155.55/155.54 <=> ! [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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 155.55/155.54 ! [V_w] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( 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)))
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( ~ 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)))
% 155.55/155.54 => 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)))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_posDivAlg__0,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_posDivAlg__correct,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_posDivAlg__div__mod,axiom,
% 155.55/155.54 ! [V_l,V_k] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_posDivAlg__eqn__number__of,axiom,
% 155.55/155.54 ! [V_w,V_v] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( 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)))
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( ~ 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)))
% 155.55/155.54 => 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)))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_posDivAlg__eqn,axiom,
% 155.55/155.54 ! [V_a,V_b] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 155.55/155.54 => 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) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 155.55/155.54 => 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))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_posDivAlg_Osimps,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 155.55/155.54 => 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) )
% 155.55/155.54 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__def,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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))) ) ) ) ) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => 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))) ) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__step,axiom,
% 155.55/155.54 ! [V_m,V_n] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__pdivmod,axiom,
% 155.55/155.54 ! [V_l_2,V_k_2] :
% 155.55/155.54 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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) )
% 155.55/155.54 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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)))) ) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__code,axiom,
% 155.55/155.54 ! [V_l_2,V_k_2] :
% 155.55/155.54 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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) )
% 155.55/155.54 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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)))) ) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_negateSnd__def,axiom,
% 155.55/155.54 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_apsnd__conv,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_apsnd__compose,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__zero,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__base,axiom,
% 155.55/155.54 ! [V_n,V_m] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_negateSnd__eq,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__div__mod,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__int__rel__neg,axiom,
% 155.55/155.54 ! [V_qr,V_b,V_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__if,axiom,
% 155.55/155.54 ! [V_m_2,V_n_2] :
% 155.55/155.54 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 155.55/155.54 => 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) )
% 155.55/155.54 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pdivmod__def,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pdivmod__posDivAlg,axiom,
% 155.55/155.54 ! [V_k,V_l] :
% 155.55/155.54 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 155.55/155.54 ! [V_a,V_r,V_q,V_c,V_b] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 155.55/155.54 => 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)))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 155.55/155.54 ! [V_c,V_r,V_q,V_b,V_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 155.55/155.54 => 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)))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_negDivAlg_Opsimps,axiom,
% 155.55/155.54 ! [V_b_2,V_a_2] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( ( 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)))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( ~ ( 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)))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 155.55/155.54 => 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))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_small_H_Opsimps,axiom,
% 155.55/155.54 ! [V_i_2,V_d_2,V_f_2] :
% 155.55/155.54 ( 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))))
% 155.55/155.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 155.55/155.54 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 155.55/155.54 => 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)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__rel__unique,axiom,
% 155.55/155.54 ! [V_qr_H,V_qr,V_n,V_m] :
% 155.55/155.54 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 155.55/155.54 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 155.55/155.54 => V_qr = V_qr_H ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_accp__downward,axiom,
% 155.55/155.54 ! [V_a_2,V_b_2,V_r_2,T_a] :
% 155.55/155.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 155.55/155.54 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_accp_Oequations,axiom,
% 155.55/155.54 ! [V_a_2,V_r_2,T_a] :
% 155.55/155.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 155.55/155.54 <=> ! [B_x] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 155.55/155.54 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_accp_Osimps,axiom,
% 155.55/155.54 ! [V_a_2,V_r_2,T_a] :
% 155.55/155.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 155.55/155.54 <=> ! [B_x] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 155.55/155.54 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__eq,axiom,
% 155.55/155.54 ! [V_qr,V_n,V_m] :
% 155.55/155.54 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 155.55/155.54 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 155.55/155.54 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__def,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_accp__subset,axiom,
% 155.55/155.54 ! [V_R2_2,V_R1_2,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 => 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mod__eq,axiom,
% 155.55/155.54 ! [V_r,V_q,V_n,V_m] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__eq,axiom,
% 155.55/155.54 ! [V_r,V_q,V_n,V_m] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = V_q ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__rel,axiom,
% 155.55/155.54 ! [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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 155.55/155.54 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( 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)))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 155.55/155.54 => 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)))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_posDivAlg_Opsimps,axiom,
% 155.55/155.54 ! [V_b_2,V_a_2] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 155.55/155.54 => 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) )
% 155.55/155.54 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 155.55/155.54 => 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))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_norm__frac_Opsimps,axiom,
% 155.55/155.54 ! [V_b_2,V_a_2] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 155.55/155.54 => 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)) )
% 155.55/155.54 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 155.55/155.54 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 155.55/155.54 => 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))) ) ) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_negDivAlg_Opinduct,axiom,
% 155.55/155.54 ! [V_P_2,V_a1_2,V_a0_2] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ! [B_a,B_b] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( ~ ( 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)))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 155.55/155.54 => 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))) )
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_small_H_Opinduct,axiom,
% 155.55/155.54 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
% 155.55/155.54 ( 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))))
% 155.55/155.54 => ( ! [B_f,B_d,B_i] :
% 155.55/155.54 ( 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))))
% 155.55/155.54 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 155.55/155.54 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 155.55/155.54 => 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)))) ) )
% 155.55/155.54 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
% 155.55/155.54 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_posDivAlg_Opinduct,axiom,
% 155.55/155.54 ! [V_P_2,V_a1_2,V_a0_2] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ! [B_a,B_b] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 155.55/155.54 => 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))) )
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_nat__gcd_Opsimps,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 155.55/155.54 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 => 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)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mod__pos__neg__1__number__of,axiom,
% 155.55/155.54 ! [V_w] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => 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))))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_in__measure,axiom,
% 155.55/155.54 ! [V_f_2,V_y_2,V_x_2,T_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 <=> 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_snd__eqD,axiom,
% 155.55/155.54 ! [V_a,V_y,V_x,T_a,T_b] :
% 155.55/155.54 ( 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
% 155.55/155.54 => V_y = V_a ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_snd__conv,axiom,
% 155.55/155.54 ! [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 ).
% 155.55/155.54
% 155.55/155.54 fof(fact_apsnd__eq__conv,axiom,
% 155.55/155.54 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] :
% 155.55/155.54 ( 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)
% 155.55/155.54 <=> 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_snd__apsnd,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_snd__def,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mod__int__def,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mod__neg__pos,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mod__pos__pos,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mod__pos__pos__1__number__of,axiom,
% 155.55/155.54 ! [V_w] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mod__pos__neg,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => 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)))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mod__neg__neg,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => 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)))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_norm__frac_Opinduct,axiom,
% 155.55/155.54 ! [V_P_2,V_a1_2,V_a0_2] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ! [B_a,B_b] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => 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))) )
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__pos__neg__1__number__of,axiom,
% 155.55/155.54 ! [V_w] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => 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))))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_nat__gcd_Opinduct,axiom,
% 155.55/155.54 ! [V_P_2,V_a1_2,V_a0_2] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ! [B_x,B_y] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 155.55/155.54 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mlex__leq,axiom,
% 155.55/155.54 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( 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))
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_prod__eqI,axiom,
% 155.55/155.54 ! [V_q,V_p,T_b,T_a] :
% 155.55/155.54 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 155.55/155.54 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 155.55/155.54 => V_p = V_q ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Pair__fst__snd__eq,axiom,
% 155.55/155.54 ! [T_b,T_a,V_t_2,V_s_2] :
% 155.55/155.54 ( V_s_2 = V_t_2
% 155.55/155.54 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2)
% 155.55/155.54 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_fst__conv,axiom,
% 155.55/155.54 ! [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 ).
% 155.55/155.54
% 155.55/155.54 fof(fact_fst__eqD,axiom,
% 155.55/155.54 ! [V_a,V_y,V_x,T_b,T_a] :
% 155.55/155.54 ( 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
% 155.55/155.54 => V_x = V_a ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_fst__apsnd,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_fst__def,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_surjective__pairing,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pair__collapse,axiom,
% 155.55/155.54 ! [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 ).
% 155.55/155.54
% 155.55/155.54 fof(fact_prod__case__beta,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__comp,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__int__def,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mod__nat__def,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__comp__eq,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__beta,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_split__def,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_The__split,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__neg__pos,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__pos__pos,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__pos__pos__1__number__of,axiom,
% 155.55/155.54 ! [V_w] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__pos__neg,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => 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)))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__neg__neg,axiom,
% 155.55/155.54 ! [V_b,V_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 155.55/155.54 => 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)))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mlex__less,axiom,
% 155.55/155.54 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_prod__size__simp,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_conjI__realizer,axiom,
% 155.55/155.54 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 155.55/155.54 ( hBOOL(hAPP(V_P_2,V_p_2))
% 155.55/155.54 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 155.55/155.54 => ( 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))))
% 155.55/155.54 & 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)))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_exI__realizer,axiom,
% 155.55/155.54 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 155.55/155.54 => 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)))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_prod_Orecs,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_div__nat__def,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_divmod__nat__rel__def,axiom,
% 155.55/155.54 ! [V_qr_2,V_n_2,V_m_2] :
% 155.55/155.54 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 155.55/155.54 <=> ( 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))
% 155.55/155.54 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 155.55/155.54 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 155.55/155.54 => ( 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)))
% 155.55/155.54 & 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)) ) )
% 155.55/155.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 155.55/155.54 => ( 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)))
% 155.55/155.54 & 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))) ) ) ) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_in__lex__prod,axiom,
% 155.55/155.54 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 <=> ( 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))
% 155.55/155.54 | ( V_a_2 = V_a_H_2
% 155.55/155.54 & 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)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__number__of__Suc,axiom,
% 155.55/155.54 ! [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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__Suc__number__of,axiom,
% 155.55/155.54 ! [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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_apsnd__apfst,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup__inf__absorb,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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 ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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 ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 155.55/155.54 ! [V_x,V_z,V_y,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 155.55/155.54 ! [V_x,V_z,V_y,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__of__mono,axiom,
% 155.55/155.54 ! [V_n_2,V_m_2,V_f_2,T_a,T_b] :
% 155.55/155.54 ( ( class_Orderings_Olinorder(T_b)
% 155.55/155.54 & class_Orderings_Olinorder(T_a) )
% 155.55/155.54 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__0R,axiom,
% 155.55/155.54 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__0L,axiom,
% 155.55/155.54 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__Suc__Suc,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__less__iff__conj,axiom,
% 155.55/155.54 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( 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))
% 155.55/155.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 155.55/155.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_less__max__iff__disj,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( 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)))
% 155.55/155.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oless__supI2,axiom,
% 155.55/155.54 ! [V_a,V_b,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Oless__supI1,axiom,
% 155.55/155.54 ! [V_b,V_a,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup_Oidem,axiom,
% 155.55/155.54 ! [V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup_Ocommute,axiom,
% 155.55/155.54 ! [V_b,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup__commute,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 155.55/155.54 ! [V_b,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup__left__idem,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 155.55/155.54 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup__left__commute,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup_Oassoc,axiom,
% 155.55/155.54 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup__assoc,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__diff__distrib__left,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__add__distrib__left,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_le__maxI1,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_le__maxI2,axiom,
% 155.55/155.54 ! [V_x,V_y,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__iff__sup,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.55/155.54 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__sup__iff,axiom,
% 155.55/155.54 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( 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))
% 155.55/155.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 155.55/155.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__supI1,axiom,
% 155.55/155.54 ! [V_b,V_a,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__supI2,axiom,
% 155.55/155.54 ! [V_a,V_b,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup__absorb2,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.54 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup__absorb1,axiom,
% 155.55/155.54 ! [V_x,V_y,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.54 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__supI,axiom,
% 155.55/155.54 ! [V_b,V_x,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 155.55/155.54 => 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)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup__least,axiom,
% 155.55/155.54 ! [V_z,V_x,V_y,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 155.55/155.54 => 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)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Osup__mono,axiom,
% 155.55/155.54 ! [V_d,V_b,V_c,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 155.55/155.54 => 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))) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Ole__supE,axiom,
% 155.55/155.54 ! [V_x,V_b,V_a,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( 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))
% 155.55/155.54 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 155.55/155.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_le__max__iff__disj,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => ( 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)))
% 155.55/155.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2))
% 155.55/155.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_sup__max,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.54 & class_Orderings_Olinorder(T_a) )
% 155.55/155.54 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_sup__nat__def,axiom,
% 155.55/155.54 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_apfst__conv,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_apfst__compose,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_fst__apfst,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_apfst__eq__conv,axiom,
% 155.55/155.54 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] :
% 155.55/155.54 ( 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)
% 155.55/155.54 <=> 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_snd__apfst,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__number__of,axiom,
% 155.55/155.54 ! [V_v,V_u,T_b] :
% 155.55/155.54 ( ( class_Int_Onumber(T_b)
% 155.55/155.54 & class_Orderings_Oord(T_b) )
% 155.55/155.54 => ( ( 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)))
% 155.55/155.54 => 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) )
% 155.55/155.54 & ( ~ 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)))
% 155.55/155.54 => 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) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Odistrib__sup__le,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Odistrib__inf__le,axiom,
% 155.55/155.54 ! [V_z,V_y,V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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)))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_minus__min__eq__max,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_minus__max__eq__min,axiom,
% 155.55/155.54 ! [V_y,V_x,T_a] :
% 155.55/155.54 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_nat__minus__add__max,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_apsnd__apfst__commute,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__Suc2,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__Suc1,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__max_Omono__sup,axiom,
% 155.55/155.54 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 155.55/155.54 ( ( class_Lattices_Osemilattice__sup(T_b)
% 155.55/155.54 & class_Orderings_Olinorder(T_a) )
% 155.55/155.54 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2)
% 155.55/155.54 => 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)))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_apfst__apsnd,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_dual__min,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_same__fstI,axiom,
% 155.55/155.54 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] :
% 155.55/155.54 ( hBOOL(hAPP(V_P_2,V_x_2))
% 155.55/155.54 => ( 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)))
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__ord__max,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( class_Orderings_Oord(T_a)
% 155.55/155.54 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pair__lessI2,axiom,
% 155.55/155.54 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Sup__fin_Oidem,axiom,
% 155.55/155.54 ! [V_x,T_a] :
% 155.55/155.54 ( class_Lattices_Olattice(T_a)
% 155.55/155.54 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Inf__fin_Oidem,axiom,
% 155.55/155.54 ! [V_x,T_a] :
% 155.55/155.54 ( class_Lattices_Olattice(T_a)
% 155.55/155.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Min_Oidem,axiom,
% 155.55/155.54 ! [V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Max_Oidem,axiom,
% 155.55/155.54 ! [V_x,T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_dual__max,axiom,
% 155.55/155.54 ! [T_a] :
% 155.55/155.54 ( class_Orderings_Olinorder(T_a)
% 155.55/155.54 => 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pair__lessI1,axiom,
% 155.55/155.54 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pair__leqI2,axiom,
% 155.55/155.54 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 155.55/155.54 => 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)) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_smax__insertI,axiom,
% 155.55/155.54 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 155.55/155.54 => ( 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))
% 155.55/155.54 => ( 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))
% 155.55/155.54 => 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)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_smin__insertI,axiom,
% 155.55/155.54 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 155.55/155.54 => ( 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))
% 155.55/155.54 => ( 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))
% 155.55/155.54 => 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)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pair__leqI1,axiom,
% 155.55/155.54 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_smin__emptyI,axiom,
% 155.55/155.54 ! [V_X_2] :
% 155.55/155.54 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 155.55/155.54 => 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_wmin__insertI,axiom,
% 155.55/155.54 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 155.55/155.54 => ( 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))
% 155.55/155.54 => ( 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))
% 155.55/155.54 => 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)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_wmax__insertI,axiom,
% 155.55/155.54 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 155.55/155.54 => ( 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))
% 155.55/155.54 => ( 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))
% 155.55/155.54 => 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)) ) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_wmin__emptyI,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__strict__def,axiom,
% 155.55/155.54 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__weak__def,axiom,
% 155.55/155.54 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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__weak__def,axiom,
% 155.55/155.54 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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__rpair__set,axiom,
% 155.55/155.54 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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_min__rpair__set,axiom,
% 155.55/155.54 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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_less__than__iff,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2] :
% 155.55/155.54 ( 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))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_pair__less__def,axiom,
% 155.55/155.54 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__strict__def,axiom,
% 155.55/155.54 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__ext__additive,axiom,
% 155.55/155.54 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 => ( 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)))
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_max__extp__max__ext__eq,axiom,
% 155.55/155.54 ! [V_xa_2,V_x_2,V_R_2,T_a] :
% 155.55/155.54 ( 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)
% 155.55/155.54 <=> 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))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_mlex__prod__def,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_intrel__iff,axiom,
% 155.55/155.54 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 155.55/155.54 ( 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))
% 155.55/155.54 <=> 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) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rp__inv__image__rp,axiom,
% 155.55/155.54 ! [V_f_2,T_b,V_P_2,T_a] :
% 155.55/155.54 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 155.55/155.54 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rp__inv__image__def,axiom,
% 155.55/155.54 ! [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))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_in__inv__image,axiom,
% 155.55/155.54 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] :
% 155.55/155.54 ( 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)))
% 155.55/155.54 <=> 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_equiv__intrel__iff,axiom,
% 155.55/155.54 ! [V_y_2,V_x_2] :
% 155.55/155.54 ( 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))))
% 155.55/155.54 <=> 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)) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 155.55/155.54 ! [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) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_accp__acc__eq,axiom,
% 155.55/155.54 ! [V_x_2,V_r_2,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Image__mono,axiom,
% 155.55/155.54 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] :
% 155.55/155.54 ( 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))
% 155.55/155.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 155.55/155.54 => 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))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Image__Int__subset,axiom,
% 155.55/155.54 ! [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)))) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Un__Image,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Image__Un,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Image__empty,axiom,
% 155.55/155.54 ! [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)) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_rev__ImageI,axiom,
% 155.55/155.54 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 155.55/155.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.54 => ( 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))
% 155.55/155.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ).
% 155.55/155.54
% 155.55/155.54 fof(fact_Image__iff,axiom,
% 155.55/155.55 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 155.55/155.55 <=> ? [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.55/155.55 & 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_acc__subset,axiom,
% 155.55/155.55 ! [V_R2_2,V_R1_2,T_a] :
% 155.55/155.55 ( 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))
% 155.55/155.55 => 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Image__singleton__iff,axiom,
% 155.55/155.55 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] :
% 155.55/155.55 ( 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))))))
% 155.55/155.55 <=> 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_acc_Osimps,axiom,
% 155.55/155.55 ! [V_r_2,V_a_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 155.55/155.55 <=> ! [B_x] :
% 155.55/155.55 ( 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))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_acc__downward,axiom,
% 155.55/155.55 ! [V_a_2,V_r_2,V_b_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 155.55/155.55 ! [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 ).
% 155.55/155.55
% 155.55/155.55 fof(fact_measure__def,axiom,
% 155.55/155.55 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_of__int,axiom,
% 155.55/155.55 ! [V_j_2,V_i_2,T_a] :
% 155.55/155.55 ( class_Rings_Oring__1(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_One__int__def,axiom,
% 155.55/155.55 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))))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_mult,axiom,
% 155.55/155.55 ! [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))))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_le,axiom,
% 155.55/155.55 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 155.55/155.55 ( 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)))))))
% 155.55/155.55 <=> 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_minus,axiom,
% 155.55/155.55 ! [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))))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Zero__int__def,axiom,
% 155.55/155.55 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))))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_int__def,axiom,
% 155.55/155.55 ! [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))))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_add,axiom,
% 155.55/155.55 ! [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))))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_nat,axiom,
% 155.55/155.55 ! [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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_less,axiom,
% 155.55/155.55 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 155.55/155.55 ( 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)))))))
% 155.55/155.55 <=> 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_irrefl__def,axiom,
% 155.55/155.55 ! [V_r_2,T_a] :
% 155.55/155.55 ( c_Relation_Oirrefl(T_a,V_r_2)
% 155.55/155.55 <=> ! [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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_eq__Abs__Integ,axiom,
% 155.55/155.55 ! [V_z_2] :
% 155.55/155.55 ~ ! [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))))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Field__insert,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ImageE,axiom,
% 155.55/155.55 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 155.55/155.55 => ~ ! [B_x] :
% 155.55/155.55 ( 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))
% 155.55/155.55 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Field__empty,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_mono__Field,axiom,
% 155.55/155.55 ! [V_s_2,V_r_2,T_a] :
% 155.55/155.55 ( 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))
% 155.55/155.55 => 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Field__Un,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_equiv__class__nondisjoint,axiom,
% 155.55/155.55 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( 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)))))))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_subset__equiv__class,axiom,
% 155.55/155.55 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( 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))))))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_smax__emptyI,axiom,
% 155.55/155.55 ! [V_Y_2] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 155.55/155.55 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_wmax__emptyI,axiom,
% 155.55/155.55 ! [V_X_2] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__Field,axiom,
% 155.55/155.55 ! [V_r_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_equiv__intrel,axiom,
% 155.55/155.55 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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_equiv__class__self,axiom,
% 155.55/155.55 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => 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)))))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_equiv__class__eq,axiom,
% 155.55/155.55 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_equiv__class__eq__iff,axiom,
% 155.55/155.55 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( 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))
% 155.55/155.55 <=> ( 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))))
% 155.55/155.55 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_eq__equiv__class__iff,axiom,
% 155.55/155.55 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 155.55/155.55 => ( 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))))
% 155.55/155.55 <=> 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_eq__equiv__class,axiom,
% 155.55/155.55 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] :
% 155.55/155.55 ( 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))))
% 155.55/155.55 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_equiv__class__subset,axiom,
% 155.55/155.55 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)))))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__Diff,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__Int,axiom,
% 155.55/155.55 ! [V_Ga_2,V_F_2,T_a] :
% 155.55/155.55 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 155.55/155.55 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) )
% 155.55/155.55 => 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__imageI,axiom,
% 155.55/155.55 ! [V_h_2,T_b,V_F_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite_OinsertI,axiom,
% 155.55/155.55 ! [V_a_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite_OemptyI,axiom,
% 155.55/155.55 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 155.55/155.55 ! [V_A_2] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 155.55/155.55 <=> 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_infinite__UNIV__nat,axiom,
% 155.55/155.55 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__dom__body,axiom,
% 155.55/155.55 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 155.55/155.55 ! [V_A_2] :
% 155.55/155.55 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 155.55/155.55 <=> 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))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__code,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Finite__Set_Ofinite(T_a)
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Finite__Set_Ofinite(T_a)
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__range__updI,axiom,
% 155.55/155.55 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( 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)))))
% 155.55/155.55 => 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))))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite_Oequations_I1_J,axiom,
% 155.55/155.55 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__insert,axiom,
% 155.55/155.55 ! [V_A_2,V_a_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)))
% 155.55/155.55 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_rev__finite__subset,axiom,
% 155.55/155.55 ! [V_A_2,V_B_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__subset,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__fun__UNIVD2,axiom,
% 155.55/155.55 ! [T_b,T_a] :
% 155.55/155.55 ( 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))))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__Plus__UNIV__iff,axiom,
% 155.55/155.55 ! [T_b,T_a] :
% 155.55/155.55 ( 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))))
% 155.55/155.55 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 155.55/155.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__UNIV,axiom,
% 155.55/155.55 ! [T_a] :
% 155.55/155.55 ( class_Finite__Set_Ofinite(T_a)
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__Un,axiom,
% 155.55/155.55 ! [V_Ga_2,V_F_2,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 155.55/155.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__UnI,axiom,
% 155.55/155.55 ! [V_Ga_2,V_F_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2))
% 155.55/155.55 => 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))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__Diff2,axiom,
% 155.55/155.55 ! [V_A_2,V_B_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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)))
% 155.55/155.55 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__surj,axiom,
% 155.55/155.55 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( 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)))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__Diff__insert,axiom,
% 155.55/155.55 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 155.55/155.55 ( 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))))
% 155.55/155.55 <=> 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__imageD,axiom,
% 155.55/155.55 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 155.55/155.55 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__compl,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 155.55/155.55 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__Prod__UNIV,axiom,
% 155.55/155.55 ! [T_b,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 155.55/155.55 => 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)))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__range__imageI,axiom,
% 155.55/155.55 ! [V_f_2,T_c,V_g_2,T_b,T_a] :
% 155.55/155.55 ( 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)))))
% 155.55/155.55 => 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))))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__surj__inj,axiom,
% 155.55/155.55 ! [V_f_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( 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)))
% 155.55/155.55 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_endo__inj__surj,axiom,
% 155.55/155.55 ! [V_f_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
% 155.55/155.55 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__UNIV__inj__surj,axiom,
% 155.55/155.55 ! [V_f_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 155.55/155.55 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__UNIV__surj__inj,axiom,
% 155.55/155.55 ! [V_f_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__option__UNIV,axiom,
% 155.55/155.55 ! [T_a] :
% 155.55/155.55 ( 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))))
% 155.55/155.55 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__vimageD,axiom,
% 155.55/155.55 ! [V_F_2,V_h_2,T_b,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2)))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__vimageI,axiom,
% 155.55/155.55 ! [V_h_2,T_b,V_F_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 155.55/155.55 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_in__finite__psubset,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Oremove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__pointwise,axiom,
% 155.55/155.55 ! [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] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2))
% 155.55/155.55 => ( ! [B_p] :
% 155.55/155.55 ( 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))))
% 155.55/155.55 => 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)))) )
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__image__simple_Oremove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 155.55/155.55 => 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)))))) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_infinite__UNIV__int,axiom,
% 155.55/155.55 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 155.55/155.55 ! [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] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Ocommute__comp,axiom,
% 155.55/155.55 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Ocommute__left__comp,axiom,
% 155.55/155.55 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__image__simple_Oempty,axiom,
% 155.55/155.55 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 155.55/155.55 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 155.55/155.55 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 155.55/155.55 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Ocommute__comp_H,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__image__simple_Oinsert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Oinsert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Ounion__inter,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.55 => 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)))))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Oinsert__remove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding_Ounion,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__one_Oremove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 155.55/155.55 ! [V_N_2] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 155.55/155.55 <=> ? [B_m] :
% 155.55/155.55 ! [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__nat__set__iff__bounded,axiom,
% 155.55/155.55 ! [V_N_2] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 155.55/155.55 <=> ? [B_m] :
% 155.55/155.55 ! [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__image_Oreindex,axiom,
% 155.55/155.55 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.55 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__image_Odistrib,axiom,
% 155.55/155.55 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__one_Osingleton,axiom,
% 155.55/155.55 ! [V_x_2,V_F_2,V_f_2,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 155.55/155.55 => 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 ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__one_Oinsert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__one_Oinsert__remove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__one_Ounion__inter,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__one_Ounion__disjoint,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_eq__equiv__class__iff2,axiom,
% 155.55/155.55 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 155.55/155.55 => ( 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)
% 155.55/155.55 <=> 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 155.55/155.55 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 155.55/155.55 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 155.55/155.55 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 155.55/155.55 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 155.55/155.55 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 155.55/155.55 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_quotient__empty,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_quotient__is__empty2,axiom,
% 155.55/155.55 ! [V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( 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)
% 155.55/155.55 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_quotient__is__empty,axiom,
% 155.55/155.55 ! [V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( 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))
% 155.55/155.55 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_singleton__quotient,axiom,
% 155.55/155.55 ! [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))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_quotient__disj,axiom,
% 155.55/155.55 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( 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)))
% 155.55/155.55 => ( 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)))
% 155.55/155.55 => ( V_X_2 = V_Y_2
% 155.55/155.55 | 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_quotientI,axiom,
% 155.55/155.55 ! [V_r_2,V_A_2,V_x_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_quotient__eq__iff,axiom,
% 155.55/155.55 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( 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)))
% 155.55/155.55 => ( 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)))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 155.55/155.55 => ( V_X_2 = V_Y_2
% 155.55/155.55 <=> 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)) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_quotient__eqI,axiom,
% 155.55/155.55 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.55 => ( 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)))
% 155.55/155.55 => ( 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)))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_quotient__diff1,axiom,
% 155.55/155.55 ! [V_a_2,V_A_2,V_r_2,T_a] :
% 155.55/155.55 ( 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)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Integ__def,axiom,
% 155.55/155.55 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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ord_OatMost__iff,axiom,
% 155.55/155.55 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2)))
% 155.55/155.55 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ord_OatLeast__iff,axiom,
% 155.55/155.55 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2)))
% 155.55/155.55 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ord_OlessThan__iff,axiom,
% 155.55/155.55 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2)))
% 155.55/155.55 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_quotientE,axiom,
% 155.55/155.55 ! [V_r_2,V_A_2,V_X_2,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 => ~ ! [B_x] :
% 155.55/155.55 ( 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))))
% 155.55/155.55 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 155.55/155.55 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 155.55/155.55 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ord_OgreaterThan__iff,axiom,
% 155.55/155.55 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2)))
% 155.55/155.55 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__fin_Oremove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__fin_Osingleton,axiom,
% 155.55/155.55 ! [V_x_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => 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 ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_sup__Inf__absorb,axiom,
% 155.55/155.55 ! [V_a_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => 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 ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__fin_Oin__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__fin_Osubset__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__fin_Ounion__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__fin_Oinsert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => 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 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__fin_Ounion__inter,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__fin_Oclosed,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( ! [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))))))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Sup__fin_Oremove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max_Oremove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min_Oremove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_minus__Min__eq__Max,axiom,
% 155.55/155.55 ! [V_S_2,T_a] :
% 155.55/155.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.55 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_minus__Max__eq__Min,axiom,
% 155.55/155.55 ! [V_S_2,T_a] :
% 155.55/155.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.55 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min_Osingleton,axiom,
% 155.55/155.55 ! [V_x_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => 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 ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max_Osingleton,axiom,
% 155.55/155.55 ! [V_x_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => 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 ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Sup__fin_Osingleton,axiom,
% 155.55/155.55 ! [V_x_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => 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 ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min__le,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max__ge,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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))) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max__in,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min__in,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Sup__fin_Oin__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_inf__Sup__absorb,axiom,
% 155.55/155.55 ! [V_a_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => 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 ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min_Oin__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max_Oin__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min__antimono,axiom,
% 155.55/155.55 ! [V_N_2,V_M_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 155.55/155.55 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.55 => 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))) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max__mono,axiom,
% 155.55/155.55 ! [V_N_2,V_M_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 155.55/155.55 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.55 => 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))) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min__insert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max__insert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Sup__fin_Osubset__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min_Osubset__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Sup__fin_Ounion__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max_Osubset__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min__Un,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max__Un,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Inf__le__Sup,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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))) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Sup__fin_Oinsert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min_Oinsert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max_Oinsert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => 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 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min_Oinsert__remove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Sup__fin_Ounion__inter,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max_Oinsert__remove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min_Ounion__disjoint,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min_Ounion__inter,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max_Ounion__disjoint,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max_Ounion__inter,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Max_Oclosed,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( ! [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))))))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Min_Oclosed,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( ! [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))))))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Sup__fin_Oclosed,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Lattices_Olattice(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( ! [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))))))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__idem_Ounion__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__idem_Oidem__comp,axiom,
% 155.55/155.55 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 155.55/155.55 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__idem_Oinsert__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_equivp__equiv,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2)
% 155.55/155.55 <=> 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_folding__one_Oclosed,axiom,
% 155.55/155.55 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.55 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( ! [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))))))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_identity__equivp,axiom,
% 155.55/155.55 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_equivp__def,axiom,
% 155.55/155.55 ! [V_R_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 155.55/155.55 <=> ! [B_x,B_y] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 155.55/155.55 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_equivp__reflp,axiom,
% 155.55/155.55 ! [V_x_2,V_R_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 155.55/155.55 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_equivp__symp,axiom,
% 155.55/155.55 ! [V_y_2,V_x_2,V_R_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 155.55/155.55 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_equivp__transp,axiom,
% 155.55/155.55 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] :
% 155.55/155.55 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 155.55/155.55 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__le__Sup,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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))) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 155.55/155.55 ! [V_x_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => 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 ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 155.55/155.55 ! [V_x_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => 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 ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 155.55/155.55 ! [V_a_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => 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 ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 155.55/155.55 ! [V_a_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => 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 ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => 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 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ( 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))
% 155.55/155.55 => 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 )
% 155.55/155.55 & ( 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))
% 155.55/155.55 => 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)))))) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( ! [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))))))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => ( ! [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))))))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Diff__singleton,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Diff__singleton__if,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__UNIV__unit,axiom,
% 155.55/155.55 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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 155.55/155.55 ! [V_A_2] :
% 155.55/155.55 ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card_Oempty,axiom,
% 155.55/155.55 ! [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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__infinite,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 155.55/155.55 => ( 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)))
% 155.55/155.55 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__image,axiom,
% 155.55/155.55 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__eq__0__iff,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.55 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__ge__0__finite,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__insert__le,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__seteq,axiom,
% 155.55/155.55 ! [V_A_2,V_B_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.55 => ( 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)))
% 155.55/155.55 => V_A_2 = V_B_2 ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__mono,axiom,
% 155.55/155.55 ! [V_A_2,V_B_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.55 => 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))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__image__le,axiom,
% 155.55/155.55 ! [V_f_2,T_b,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_eq__card__imp__inj__on,axiom,
% 155.55/155.55 ! [V_f_2,T_b,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( 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)
% 155.55/155.55 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_inj__on__iff__eq__card,axiom,
% 155.55/155.55 ! [V_f_2,T_b,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.55 <=> 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) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_pigeonhole,axiom,
% 155.55/155.55 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__quotient__disjoint,axiom,
% 155.55/155.55 ! [V_r_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( 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)
% 155.55/155.55 => 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) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_psubset__card__mono,axiom,
% 155.55/155.55 ! [V_A_2,V_B_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.55 => 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))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__insert__if,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__insert__disjoint,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__gt__0__iff,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__UNIV__card__ge__0,axiom,
% 155.55/155.55 ! [T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 155.55/155.55 => 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))))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Un__Int,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => 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))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card_Ounion__inter,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__bij__eq,axiom,
% 155.55/155.55 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.55 => ( 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))
% 155.55/155.55 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
% 155.55/155.55 => ( 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))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 155.55/155.55 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Diff__subset,axiom,
% 155.55/155.55 ! [V_A_2,V_B_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Diff__subset__Int,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 => 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_diff__card__le__card__Diff,axiom,
% 155.55/155.55 ! [V_A_2,V_B_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => 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)))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__UNIV__bool,axiom,
% 155.55/155.55 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))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__psubset,axiom,
% 155.55/155.55 ! [V_A_2,V_B_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.55 => ( 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)))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__insert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)))))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Un__disjoint,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Diff1__le,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card_Oinsert,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__inj__on__le,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.55 => ( 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))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 155.55/155.55 => 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))) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_inj__on__iff__card__le,axiom,
% 155.55/155.55 ! [V_B_2,T_b,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 155.55/155.55 => ( ? [B_f] :
% 155.55/155.55 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 155.55/155.55 & 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)) )
% 155.55/155.55 <=> 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))) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Suc__Diff1,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Diff1__less,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Diff2__less,axiom,
% 155.55/155.55 ! [V_y_2,V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 155.55/155.55 => 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))) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Diff__insert,axiom,
% 155.55/155.55 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card_Oinsert__remove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)))))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__fun__UNIVD1,axiom,
% 155.55/155.55 ! [T_b,T_a] :
% 155.55/155.55 ( 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))))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card_Oremove,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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)))))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card_Ounion__inter__neutral,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( ( ? [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)))
% 155.55/155.55 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Suc__eq,axiom,
% 155.55/155.55 ! [V_k_2,V_A_2,T_a] :
% 155.55/155.55 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 155.55/155.55 <=> ? [B_b,B_B] :
% 155.55/155.55 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B)
% 155.55/155.55 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B))
% 155.55/155.55 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2
% 155.55/155.55 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.55 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Plus__conv__if,axiom,
% 155.55/155.55 ! [V_B_2,T_b,V_A_2,T_a] :
% 155.55/155.55 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 155.55/155.55 => 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) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Plus__eq__empty__conv,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.55 ( 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))
% 155.55/155.55 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__Plus__iff,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__Plus,axiom,
% 155.55/155.55 ! [V_B_2,T_b,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 155.55/155.55 => 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))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__PlusD_I1_J,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__PlusD_I2_J,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UNIV__Plus__UNIV,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Plus,axiom,
% 155.55/155.55 ! [V_B_2,T_b,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__Pow,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__greaterThanLessThan__int,axiom,
% 155.55/155.55 ! [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)))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__gen__delta,axiom,
% 155.55/155.55 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.55 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 155.55/155.55 => 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)))) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__greaterThanLessThan__int,axiom,
% 155.55/155.55 ! [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))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_PowI,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Pow__UNIV,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Pow__insert,axiom,
% 155.55/155.55 ! [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))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Pow__top,axiom,
% 155.55/155.55 ! [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))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_int__setprod,axiom,
% 155.55/155.55 ! [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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_of__nat__setprod,axiom,
% 155.55/155.55 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 155.55/155.55 & class_Rings_Osemiring__1(T_a) )
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_of__int__setprod,axiom,
% 155.55/155.55 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 155.55/155.55 & class_Rings_Oring__1(T_a) )
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Pow__Int__eq,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_abs__setprod,axiom,
% 155.55/155.55 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__timesf,axiom,
% 155.55/155.55 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__1,axiom,
% 155.55/155.55 ! [V_A_2,T_b,T_a] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 155.55/155.55 ! [V_A_2,V_f_2,T_a] :
% 155.55/155.55 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.55 & class_Groups_Ocomm__monoid__mult(T_a) )
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_image__Pow__surj,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 155.55/155.55 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Cantors__paradox,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ~ ? [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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__Pow__iff,axiom,
% 155.55/155.55 ! [V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)))
% 155.55/155.55 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Pow__not__empty,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__zero,axiom,
% 155.55/155.55 ! [V_f_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Rings_Ocomm__semiring__1(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ? [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.55 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__zero__iff,axiom,
% 155.55/155.55 ! [V_f_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( ( class_Rings_Ocomm__semiring__1(T_b)
% 155.55/155.55 & class_Rings_Ono__zero__divisors(T_b) )
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( 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)
% 155.55/155.55 <=> ? [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.55 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__empty,axiom,
% 155.55/155.55 ! [V_f_2,T_b,T_a] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod_Oempty,axiom,
% 155.55/155.55 ! [V_g_2,T_b,T_a] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod_Oinfinite,axiom,
% 155.55/155.55 ! [V_g_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__infinite,axiom,
% 155.55/155.55 ! [V_f_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__eq__1__iff,axiom,
% 155.55/155.55 ! [V_f_2,V_F_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 155.55/155.55 => ( 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)
% 155.55/155.55 <=> ! [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2))
% 155.55/155.55 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 155.55/155.55 ! [V_f_2,V_A_2,T_a] :
% 155.55/155.55 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.55 & class_Groups_Ocomm__monoid__mult(T_a) )
% 155.55/155.55 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod_Odistrib,axiom,
% 155.55/155.55 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Pow__bottom,axiom,
% 155.55/155.55 ! [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))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Pow__iff,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 155.55/155.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_PowD,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__pos__nat__iff,axiom,
% 155.55/155.55 ! [V_f_2,V_S_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.55 => ( 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)))
% 155.55/155.55 <=> ! [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 155.55/155.55 => 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))) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__reindex,axiom,
% 155.55/155.55 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_c)
% 155.55/155.55 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 155.55/155.55 => 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) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__reindex__cong,axiom,
% 155.55/155.55 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_c)
% 155.55/155.55 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.55 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 155.55/155.55 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)
% 155.55/155.55 => 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) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_greaterThanLessThan__empty,axiom,
% 155.55/155.55 ! [V_k_2,V_l_2,T_a] :
% 155.55/155.55 ( class_Orderings_Oorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Pow__mono,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.55 => 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Un__Pow__subset,axiom,
% 155.55/155.55 ! [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)))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 155.55/155.55 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__delta_H,axiom,
% 155.55/155.55 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.55 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 155.55/155.55 => 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) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 155.55/155.55 => 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) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__delta,axiom,
% 155.55/155.55 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.55 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 155.55/155.55 => 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) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 155.55/155.55 => 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) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__constant,axiom,
% 155.55/155.55 ! [V_y_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod_Oinsert,axiom,
% 155.55/155.55 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__insert,axiom,
% 155.55/155.55 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__Un__Int,axiom,
% 155.55/155.55 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod_Ounion__inter,axiom,
% 155.55/155.55 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod_Oreindex,axiom,
% 155.55/155.55 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_image__Pow__mono,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.55 ( 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))
% 155.55/155.55 => 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Pow__empty,axiom,
% 155.55/155.55 ! [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))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Int__greaterThanLessThan,axiom,
% 155.55/155.55 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod_Oinsert__remove,axiom,
% 155.55/155.55 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)))))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod_Ounion__disjoint,axiom,
% 155.55/155.55 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__Un__disjoint,axiom,
% 155.55/155.55 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( 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))
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Powp__Pow__eq,axiom,
% 155.55/155.55 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.55 ( 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))
% 155.55/155.55 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod_Oremove,axiom,
% 155.55/155.55 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.55 => 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)))))) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 155.55/155.55 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.55 => ( ! [B_x] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__Un__one,axiom,
% 155.55/155.55 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 155.55/155.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 155.55/155.55 => ( ! [B_x] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 155.55/155.55 => 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)) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ivl__disj__un_I4_J,axiom,
% 155.55/155.55 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 155.55/155.55 => 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) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__greaterThanAtMost,axiom,
% 155.55/155.55 ! [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))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__greaterThanLessThan,axiom,
% 155.55/155.55 ! [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))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__greaterThanAtMost__int,axiom,
% 155.55/155.55 ! [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))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_greaterThanAtMost__empty,axiom,
% 155.55/155.55 ! [V_k_2,V_l_2,T_a] :
% 155.55/155.55 ( class_Orderings_Oorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 155.55/155.55 ! [V_l_2,V_k_2,T_a] :
% 155.55/155.55 ( class_Orderings_Oorder(T_a)
% 155.55/155.55 => ( 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))
% 155.55/155.55 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 155.55/155.55 ! [V_l_2,V_k_2,T_a] :
% 155.55/155.55 ( class_Orderings_Oorder(T_a)
% 155.55/155.55 => ( 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)
% 155.55/155.55 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ivl__disj__un_I20_J,axiom,
% 155.55/155.55 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ivl__disj__int_I14_J,axiom,
% 155.55/155.55 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.55 ( class_Orderings_Oorder(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__greaterThanAtMost,axiom,
% 155.55/155.55 ! [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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Int__greaterThanAtMost,axiom,
% 155.55/155.55 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ivl__disj__int_I10_J,axiom,
% 155.55/155.55 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.55 ( class_Orderings_Oorder(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__greaterThanLessThan,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_card__greaterThanAtMost__int,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ivl__disj__un_I16_J,axiom,
% 155.55/155.55 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.55 ( class_Orderings_Olinorder(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 155.55/155.55 => 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) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 155.55/155.55 ! [V_f_2,V_A_2,T_a] :
% 155.55/155.55 ( ! [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.55 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__diff1,axiom,
% 155.55/155.55 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Fields_Ofield(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b)
% 155.55/155.55 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => 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) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_quotient__def,axiom,
% 155.55/155.55 ! [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)))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_SUP1__I,axiom,
% 155.55/155.55 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_finite__UN,axiom,
% 155.55/155.55 ! [V_B_2,T_b,V_A_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => ( 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)))
% 155.55/155.55 <=> ! [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__o,axiom,
% 155.55/155.55 ! [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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_diff__divide__distrib,axiom,
% 155.55/155.55 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__1,axiom,
% 155.55/155.55 ! [V_a,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_SUP1__iff,axiom,
% 155.55/155.55 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.55 ( 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))
% 155.55/155.55 <=> ? [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.55 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_times__divide__eq__right,axiom,
% 155.55/155.55 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_add__divide__distrib,axiom,
% 155.55/155.55 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__zero,axiom,
% 155.55/155.55 ! [V_a,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__zero__left,axiom,
% 155.55/155.55 ! [V_a,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_power__divide,axiom,
% 155.55/155.55 ! [V_n,V_b,V_a,T_a] :
% 155.55/155.55 ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_minus__divide__left,axiom,
% 155.55/155.55 ! [V_b,V_a,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Image__UN,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_nonzero__eq__divide__eq,axiom,
% 155.55/155.55 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)
% 155.55/155.55 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_nonzero__divide__eq__eq,axiom,
% 155.55/155.55 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2
% 155.55/155.55 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__eq__imp,axiom,
% 155.55/155.55 ! [V_a,V_b,V_c,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 155.55/155.55 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_eq__divide__imp,axiom,
% 155.55/155.55 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 155.55/155.55 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__self__if,axiom,
% 155.55/155.55 ! [V_a,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 155.55/155.55 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 155.55/155.55 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__self,axiom,
% 155.55/155.55 ! [V_a,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_right__inverse__eq,axiom,
% 155.55/155.55 ! [V_a_2,V_b_2,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 155.55/155.55 <=> V_a_2 = V_b_2 ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_nonzero__minus__divide__right,axiom,
% 155.55/155.55 ! [V_a,V_b,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_nonzero__minus__divide__divide,axiom,
% 155.55/155.55 ! [V_a,V_b,T_a] :
% 155.55/155.55 ( class_Rings_Odivision__ring(T_a)
% 155.55/155.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => 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) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_nonzero__power__divide,axiom,
% 155.55/155.55 ! [V_n,V_a,V_b,T_a] :
% 155.55/155.55 ( class_Fields_Ofield(T_a)
% 155.55/155.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_power__one__over,axiom,
% 155.55/155.55 ! [V_n,V_a,T_a] :
% 155.55/155.55 ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_SUP__UN__eq,axiom,
% 155.55/155.55 ! [V_x_2,V_r_2,T_b,T_a] :
% 155.55/155.55 ( 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))
% 155.55/155.55 <=> 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_setprod__dividef,axiom,
% 155.55/155.55 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( class_Fields_Ofield__inverse__zero(T_b)
% 155.55/155.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__eq__eq__number__of1,axiom,
% 155.55/155.55 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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
% 155.55/155.55 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__eq__eq__number__of,axiom,
% 155.55/155.55 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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)
% 155.55/155.55 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => 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) )
% 155.55/155.55 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_eq__divide__eq__number__of,axiom,
% 155.55/155.55 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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)
% 155.55/155.55 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => 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 )
% 155.55/155.55 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_eq__divide__eq__number__of1,axiom,
% 155.55/155.55 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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))
% 155.55/155.55 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => 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 )
% 155.55/155.55 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__Numeral0,axiom,
% 155.55/155.55 ! [V_x,T_a] :
% 155.55/155.55 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber__ring(T_a) )
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__Numeral1,axiom,
% 155.55/155.55 ! [V_x,T_a] :
% 155.55/155.55 ( ( class_Fields_Ofield(T_a)
% 155.55/155.55 & class_Int_Onumber__ring(T_a) )
% 155.55/155.55 => 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 ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__numeral__1,axiom,
% 155.55/155.55 ! [V_a,T_a] :
% 155.55/155.55 ( ( class_Fields_Ofield(T_a)
% 155.55/155.55 & class_Int_Onumber__ring(T_a) )
% 155.55/155.55 => 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 ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__minus1,axiom,
% 155.55/155.55 ! [V_x,T_a] :
% 155.55/155.55 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber__ring(T_a) )
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Image__eq__UN,axiom,
% 155.55/155.55 ! [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))))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_less__divide__eq__number__of1,axiom,
% 155.55/155.55 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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))))
% 155.55/155.55 <=> ( ( 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)))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ 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)))
% 155.55/155.55 => ( ( 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)))
% 155.55/155.55 => 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)))) )
% 155.55/155.55 & ( ~ 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)))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_less__divide__eq__number__of,axiom,
% 155.55/155.55 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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)))
% 155.55/155.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.55 => 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))) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.55 => 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))) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__less__eq__number__of,axiom,
% 155.55/155.55 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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)))
% 155.55/155.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.55 => 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))) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.55 => 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))) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__less__eq__number__of1,axiom,
% 155.55/155.55 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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))
% 155.55/155.55 <=> ( ( 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)))
% 155.55/155.55 => 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)))) )
% 155.55/155.55 & ( ~ 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)))
% 155.55/155.55 => ( ( 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)))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ 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)))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_power__diff,axiom,
% 155.55/155.55 ! [V_m,V_n,V_a,T_a] :
% 155.55/155.55 ( class_Fields_Ofield(T_a)
% 155.55/155.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 155.55/155.55 => 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)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_minus1__divide,axiom,
% 155.55/155.55 ! [V_x,T_a] :
% 155.55/155.55 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber__ring(T_a) )
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_le__divide__eq__number__of1,axiom,
% 155.55/155.55 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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))))
% 155.55/155.55 <=> ( ( 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)))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ 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)))
% 155.55/155.55 => ( ( 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)))
% 155.55/155.55 => 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)))) )
% 155.55/155.55 & ( ~ 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)))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_le__divide__eq__number__of,axiom,
% 155.55/155.55 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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)))
% 155.55/155.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.55 => 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))) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.55 => 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))) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__le__eq__number__of,axiom,
% 155.55/155.55 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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)))
% 155.55/155.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.55 => 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))) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.55 => 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))) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_divide__le__eq__number__of1,axiom,
% 155.55/155.55 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber(T_a) )
% 155.55/155.55 => ( 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))
% 155.55/155.55 <=> ( ( 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)))
% 155.55/155.55 => 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)))) )
% 155.55/155.55 & ( ~ 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)))
% 155.55/155.55 => ( ( 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)))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ 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)))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_half__gt__zero__iff,axiom,
% 155.55/155.55 ! [V_r_2,T_a] :
% 155.55/155.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber__ring(T_a) )
% 155.55/155.55 => ( 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))))))
% 155.55/155.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_half__gt__zero,axiom,
% 155.55/155.55 ! [V_r,T_a] :
% 155.55/155.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 & class_Int_Onumber__ring(T_a) )
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 155.55/155.55 => 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)))))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__I,axiom,
% 155.55/155.55 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 155.55/155.55 => 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))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__Pow__subset,axiom,
% 155.55/155.55 ! [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)))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_le__divide__eq,axiom,
% 155.55/155.55 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.55 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 => ( 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)))
% 155.55/155.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.55 => 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))) )
% 155.55/155.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_ball__UN,axiom,
% 155.55/155.55 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.55 ( ! [B_x] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.55 <=> ! [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.55/155.55 => ! [B_xa] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x)))
% 155.55/155.55 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_SUP__commute,axiom,
% 155.55/155.55 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 155.55/155.55 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.55 => 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))) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__UN__flatten,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__simps_I9_J,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__extend__simps_I9_J,axiom,
% 155.55/155.55 ! [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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_times__divide__times__eq,axiom,
% 155.55/155.55 ! [V_w,V_z,V_y,V_x,T_a] :
% 155.55/155.55 ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_minus__divide__divide,axiom,
% 155.55/155.55 ! [V_b,V_a,T_a] :
% 155.55/155.55 ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 => 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) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_minus__divide__right,axiom,
% 155.55/155.55 ! [V_b,V_a,T_a] :
% 155.55/155.55 ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_abs__divide,axiom,
% 155.55/155.55 ! [V_b,V_a,T_a] :
% 155.55/155.55 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_SUP__le__iff,axiom,
% 155.55/155.55 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] :
% 155.55/155.55 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.55 => ( 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))
% 155.55/155.55 <=> ! [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.55/155.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_less__SUP__iff,axiom,
% 155.55/155.55 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] :
% 155.55/155.55 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.55 & class_Orderings_Olinorder(T_a) )
% 155.55/155.55 => ( 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)))
% 155.55/155.55 <=> ? [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.55/155.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__iff,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 155.55/155.55 ( 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)))
% 155.55/155.55 <=> ? [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.55/155.55 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_SUP__const,axiom,
% 155.55/155.55 ! [V_M_2,T_a,V_A_2,T_b] :
% 155.55/155.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 155.55/155.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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 ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UNION__empty__conv_I1_J,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.55 ( 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)
% 155.55/155.55 <=> ! [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.55/155.55 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__empty2,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__constant,axiom,
% 155.55/155.55 ! [V_ca_2,T_b,T_a,V_A_2] :
% 155.55/155.55 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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)) )
% 155.55/155.55 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.55 => 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 ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UNION__empty__conv_I2_J,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.55 ( 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))
% 155.55/155.55 <=> ! [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.55/155.55 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__subset__iff,axiom,
% 155.55/155.55 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] :
% 155.55/155.55 ( 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))
% 155.55/155.55 <=> ! [B_x] :
% 155.55/155.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 155.55/155.55 => 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)) ) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__simps_I10_J,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_image__UN,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__extend__simps_I10_J,axiom,
% 155.55/155.55 ! [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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__Un,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__Un__distrib,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__simps_I5_J,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__simps_I4_J,axiom,
% 155.55/155.55 ! [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) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__extend__simps_I5_J,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Int__UN__distrib,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__extend__simps_I4_J,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_Int__UN__distrib2,axiom,
% 155.55/155.55 ! [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))) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_SUPR__apply,axiom,
% 155.55/155.55 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 155.55/155.55 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.55/155.55 => 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)) ) ).
% 155.55/155.55
% 155.55/155.55 fof(fact_UN__extend__simps_I6_J,axiom,
% 155.55/155.55 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__simps_I6_J,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_vimage__UN,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__right__mono__neg,axiom,
% 155.55/155.56 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__right__mono,axiom,
% 155.55/155.56 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__le__0__iff,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 155.55/155.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_zero__le__divide__iff,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 155.55/155.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_zero__less__divide__iff,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 155.55/155.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__less__0__iff,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 155.55/155.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__pos__pos,axiom,
% 155.55/155.56 ! [V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__pos__neg,axiom,
% 155.55/155.56 ! [V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__neg__pos,axiom,
% 155.55/155.56 ! [V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__neg__neg,axiom,
% 155.55/155.56 ! [V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__strict__right__mono,axiom,
% 155.55/155.56 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__strict__right__mono__neg,axiom,
% 155.55/155.56 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_eq__divide__eq,axiom,
% 155.55/155.56 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.56 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)
% 155.55/155.56 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 )
% 155.55/155.56 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__eq__eq,axiom,
% 155.55/155.56 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 155.55/155.56 ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.56 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2
% 155.55/155.56 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) )
% 155.55/155.56 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_mult__divide__mult__cancel__right,axiom,
% 155.55/155.56 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.56 ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.56 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_mult__divide__mult__cancel__left,axiom,
% 155.55/155.56 ! [V_b,V_a,V_c,T_a] :
% 155.55/155.56 ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.56 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_frac__eq__eq,axiom,
% 155.55/155.56 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] :
% 155.55/155.56 ( class_Fields_Ofield(T_a)
% 155.55/155.56 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => ( 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)
% 155.55/155.56 <=> 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SUP__subset,axiom,
% 155.55/155.56 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_nonzero__abs__divide,axiom,
% 155.55/155.56 ! [V_a,V_b,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_le__SUPI,axiom,
% 155.55/155.56 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 155.55/155.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__insert__distrib,axiom,
% 155.55/155.56 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__upper,axiom,
% 155.55/155.56 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__absorb,axiom,
% 155.55/155.56 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__simps_I1_J,axiom,
% 155.55/155.56 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 155.55/155.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__singleton,axiom,
% 155.55/155.56 ! [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 ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__extend__simps_I1_J,axiom,
% 155.55/155.56 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 155.55/155.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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))) )
% 155.55/155.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__extend__simps_I2_J,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.55/155.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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 )
% 155.55/155.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__extend__simps_I3_J,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.55/155.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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 )
% 155.55/155.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__simps_I2_J,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.55/155.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__simps_I3_J,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.55/155.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__insert,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__nonpos__neg,axiom,
% 155.55/155.56 ! [V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__nonpos__pos,axiom,
% 155.55/155.56 ! [V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_frac__le,axiom,
% 155.55/155.56 ! [V_z,V_w,V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 155.55/155.56 => 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))) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_frac__less,axiom,
% 155.55/155.56 ! [V_z,V_w,V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 155.55/155.56 => 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))) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_frac__less2,axiom,
% 155.55/155.56 ! [V_z,V_w,V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 155.55/155.56 => 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))) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__nonneg__neg,axiom,
% 155.55/155.56 ! [V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__nonneg__pos,axiom,
% 155.55/155.56 ! [V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__strict__left__mono__neg,axiom,
% 155.55/155.56 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => 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))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__strict__left__mono,axiom,
% 155.55/155.56 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => 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))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_neg__divide__less__eq,axiom,
% 155.55/155.56 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => ( 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))
% 155.55/155.56 <=> 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_neg__less__divide__eq,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_mult__imp__less__div__pos,axiom,
% 155.55/155.56 ! [V_x,V_z,V_y,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.56 => ( 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))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_mult__imp__div__pos__less,axiom,
% 155.55/155.56 ! [V_z,V_x,V_y,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_pos__divide__less__eq,axiom,
% 155.55/155.56 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.56 => ( 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))
% 155.55/155.56 <=> 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_pos__less__divide__eq,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__less__eq,axiom,
% 155.55/155.56 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( 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))
% 155.55/155.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.56 => 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))) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_less__divide__eq,axiom,
% 155.55/155.56 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => 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))) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_add__num__frac,axiom,
% 155.55/155.56 ! [V_x,V_z,V_y,T_a] :
% 155.55/155.56 ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.56 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_add__divide__eq__iff,axiom,
% 155.55/155.56 ! [V_y,V_x,V_z,T_a] :
% 155.55/155.56 ( class_Fields_Ofield(T_a)
% 155.55/155.56 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_add__frac__num,axiom,
% 155.55/155.56 ! [V_z,V_x,V_y,T_a] :
% 155.55/155.56 ( class_Fields_Ofield__inverse__zero(T_a)
% 155.55/155.56 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__add__eq__iff,axiom,
% 155.55/155.56 ! [V_y,V_x,V_z,T_a] :
% 155.55/155.56 ( class_Fields_Ofield(T_a)
% 155.55/155.56 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_add__frac__eq,axiom,
% 155.55/155.56 ! [V_w,V_x,V_z,V_y,T_a] :
% 155.55/155.56 ( class_Fields_Ofield(T_a)
% 155.55/155.56 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_diff__frac__eq,axiom,
% 155.55/155.56 ! [V_w,V_x,V_z,V_y,T_a] :
% 155.55/155.56 ( class_Fields_Ofield(T_a)
% 155.55/155.56 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__diff__eq__iff,axiom,
% 155.55/155.56 ! [V_y,V_x,V_z,T_a] :
% 155.55/155.56 ( class_Fields_Ofield(T_a)
% 155.55/155.56 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_diff__divide__eq__iff,axiom,
% 155.55/155.56 ! [V_y,V_x,V_z,T_a] :
% 155.55/155.56 ( class_Fields_Ofield(T_a)
% 155.55/155.56 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_gt__half__sum,axiom,
% 155.55/155.56 ! [V_b,V_a,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_less__half__sum,axiom,
% 155.55/155.56 ! [V_b,V_a,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 155.55/155.56 => 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))))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_abs__div__pos,axiom,
% 155.55/155.56 ! [V_x,V_y,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__eq__UN,axiom,
% 155.55/155.56 ! [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)))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_vimage__eq__UN,axiom,
% 155.55/155.56 ! [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))))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__left__mono__neg,axiom,
% 155.55/155.56 ! [V_c,V_b,V_a,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => 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))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__left__mono,axiom,
% 155.55/155.56 ! [V_c,V_a,V_b,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => 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))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_neg__divide__le__eq,axiom,
% 155.55/155.56 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => ( 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))
% 155.55/155.56 <=> 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_neg__le__divide__eq,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_mult__imp__le__div__pos,axiom,
% 155.55/155.56 ! [V_x,V_z,V_y,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.56 => ( 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))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_mult__imp__div__pos__le,axiom,
% 155.55/155.56 ! [V_z,V_x,V_y,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_pos__divide__le__eq,axiom,
% 155.55/155.56 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.56 => ( 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))
% 155.55/155.56 <=> 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_pos__le__divide__eq,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_divide__le__eq,axiom,
% 155.55/155.56 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( 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))
% 155.55/155.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.56 => 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))) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 155.55/155.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_minus__int__def,axiom,
% 155.55/155.56 ! [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))))))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__equiv__class2,axiom,
% 155.55/155.56 ! [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] :
% 155.55/155.56 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 155.55/155.56 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 155.55/155.56 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2))
% 155.55/155.56 => 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) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__equiv__class,axiom,
% 155.55/155.56 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.56 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SUP2__I,axiom,
% 155.55/155.56 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Rep__Integ__inject,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2] :
% 155.55/155.56 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 155.55/155.56 <=> V_x_2 = V_y_2 ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Rep__Integ__inverse,axiom,
% 155.55/155.56 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 155.55/155.56
% 155.55/155.56 fof(fact_congruent2__implies__congruent,axiom,
% 155.55/155.56 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2)
% 155.55/155.56 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Rep__Integ,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SUP__UN__eq2,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 155.55/155.56 ( 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))
% 155.55/155.56 <=> 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_congruent__def,axiom,
% 155.55/155.56 ! [V_f_2,V_r_2,T_b,T_a] :
% 155.55/155.56 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 155.55/155.56 <=> ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_congruent2D,axiom,
% 155.55/155.56 ! [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] :
% 155.55/155.56 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 155.55/155.56 => ( 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))
% 155.55/155.56 => ( 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))
% 155.55/155.56 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_congruentD,axiom,
% 155.55/155.56 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] :
% 155.55/155.56 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 155.55/155.56 => ( 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))
% 155.55/155.56 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_congruent2__implies__congruent__UN,axiom,
% 155.55/155.56 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
% 155.55/155.56 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 155.55/155.56 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 155.55/155.56 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_nat__def,axiom,
% 155.55/155.56 ! [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)))))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__equiv__class__inject,axiom,
% 155.55/155.56 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.56 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 155.55/155.56 => ( 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)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.56 => ! [B_y] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 155.55/155.56 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 155.55/155.56 => 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)) ) ) )
% 155.55/155.56 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__equiv__class__type2,axiom,
% 155.55/155.56 ! [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] :
% 155.55/155.56 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 155.55/155.56 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 155.55/155.56 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => ( ! [B_x1] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2))
% 155.55/155.56 => ! [B_x2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 155.55/155.56 => 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)) ) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__equiv__class__type,axiom,
% 155.55/155.56 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.56 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SUP2__iff,axiom,
% 155.55/155.56 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 155.55/155.56 ( 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))
% 155.55/155.56 <=> ? [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.56 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setprod__Un,axiom,
% 155.55/155.56 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Fields_Ofield(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) )
% 155.55/155.56 => 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))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Id__on__def,axiom,
% 155.55/155.56 ! [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)))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_refl__on__def_H,axiom,
% 155.55/155.56 ! [V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 155.55/155.56 <=> ( ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_refl__on__Id__on,axiom,
% 155.55/155.56 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Id__on__def_H,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_refl__on__empty,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_refl__on__Un,axiom,
% 155.55/155.56 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 155.55/155.56 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_refl__on__Int,axiom,
% 155.55/155.56 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 155.55/155.56 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Id__on__empty,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Image__Id__on,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_refl__onD2,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 155.55/155.56 => ( 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))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_refl__onD1,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 155.55/155.56 => ( 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))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_refl__onD,axiom,
% 155.55/155.56 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Id__on__eqI,axiom,
% 155.55/155.56 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 155.55/155.56 ( V_a_2 = V_b_2
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Id__on__iff,axiom,
% 155.55/155.56 ! [V_A_2,V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 <=> ( V_x_2 = V_y_2
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Id__onE,axiom,
% 155.55/155.56 ! [V_A_2,V_ca_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2)))
% 155.55/155.56 => ~ ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.56 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_type__definition__Integ,axiom,
% 155.55/155.56 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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__Un__disjoint,axiom,
% 155.55/155.56 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => ( 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))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__image__empty,axiom,
% 155.55/155.56 ! [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 ).
% 155.55/155.56
% 155.55/155.56 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 155.55/155.56 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_folding__image_Oeq__fold,axiom,
% 155.55/155.56 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__image__distrib,axiom,
% 155.55/155.56 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__image__insert,axiom,
% 155.55/155.56 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Oab__semigroup__mult(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setprod_OF__eq,axiom,
% 155.55/155.56 ! [V_g_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.56 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setprod_Oeq__fold,axiom,
% 155.55/155.56 ! [V_g_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__image__Un__Int,axiom,
% 155.55/155.56 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__image__reindex,axiom,
% 155.55/155.56 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] :
% 155.55/155.56 ( class_Groups_Oab__semigroup__mult(T_c)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2)
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__eq__fold__image,axiom,
% 155.55/155.56 ! [V_f_2,T_b,V_A_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card__def,axiom,
% 155.55/155.56 ! [V_A_2,T_a] :
% 155.55/155.56 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card_Oeq__fold__g,axiom,
% 155.55/155.56 ! [V_A_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_type__definition_OAbs__image,axiom,
% 155.55/155.56 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 155.55/155.56 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_type__definition_ORep__range,axiom,
% 155.55/155.56 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 155.55/155.56 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 155.55/155.56 => 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 ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_comm__monoid__big_OF__eq,axiom,
% 155.55/155.56 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 155.55/155.56 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.56 => 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) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.56 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_type__definition_ORep__inverse,axiom,
% 155.55/155.56 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 155.55/155.56 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 155.55/155.56 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_type__definition_ORep__inject,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 155.55/155.56 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 155.55/155.56 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 155.55/155.56 <=> V_x_2 = V_y_2 ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 155.55/155.56 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 155.55/155.56 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.56 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_type__definition_OAbs__inject,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 155.55/155.56 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 155.55/155.56 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 155.55/155.56 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_type__definition_OAbs__inverse,axiom,
% 155.55/155.56 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 155.55/155.56 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 155.55/155.56 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_type__definition_ORep,axiom,
% 155.55/155.56 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 155.55/155.56 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__image__Un__one,axiom,
% 155.55/155.56 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 155.55/155.56 ! [V_N_2,V_h_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( ! [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))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 155.55/155.56 ! [V_N_2,V_h_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( ! [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))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Max_Ohom__commute,axiom,
% 155.55/155.56 ! [V_N_2,V_h_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( ! [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))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Min_Ohom__commute,axiom,
% 155.55/155.56 ! [V_N_2,V_h_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( ! [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))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Inf__fin_Ohom__commute,axiom,
% 155.55/155.56 ! [V_N_2,V_h_2,T_a] :
% 155.55/155.56 ( class_Lattices_Olattice(T_a)
% 155.55/155.56 => ( ! [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))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Sup__fin_Ohom__commute,axiom,
% 155.55/155.56 ! [V_N_2,V_h_2,T_a] :
% 155.55/155.56 ( class_Lattices_Olattice(T_a)
% 155.55/155.56 => ( ! [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))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_strong__setprod__reindex__cong,axiom,
% 155.55/155.56 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__mult(T_c)
% 155.55/155.56 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.56 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.56 => 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) )
% 155.55/155.56 => 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setprod__mono__one__right,axiom,
% 155.55/155.56 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 155.55/155.56 => 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setprod__mono__one__left,axiom,
% 155.55/155.56 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 155.55/155.56 => 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__empty__induct,axiom,
% 155.55/155.56 ! [V_P_2,V_A_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 155.55/155.56 => ( ! [B_a,B_A] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
% 155.55/155.56 => ( hBOOL(hAPP(V_P_2,B_A))
% 155.55/155.56 => 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)))))) ) ) )
% 155.55/155.56 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I19_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__atLeastAtMost,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__atLeastAtMost__int,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__add__atLeastAtMost,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__Suc__atLeastAtMost,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 155.55/155.56 ! [V_n_2,V_m_2] :
% 155.55/155.56 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 155.55/155.56 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2] :
% 155.55/155.56 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 155.55/155.56 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastatMost__empty__iff,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( 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))
% 155.55/155.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastatMost__empty__iff2,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( 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)
% 155.55/155.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastatMost__empty,axiom,
% 155.55/155.56 ! [V_a_2,V_b_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastatMost__subset__iff,axiom,
% 155.55/155.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 155.55/155.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastAtMost__singleton,axiom,
% 155.55/155.56 ! [V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 155.55/155.56 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> ( V_a_2 = V_b_2
% 155.55/155.56 & V_b_2 = V_ca_2 ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastAtMost__singleton_H,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( V_a_2 = V_b_2
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__uminus__atLeastAtMost,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 155.55/155.56 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card__atLeastAtMost,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastAtMostSuc__conv,axiom,
% 155.55/155.56 ! [V_n_2,V_m_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Int__atLeastAtMost,axiom,
% 155.55/155.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastatMost__psubset__iff,axiom,
% 155.55/155.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 155.55/155.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
% 155.55/155.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2))
% 155.55/155.56 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) )
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I22_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I16_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I13_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I12_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_simp__from__to,axiom,
% 155.55/155.56 ! [V_i_2,V_j_2] :
% 155.55/155.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card__atLeastAtMost__int,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I5_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_bset_I8_J,axiom,
% 155.55/155.56 ! [V_B_2,V_t_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ( 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))
% 155.55/155.56 => ! [B_x] :
% 155.55/155.56 ( ! [B_xa] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xb] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 155.55/155.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 155.55/155.56 => 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))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_aset_I6_J,axiom,
% 155.55/155.56 ! [V_A_2,V_t_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ( 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))
% 155.55/155.56 => ! [B_x] :
% 155.55/155.56 ( ! [B_xa] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xb] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 155.55/155.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_aset_I4_J,axiom,
% 155.55/155.56 ! [V_A_2,V_t_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 155.55/155.56 => ! [B_x] :
% 155.55/155.56 ( ! [B_xa] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xb] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 155.55/155.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 155.55/155.56 => ( B_x != V_t_2
% 155.55/155.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ex__nat__less,axiom,
% 155.55/155.56 ! [V_P_2,V_n_2] :
% 155.55/155.56 ( ? [B_m] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 155.55/155.56 & hBOOL(hAPP(V_P_2,B_m)) )
% 155.55/155.56 <=> ? [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_all__nat__less,axiom,
% 155.55/155.56 ! [V_P_2,V_n_2] :
% 155.55/155.56 ( ! [B_m] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 155.55/155.56 => hBOOL(hAPP(V_P_2,B_m)) )
% 155.55/155.56 <=> ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_bset_I3_J,axiom,
% 155.55/155.56 ! [V_B_2,V_t_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ( 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))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xa] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 155.55/155.56 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 155.55/155.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_bset_I4_J,axiom,
% 155.55/155.56 ! [V_B_2,V_t_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 155.55/155.56 => ! [B_x] :
% 155.55/155.56 ( ! [B_xa] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xb] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 155.55/155.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 155.55/155.56 => ( B_x != V_t_2
% 155.55/155.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_bset_I7_J,axiom,
% 155.55/155.56 ! [V_B_2,V_t_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 155.55/155.56 => ! [B_x] :
% 155.55/155.56 ( ! [B_xa] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xb] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 155.55/155.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 155.55/155.56 => 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))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_aset_I5_J,axiom,
% 155.55/155.56 ! [V_A_2,V_t_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 155.55/155.56 => ! [B_x] :
% 155.55/155.56 ( ! [B_xa] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xb] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 155.55/155.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_aset_I3_J,axiom,
% 155.55/155.56 ! [V_A_2,V_t_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ( 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))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xa] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 155.55/155.56 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 155.55/155.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_bset_I6_J,axiom,
% 155.55/155.56 ! [V_t_2,V_B_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ! [B_x] :
% 155.55/155.56 ( ! [B_xa] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xb] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 155.55/155.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_aset_I8_J,axiom,
% 155.55/155.56 ! [V_t_2,V_A_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ! [B_x] :
% 155.55/155.56 ( ! [B_xa] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xb] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 155.55/155.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_periodic__finite__ex,axiom,
% 155.55/155.56 ! [V_P_2,V_d_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 155.55/155.56 => ( ! [B_x,B_k] :
% 155.55/155.56 ( hBOOL(hAPP(V_P_2,B_x))
% 155.55/155.56 <=> 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)))) )
% 155.55/155.56 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 155.55/155.56 <=> ? [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_aset_I7_J,axiom,
% 155.55/155.56 ! [V_t_2,V_A_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ! [B_x] :
% 155.55/155.56 ( ! [B_xa] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xb] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 155.55/155.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_bset_I5_J,axiom,
% 155.55/155.56 ! [V_t_2,V_B_2,V_D_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 155.55/155.56 => ! [B_x] :
% 155.55/155.56 ( ! [B_xa] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ! [B_xb] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 155.55/155.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 155.55/155.56 ! [V_x_2,V_y_2,V_ca_2] :
% 155.55/155.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 155.55/155.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 155.55/155.56 => 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))) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_greaterThan__0,axiom,
% 155.55/155.56 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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__atLeastLessThan,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__atMost,axiom,
% 155.55/155.56 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 155.55/155.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( 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)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 155.55/155.56 => V_b_2 = V_d_2 ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 155.55/155.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( 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)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 155.55/155.56 => V_a_2 = V_ca_2 ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThan__eq__iff,axiom,
% 155.55/155.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 155.55/155.56 => ( 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)
% 155.55/155.56 <=> ( V_a_2 = V_ca_2
% 155.55/155.56 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Compl__atMost,axiom,
% 155.55/155.56 ! [V_k_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Compl__greaterThan,axiom,
% 155.55/155.56 ! [V_k_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_greaterThan__eq__iff,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)
% 155.55/155.56 <=> V_x_2 = V_y_2 ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atMost__eq__iff,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)
% 155.55/155.56 <=> V_x_2 = V_y_2 ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_all__nat__less__eq,axiom,
% 155.55/155.56 ! [V_P_2,V_n_2] :
% 155.55/155.56 ( ! [B_m] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 155.55/155.56 => hBOOL(hAPP(V_P_2,B_m)) )
% 155.55/155.56 <=> ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ex__nat__less__eq,axiom,
% 155.55/155.56 ! [V_P_2,V_n_2] :
% 155.55/155.56 ( ? [B_m] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 155.55/155.56 & hBOOL(hAPP(V_P_2,B_m)) )
% 155.55/155.56 <=> ? [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__atMost__UNIV,axiom,
% 155.55/155.56 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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThan0,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card__atLeastLessThan,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__Suc__atLeastLessThan,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThan__empty,axiom,
% 155.55/155.56 ! [V_a_2,V_b_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThan__empty__iff,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( 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))
% 155.55/155.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( 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)
% 155.55/155.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThan__subset__iff,axiom,
% 155.55/155.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 155.55/155.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I17_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__diff,axiom,
% 155.55/155.56 ! [V_m_2,V_n_2,V_i_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__UN__finite__eq,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I11_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeast0AtMost,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__add__atLeastLessThan,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card__atMost,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atMost__Suc,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atMost__iff,axiom,
% 155.55/155.56 ! [V_k_2,V_i_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oord(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)))
% 155.55/155.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atMost__subset__iff,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_greaterThan__iff,axiom,
% 155.55/155.56 ! [V_k_2,V_i_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oord(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)))
% 155.55/155.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_greaterThan__subset__iff,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__le__add__shift,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThan__singleton,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I21_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThan__add__Un,axiom,
% 155.55/155.56 ! [V_k_2,V_j_2,V_i_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I15_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Int__atLeastLessThan,axiom,
% 155.55/155.56 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_subset__card__intvl__is__intvl,axiom,
% 155.55/155.56 ! [V_k_2,V_A_2] :
% 155.55/155.56 ( 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)))))
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I9_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__uminus__atLeastLessThan,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThanSuc,axiom,
% 155.55/155.56 ! [V_n_2,V_m_2] :
% 155.55/155.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atMost__0,axiom,
% 155.55/155.56 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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Int__atLeastAtMostR1,axiom,
% 155.55/155.56 ! [V_d_2,V_ca_2,V_b_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Int__atLeastAtMostL1,axiom,
% 155.55/155.56 ! [V_d_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I9_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I3_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I1_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I7_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I15_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I11_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I5_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_greaterThan__Suc,axiom,
% 155.55/155.56 ! [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)))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__le__eq__Un0,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I6_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I3_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I18_J,axiom,
% 155.55/155.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__finite2__subset,axiom,
% 155.55/155.56 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 155.55/155.56 ( ! [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)))
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I12_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I7_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__lessThan,axiom,
% 155.55/155.56 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__atLeastLessThan__int,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeast__eq__iff,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)
% 155.55/155.56 <=> V_x_2 = V_y_2 ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_lessThan__eq__iff,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)
% 155.55/155.56 <=> V_x_2 = V_y_2 ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Compl__lessThan,axiom,
% 155.55/155.56 ! [V_k_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Compl__atLeast,axiom,
% 155.55/155.56 ! [V_k_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card__lessThan,axiom,
% 155.55/155.56 ! [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 ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__lessThan__UNIV,axiom,
% 155.55/155.56 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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__atLeast__UNIV,axiom,
% 155.55/155.56 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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeast0LessThan,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_lessThan__0,axiom,
% 155.55/155.56 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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_lessThan__Suc,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_lessThan__Suc__atMost,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 155.55/155.56 ! [V_u_2] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeast__iff,axiom,
% 155.55/155.56 ! [V_k_2,V_i_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oord(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)))
% 155.55/155.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_lessThan__iff,axiom,
% 155.55/155.56 ! [V_k_2,V_i_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oord(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)))
% 155.55/155.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_lessThan__subset__iff,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeast__subset__iff,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeast__0,axiom,
% 155.55/155.56 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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_lessThan__strict__subset__iff,axiom,
% 155.55/155.56 ! [V_n_2,V_m_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( 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)))
% 155.55/155.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeast__Suc__greaterThan,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__add__int__atLeastLessThan,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card__atLeastLessThan__int,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_single__Diff__lessThan,axiom,
% 155.55/155.56 ! [V_k_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I14_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I8_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I4_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I2_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I8_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Int__atLeastAtMostR2,axiom,
% 155.55/155.56 ! [V_d_2,V_ca_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Int__atLeastAtMostL2,axiom,
% 155.55/155.56 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__int_I6_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__uminus__atLeast,axiom,
% 155.55/155.56 ! [V_x_2,T_a] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__uminus__atMost,axiom,
% 155.55/155.56 ! [V_x_2,T_a] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atLeast__Suc,axiom,
% 155.55/155.56 ! [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)))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__uminus__greaterThan,axiom,
% 155.55/155.56 ! [V_x_2,T_a] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__uminus__lessThan,axiom,
% 155.55/155.56 ! [V_x_2,T_a] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I2_J,axiom,
% 155.55/155.56 ! [V_u_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_atMost__Int__atLeast,axiom,
% 155.55/155.56 ! [V_n_2,T_a] :
% 155.55/155.56 ( class_Orderings_Oorder(T_a)
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I10_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I1_J,axiom,
% 155.55/155.56 ! [V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_ivl__disj__un_I13_J,axiom,
% 155.55/155.56 ! [V_u_2,V_l_2,T_a] :
% 155.55/155.56 ( class_Orderings_Olinorder(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_arith__series__int,axiom,
% 155.55/155.56 ! [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)))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__finite2__eq,axiom,
% 155.55/155.56 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 155.55/155.56 ( ! [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)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__finite__subset,axiom,
% 155.55/155.56 ! [V_C_2,V_A_2,T_a] :
% 155.55/155.56 ( ! [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))
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__abs,axiom,
% 155.55/155.56 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__abs__ge__zero,axiom,
% 155.55/155.56 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__subtractf,axiom,
% 155.55/155.56 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_of__nat__setsum,axiom,
% 155.55/155.56 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_of__int__setsum,axiom,
% 155.55/155.56 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Rings_Oring__1(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__0,axiom,
% 155.55/155.56 ! [V_A_2,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_abs__setsum__abs,axiom,
% 155.55/155.56 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__addf,axiom,
% 155.55/155.56 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__negf,axiom,
% 155.55/155.56 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__commute,axiom,
% 155.55/155.56 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__product,axiom,
% 155.55/155.56 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Rings_Osemiring__0(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__left__distrib,axiom,
% 155.55/155.56 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Rings_Osemiring__0(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__right__distrib,axiom,
% 155.55/155.56 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] :
% 155.55/155.56 ( class_Rings_Osemiring__0(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__divide__distrib,axiom,
% 155.55/155.56 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Fields_Ofield(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__infinite,axiom,
% 155.55/155.56 ! [V_f_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum_Oinfinite,axiom,
% 155.55/155.56 ! [V_g_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum_Oempty,axiom,
% 155.55/155.56 ! [V_g_2,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__empty,axiom,
% 155.55/155.56 ! [V_f_2,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum_Odistrib,axiom,
% 155.55/155.56 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__lessThan__Suc,axiom,
% 155.55/155.56 ! [V_n_2,V_f_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 155.55/155.56 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 155.55/155.56 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 155.55/155.56 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 155.55/155.56 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__reindex,axiom,
% 155.55/155.56 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_c)
% 155.55/155.56 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__add__nat__ivl,axiom,
% 155.55/155.56 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__diff__nat__ivl,axiom,
% 155.55/155.56 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 155.55/155.56 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__delta,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 155.55/155.56 => 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) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 155.55/155.56 => 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__delta_H,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 155.55/155.56 => 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) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 155.55/155.56 => 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__constant,axiom,
% 155.55/155.56 ! [V_A_2,V_y_2,T_b,T_a] :
% 155.55/155.56 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.56 => 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) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__atMost__Suc,axiom,
% 155.55/155.56 ! [V_n_2,V_f_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum_Oinsert,axiom,
% 155.55/155.56 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__insert,axiom,
% 155.55/155.56 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 155.55/155.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__Un__Int,axiom,
% 155.55/155.56 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__diff,axiom,
% 155.55/155.56 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Oab__group__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum_Oreindex,axiom,
% 155.55/155.56 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum_OF__eq,axiom,
% 155.55/155.56 ! [V_g_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum_Oeq__fold,axiom,
% 155.55/155.56 ! [V_g_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 155.55/155.56 ! [V_k_2,V_f_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a)
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__head__upt__Suc,axiom,
% 155.55/155.56 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__head__Suc,axiom,
% 155.55/155.56 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__restrict__set,axiom,
% 155.55/155.56 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum_Oinsert__remove,axiom,
% 155.55/155.56 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => 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)))))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__Un__disjoint,axiom,
% 155.55/155.56 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => ( 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))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__Un,axiom,
% 155.55/155.56 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Oab__group__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__op__ivl__Suc,axiom,
% 155.55/155.56 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 155.55/155.56 => 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) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__cl__ivl__Suc,axiom,
% 155.55/155.56 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 155.55/155.56 => 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) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__head,axiom,
% 155.55/155.56 ! [V_P_2,V_n_2,V_m_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__ub__add__nat,axiom,
% 155.55/155.56 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => ( 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))))
% 155.55/155.56 => 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)))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__diff1_H,axiom,
% 155.55/155.56 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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)))))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum_Oremove,axiom,
% 155.55/155.56 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.56 => 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)))))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__diff1,axiom,
% 155.55/155.56 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Oab__group__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__diff1__ring,axiom,
% 155.55/155.56 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Rings_Oring(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_arith__series__general,axiom,
% 155.55/155.56 ! [V_n_2,V_d_2,V_a_2,T_a] :
% 155.55/155.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.56 => 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)))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_geometric__sum,axiom,
% 155.55/155.56 ! [V_n_2,V_x_2,T_a] :
% 155.55/155.56 ( class_Fields_Ofield(T_a)
% 155.55/155.56 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a)
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_gauss__sum,axiom,
% 155.55/155.56 ! [V_n_2,T_a] :
% 155.55/155.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__natinterval__difff,axiom,
% 155.55/155.56 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 155.55/155.56 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.56 => 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)))) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__mono2,axiom,
% 155.55/155.56 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.56 => ( ! [B_b] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) )
% 155.55/155.56 => 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))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__bounded,axiom,
% 155.55/155.56 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( ( class_Groups_Oordered__ab__semigroup__add(T_b)
% 155.55/155.56 & class_Rings_Osemiring__1(T_b) )
% 155.55/155.56 => ( ! [B_i] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) )
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 155.55/155.56 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__eq__0__iff,axiom,
% 155.55/155.56 ! [V_f_2,V_F_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 155.55/155.56 => ( 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)
% 155.55/155.56 <=> ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2))
% 155.55/155.56 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card__eq__setsum,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_int__setsum,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__eq__Suc0__iff,axiom,
% 155.55/155.56 ! [V_f_2,V_A_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( 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))
% 155.55/155.56 <=> ? [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.56 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 155.55/155.56 & ! [B_xa] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 155.55/155.56 => ( B_x != B_xa
% 155.55/155.56 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__eq__1__iff,axiom,
% 155.55/155.56 ! [V_f_2,V_A_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( 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)
% 155.55/155.56 <=> ? [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.56 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 155.55/155.56 & ! [B_xa] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 155.55/155.56 => ( B_x != B_xa
% 155.55/155.56 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 155.55/155.56 ! [V_k_2,V_f_2] :
% 155.55/155.56 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__diff__nat,axiom,
% 155.55/155.56 ! [V_f_2,V_A_2,V_B_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 155.55/155.56 ! [V_A_2,V_f_2,T_a] :
% 155.55/155.56 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 & class_Groups_Ocomm__monoid__mult(T_a) )
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__diff1__nat,axiom,
% 155.55/155.56 ! [V_f_2,V_A_2,V_a_2,T_a] :
% 155.55/155.56 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__Un__nat,axiom,
% 155.55/155.56 ! [V_f_2,V_B_2,V_A_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 155.55/155.56 ! [V_f_2,V_A_2,T_a] :
% 155.55/155.56 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 & class_Groups_Ocomm__monoid__mult(T_a) )
% 155.55/155.56 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_arith__series__nat,axiom,
% 155.55/155.56 ! [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)))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 155.55/155.56 ! [V_f_2,V_A_2,T_a] :
% 155.55/155.56 ( ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.56 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__Un__zero,axiom,
% 155.55/155.56 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__mono3,axiom,
% 155.55/155.56 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 155.55/155.56 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 155.55/155.56 => 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))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__reindex__nonzero,axiom,
% 155.55/155.56 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_c)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 155.55/155.56 => ! [B_y] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2))
% 155.55/155.56 => ( B_x != B_y
% 155.55/155.56 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 155.55/155.56 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) )
% 155.55/155.56 => 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) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__nonneg__0,axiom,
% 155.55/155.56 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 155.55/155.56 => ( ! [B_i] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 155.55/155.56 => ( 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)
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 155.55/155.56 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__nonneg__leq__bound,axiom,
% 155.55/155.56 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Oordered__ab__group__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 155.55/155.56 => ( ! [B_i] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 155.55/155.56 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_sum__diff__distrib,axiom,
% 155.55/155.56 ! [V_n_2,V_P_2,V_Q_2] :
% 155.55/155.56 ( ! [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)))
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__mono__zero__left,axiom,
% 155.55/155.56 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 155.55/155.56 => 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__mono__zero__right,axiom,
% 155.55/155.56 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 155.55/155.56 => 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.56 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.56 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.55/155.56 => 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__subset__induct,axiom,
% 155.55/155.56 ! [V_P_2,V_A_2,V_F_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 155.55/155.56 => ( ! [B_a,B_F] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 155.55/155.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F))
% 155.55/155.56 => ( hBOOL(hAPP(V_P_2,B_F))
% 155.55/155.56 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) )
% 155.55/155.56 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_folding__one__idem_Oidem,axiom,
% 155.55/155.56 ! [V_x_2,V_F_2,V_f_2,T_a] :
% 155.55/155.56 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 155.55/155.56 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_folding__one__idem_Oin__idem,axiom,
% 155.55/155.56 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.56 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.56 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 155.55/155.56 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.56 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__strict__mono,axiom,
% 155.55/155.56 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 155.55/155.56 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.56 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) )
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 155.55/155.56 => 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))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_field__le__mult__one__interval,axiom,
% 155.55/155.56 ! [V_y,V_x,T_a] :
% 155.55/155.56 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 155.55/155.56 => ( ! [B_z] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 155.55/155.56 => 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)) ) )
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 155.55/155.56 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 155.55/155.56 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 & class_Groups_Ocomm__monoid__mult(T_a) )
% 155.55/155.56 => ( V_A_2 = V_B_2
% 155.55/155.56 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 155.55/155.56 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 155.55/155.56 => 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__graph__permute__diff,axiom,
% 155.55/155.56 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] :
% 155.55/155.56 ( class_Groups_Oab__semigroup__mult(T_a)
% 155.55/155.56 => ( 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))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 155.55/155.56 => 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)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 155.55/155.56 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 155.55/155.56 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 & class_Groups_Ocomm__monoid__mult(T_a) )
% 155.55/155.56 => ( V_A_2 = V_B_2
% 155.55/155.56 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 155.55/155.56 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 155.55/155.56 => 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) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_max__extp_Oequations,axiom,
% 155.55/155.56 ! [V_a2_2,V_a1_2,V_R_2,T_a] :
% 155.55/155.56 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2)
% 155.55/155.56 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 155.55/155.56 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 155.55/155.56 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 & ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 155.55/155.56 => ? [B_xa] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 155.55/155.56 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_empty__fold__graphE,axiom,
% 155.55/155.56 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( 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))
% 155.55/155.56 => V_x_2 = V_z_2 ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__graph_OemptyI,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__graph__imp__finite,axiom,
% 155.55/155.56 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
% 155.55/155.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__graph_OinsertI,axiom,
% 155.55/155.56 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 155.55/155.56 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold__graph__insert__swap,axiom,
% 155.55/155.56 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] :
% 155.55/155.56 ( class_Groups_Oab__semigroup__mult(T_a)
% 155.55/155.56 => ( 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))
% 155.55/155.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 155.55/155.56 => 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))) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Diff1__fold__graph,axiom,
% 155.55/155.56 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.56 ( 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))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold1Set_Ointros,axiom,
% 155.55/155.56 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2))
% 155.55/155.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => 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)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_max__ext_Ointros,axiom,
% 155.55/155.56 ! [V_R_2,V_Y_2,V_X_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2))
% 155.55/155.56 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => ( ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2))
% 155.55/155.56 => ? [B_xa] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2))
% 155.55/155.56 & 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)) ) )
% 155.55/155.56 => 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))) ) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_empty__fold1SetE,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold1Set__nonempty,axiom,
% 155.55/155.56 ! [V_x_2,V_A_2,V_f_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2))
% 155.55/155.56 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold1Set__sing,axiom,
% 155.55/155.56 ! [V_b_2,V_a_2,V_f_2,T_a] :
% 155.55/155.56 ( 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))
% 155.55/155.56 <=> V_a_2 = V_b_2 ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Nitpick_Oone__frac__def,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Nitpick_Ofrac__def,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fold1Set_Oequations,axiom,
% 155.55/155.56 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] :
% 155.55/155.56 ( 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))
% 155.55/155.56 <=> ? [B_a,B_A] :
% 155.55/155.56 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 155.55/155.56 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2))
% 155.55/155.56 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_insert__fold1SetE,axiom,
% 155.55/155.56 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] :
% 155.55/155.56 ( 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))
% 155.55/155.56 => ~ ! [B_a,B_A] :
% 155.55/155.56 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_image__split__eq__Sigma,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SigmaI,axiom,
% 155.55/155.56 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Sigma__Diff__distrib2,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Times__Diff__distrib1,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Sigma__Diff__distrib1,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Sigma__empty1,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Times__eq__cancel2,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 155.55/155.56 => ( 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))
% 155.55/155.56 <=> V_A_2 = V_B_2 ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card__cartesian__product,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setsum__cartesian__product,axiom,
% 155.55/155.56 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Sigma__empty2,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Times__empty,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.56 ( 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))
% 155.55/155.56 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Compl__Times__UNIV1,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Compl__Times__UNIV2,axiom,
% 155.55/155.56 ! [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)))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_setprod__cartesian__product,axiom,
% 155.55/155.56 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 155.55/155.56 ( class_Groups_Ocomm__monoid__mult(T_a)
% 155.55/155.56 => 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))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Sigma__Un__distrib2,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Times__Un__distrib1,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Sigma__Un__distrib1,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_swap__product,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__cartesian__product,axiom,
% 155.55/155.56 ! [V_B_2,T_b,V_A_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 155.55/155.56 => 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)))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_equiv__type,axiom,
% 155.55/155.56 ! [V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.56 => 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)))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Sigma__Int__distrib1,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Times__Int__distrib1,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Sigma__Int__distrib2,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Id__on__subset__Times,axiom,
% 155.55/155.56 ! [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)))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UNIV__Times__UNIV,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_mem__Sigma__iff,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SigmaD1,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SigmaD2,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_SigmaE2,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.56 ( 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)))
% 155.55/155.56 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.56 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_card__cartesian__product__singleton,axiom,
% 155.55/155.56 ! [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) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Times__subset__cancel2,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 155.55/155.56 => ( 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))))
% 155.55/155.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Image__subset,axiom,
% 155.55/155.56 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 155.55/155.56 ( 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))))
% 155.55/155.56 => 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)) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__cartesian__productD2,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.56 ( 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))))
% 155.55/155.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__cartesian__productD1,axiom,
% 155.55/155.56 ! [V_B_2,V_A_2,T_b,T_a] :
% 155.55/155.56 ( 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))))
% 155.55/155.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 155.55/155.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_fst__image__times,axiom,
% 155.55/155.56 ! [V_A_2,T_b,T_a,V_B_2] :
% 155.55/155.56 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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 ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_snd__image__times,axiom,
% 155.55/155.56 ! [V_B_2,T_b,T_a,V_A_2] :
% 155.55/155.56 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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)) )
% 155.55/155.56 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.56 => 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 ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_refl__on__def,axiom,
% 155.55/155.56 ! [V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 155.55/155.56 <=> ( 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))))
% 155.55/155.56 & ! [B_x] :
% 155.55/155.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.56 => 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)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_insert__times__insert,axiom,
% 155.55/155.56 ! [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)))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__equiv__class,axiom,
% 155.55/155.56 ! [V_X_2,V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( 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))))
% 155.55/155.56 => ( 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)))
% 155.55/155.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_vimage__Times,axiom,
% 155.55/155.56 ! [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)) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_UN__Times__distrib,axiom,
% 155.55/155.56 ! [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))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_Sigma__def,axiom,
% 155.55/155.56 ! [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))))) ).
% 155.55/155.56
% 155.55/155.56 fof(fact_finite__quotient,axiom,
% 155.55/155.56 ! [V_r_2,V_A_2,T_a] :
% 155.55/155.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.56 => ( 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))))
% 155.55/155.56 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 155.55/155.57 ! [V_A_2,V_I_2,T_b,T_a] :
% 155.55/155.57 ? [B_f] :
% 155.55/155.57 ( 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))
% 155.55/155.57 & 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_refl__onI,axiom,
% 155.55/155.57 ! [V_A_2,V_r_2,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 => 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)) )
% 155.55/155.57 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold__image__Sigma,axiom,
% 155.55/155.57 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__mult(T_c)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setprod__Sigma,axiom,
% 155.55/155.57 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__mult(T_c)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setsum__Sigma,axiom,
% 155.55/155.57 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_c)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_card__SigmaI,axiom,
% 155.55/155.57 ! [V_B_2,T_b,V_A_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__SigmaI,axiom,
% 155.55/155.57 ! [V_B_2,T_b,V_A_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( ! [B_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 155.55/155.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_SigmaE,axiom,
% 155.55/155.57 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ~ ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 => ! [B_y] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x)))
% 155.55/155.57 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair__surj,axiom,
% 155.55/155.57 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => ( 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))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair__imageI,axiom,
% 155.55/155.57 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_snd__prod__fun,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fst__map__pair,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair__ident,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair__simp,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_snd__comp__map__pair,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fst__comp__map__pair,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair_Ocompositionality,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair__compose,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair_Ocomp,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair__def,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair__surj__on,axiom,
% 155.55/155.57 ! [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] :
% 155.55/155.57 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2
% 155.55/155.57 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair__inj__on,axiom,
% 155.55/155.57 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.55/155.57 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2)
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_prod__fun__imageE,axiom,
% 155.55/155.57 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ~ ! [B_x,B_y] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => ~ 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__Un,axiom,
% 155.55/155.57 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Groups_Oab__semigroup__mult(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( 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))
% 155.55/155.57 => 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)) ) ) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__antimono,axiom,
% 155.55/155.57 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.57 => 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))) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__singleton__def,axiom,
% 155.55/155.57 ! [V_a_2,V_f_2,T_a,V_g_2] :
% 155.55/155.57 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2)
% 155.55/155.57 => 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 ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__singleton,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_folding__one_Oeq__fold,axiom,
% 155.55/155.57 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.57 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__def,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Sup__fin_OF__eq,axiom,
% 155.55/155.57 ! [V_A_2,T_a] :
% 155.55/155.57 ( class_Lattices_Olattice(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Inf__fin_OF__eq,axiom,
% 155.55/155.57 ! [V_A_2,T_a] :
% 155.55/155.57 ( class_Lattices_Olattice(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Min_OF__eq,axiom,
% 155.55/155.57 ! [V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Max_OF__eq,axiom,
% 155.55/155.57 ! [V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 155.55/155.57 ! [V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 155.55/155.57 ! [V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__belowI,axiom,
% 155.55/155.57 ! [V_a_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_below__fold1__iff,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 <=> ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__max_Ofold1__belowI,axiom,
% 155.55/155.57 ! [V_a_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__insert__idem,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__below__iff,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( 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))
% 155.55/155.57 <=> ? [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 <=> ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__Un2,axiom,
% 155.55/155.57 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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)) ) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_strict__below__fold1__iff,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 <=> ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__strict__below__iff,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( 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))
% 155.55/155.57 <=> ? [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__insert,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Groups_Oab__semigroup__mult(T_a)
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.57 => 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)) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_semilattice__big_OF__eq,axiom,
% 155.55/155.57 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 155.55/155.57 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fold1__in,axiom,
% 155.55/155.57 ! [V_A_2,T_a] :
% 155.55/155.57 ( class_Groups_Oab__semigroup__mult(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( ! [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))))))
% 155.55/155.57 => 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)) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_hom__fold1__commute,axiom,
% 155.55/155.57 ! [V_N_2,V_h_2,T_a] :
% 155.55/155.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 155.55/155.57 => ( ! [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))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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)) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setprod__pos__nat,axiom,
% 155.55/155.57 ! [V_f_2,V_S_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 155.55/155.57 => 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))) )
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 155.55/155.57 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] :
% 155.55/155.57 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 155.55/155.57 => ( ! [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))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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)) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Rep__Integ__cases,axiom,
% 155.55/155.57 ! [V_y_2] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 155.55/155.57 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Rep__Integ__induct,axiom,
% 155.55/155.57 ! [V_P_2,V_y_2] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 155.55/155.57 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 155.55/155.57 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 155.55/155.57 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => hAPP(V_g_2,B_x) = V_z_2 )
% 155.55/155.57 => 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)) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fun__left__comm__idem__remove,axiom,
% 155.55/155.57 ! [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))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 155.55/155.57 ! [V_x_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 155.55/155.57 ! [T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fun__left__comm__idem,axiom,
% 155.55/155.57 ! [T_a] :
% 155.55/155.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 155.55/155.57 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 155.55/155.57 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 155.55/155.57 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 155.55/155.57 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fun__left__comm__idem__insert,axiom,
% 155.55/155.57 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fun__left__comm__idem__inf,axiom,
% 155.55/155.57 ! [T_a] :
% 155.55/155.57 ( class_Lattices_Osemilattice__inf(T_a)
% 155.55/155.57 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fun__left__comm__idem__sup,axiom,
% 155.55/155.57 ! [T_a] :
% 155.55/155.57 ( class_Lattices_Osemilattice__sup(T_a)
% 155.55/155.57 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 155.55/155.57 ! [T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_card__less__Suc,axiom,
% 155.55/155.57 ! [V_i_2,V_M_2] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 155.55/155.57 => 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))))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_card__less,axiom,
% 155.55/155.57 ! [V_i_2,V_M_2] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_card__less__Suc2,axiom,
% 155.55/155.57 ! [V_i_2,V_M_2] :
% 155.55/155.57 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 155.55/155.57 => 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))))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_CollectI,axiom,
% 155.55/155.57 ! [T_a,V_a_2,V_P_2] :
% 155.55/155.57 ( hBOOL(hAPP(V_P_2,V_a_2))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__Collect__conjI,axiom,
% 155.55/155.57 ! [V_Q_2,V_P_2,T_a] :
% 155.55/155.57 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 155.55/155.57 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) )
% 155.55/155.57 => 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__Collect__less__nat,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__Collect__le__nat,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Collect__split,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_SetCompr__Sigma__eq,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_vimage__Collect__eq,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Collect__neg__eq,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_insert__Collect,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_CollectE,axiom,
% 155.55/155.57 ! [V_P_2,V_a_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 155.55/155.57 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_CollectD,axiom,
% 155.55/155.57 ! [V_P_2,V_a_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 155.55/155.57 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_mem__Collect__eq,axiom,
% 155.55/155.57 ! [V_P_2,V_a_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 155.55/155.57 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Collect__mem__eq,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__Collect__disjI,axiom,
% 155.55/155.57 ! [V_Q_2,V_P_2,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 155.55/155.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Collect__conj__eq,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Collect__disj__eq,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_UNIV__def,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Collect__def,axiom,
% 155.55/155.57 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_empty__Collect__eq,axiom,
% 155.55/155.57 ! [V_P_2,T_a] :
% 155.55/155.57 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2)
% 155.55/155.57 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Collect__empty__eq,axiom,
% 155.55/155.57 ! [V_P_2,T_a] :
% 155.55/155.57 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_empty__def,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_insert__compr__raw,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_insert__compr,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Un__def,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Int__Collect,axiom,
% 155.55/155.57 ! [V_P_2,V_A_2,V_x_2,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.57 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Int__def,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_singleton__conv2,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_singleton__conv,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Collect__conv__if2,axiom,
% 155.55/155.57 ! [T_a,V_a_2,V_P_2] :
% 155.55/155.57 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 155.55/155.57 => 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))) )
% 155.55/155.57 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Collect__conv__if,axiom,
% 155.55/155.57 ! [T_a,V_a_2,V_P_2] :
% 155.55/155.57 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 155.55/155.57 => 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))) )
% 155.55/155.57 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__diff__eq,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__Collect__not,axiom,
% 155.55/155.57 ! [V_P_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 155.55/155.57 => ( 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))))
% 155.55/155.57 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_insert__def,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Compl__eq,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_vimage__def,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Collect__imp__eq,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_dom__def,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__M__bounded__by__nat,axiom,
% 155.55/155.57 ! [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))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setsum__setsum__restrict,axiom,
% 155.55/155.57 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_c)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 155.55/155.57 => 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) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_if__image__distrib,axiom,
% 155.55/155.57 ! [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))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_dom__if,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nat__seg__image__imp__finite,axiom,
% 155.55/155.57 ! [V_n_2,V_f_2,T_a,V_A_2] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setsum__restrict__set_H,axiom,
% 155.55/155.57 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setsum__image__gen,axiom,
% 155.55/155.57 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Image__singleton,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setsum__cases,axiom,
% 155.55/155.57 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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))))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_dom__override__on,axiom,
% 155.55/155.57 ! [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))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setsum__multicount,axiom,
% 155.55/155.57 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2))
% 155.55/155.57 => 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 )
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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))))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__Collect__subsets,axiom,
% 155.55/155.57 ! [V_A_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Pow__Compl,axiom,
% 155.55/155.57 ! [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))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Pow__def,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__Collect__bounded__ex,axiom,
% 155.55/155.57 ! [V_Q_2,T_b,V_P_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 155.55/155.57 => ( 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)))))
% 155.55/155.57 <=> ! [B_y] :
% 155.55/155.57 ( hBOOL(hAPP(V_P_2,B_y))
% 155.55/155.57 => 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)))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__image__set,axiom,
% 155.55/155.57 ! [V_f_2,T_b,V_P_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 155.55/155.57 => 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))))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_override__on__apply__notin,axiom,
% 155.55/155.57 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 155.55/155.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_override__on__apply__in,axiom,
% 155.55/155.57 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_override__on__emptyset,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_inj__graph,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_override__on__def,axiom,
% 155.55/155.57 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 155.55/155.57 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.57 => 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) )
% 155.55/155.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__psubset__def,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_ran__def,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_inv__image__def,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_add__Max__commute,axiom,
% 155.55/155.57 ! [V_k_2,V_N_2,T_a] :
% 155.55/155.57 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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))))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_add__Min__commute,axiom,
% 155.55/155.57 ! [V_k_2,V_N_2,T_a] :
% 155.55/155.57 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 155.55/155.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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))))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_sup__Inf1__distrib,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Lattices_Odistrib__lattice(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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))))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_sup__Inf2__distrib,axiom,
% 155.55/155.57 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Lattices_Odistrib__lattice(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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))))))) ) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_inf__Sup1__distrib,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Lattices_Odistrib__lattice(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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))))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_inf__Sup2__distrib,axiom,
% 155.55/155.57 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Lattices_Odistrib__lattice(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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))))))) ) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 155.55/155.57 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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))))))) ) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 155.55/155.57 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 155.55/155.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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))))))) ) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 => 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))))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Nitpick_Oprod__def,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_int__ge__less__than2__def,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_int__ge__less__than__def,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_reflp__def,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Predicate_Oreflp(T_a,V_r_2)
% 155.55/155.57 <=> 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 155.55/155.57 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] :
% 155.55/155.57 ( class_Rings_Osemiring__0(T_c)
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => 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))))))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_def__lfp__induct__set,axiom,
% 155.55/155.57 ! [V_P_2,V_a_2,V_f_2,T_a,V_A_2] :
% 155.55/155.57 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 155.55/155.57 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( 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)))))
% 155.55/155.57 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.57 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_inj__on__id,axiom,
% 155.55/155.57 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_id__o,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_o__id,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_o__eq__id__dest,axiom,
% 155.55/155.57 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_of__int__eq__id,axiom,
% 155.55/155.57 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Option_Omap_Oidentity,axiom,
% 155.55/155.57 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_apsnd__id,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Option_Omap_Oid,axiom,
% 155.55/155.57 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_id__apply,axiom,
% 155.55/155.57 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 155.55/155.57
% 155.55/155.57 fof(fact_reflpE,axiom,
% 155.55/155.57 ! [V_x_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Predicate_Oreflp(T_a,V_r_2)
% 155.55/155.57 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_id__def,axiom,
% 155.55/155.57 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_apfst__id,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_vimage__id,axiom,
% 155.55/155.57 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair_Oid,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__pair_Oidentity,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_image__id,axiom,
% 155.55/155.57 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_surj__id,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_folding_Oempty,axiom,
% 155.55/155.57 ! [V_F_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.55/155.57 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_apsnd__def,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_apfst__def,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_split__Pair,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setsum__reindex__id,axiom,
% 155.55/155.57 ! [V_B_2,V_f_2,T_a,T_b] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.57 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setprod__reindex__id,axiom,
% 155.55/155.57 ! [V_B_2,V_f_2,T_a,T_b] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.55/155.57 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lfp__induct__set,axiom,
% 155.55/155.57 ! [V_P_2,V_f_2,V_a_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2)
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( 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)))))
% 155.55/155.57 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.57 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_def__Collect__coinduct,axiom,
% 155.55/155.57 ! [V_X_2,V_a_2,V_P_2,T_a,V_A_2] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => ( 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))
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2))
% 155.55/155.57 => ( ! [B_z] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_z),V_X_2))
% 155.55/155.57 => 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)) )
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lfp__induct2,axiom,
% 155.55/155.57 ! [V_P_2,V_f_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( 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)
% 155.55/155.57 => ( ! [B_a,B_b] :
% 155.55/155.57 ( 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))))))
% 155.55/155.57 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) )
% 155.55/155.57 => hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setsum__multicount__gen,axiom,
% 155.55/155.57 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2))
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2))
% 155.55/155.57 => 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) )
% 155.55/155.57 => 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) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__conv__nat__seg__image,axiom,
% 155.55/155.57 ! [V_A_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 <=> ? [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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_rel__comp__def,axiom,
% 155.55/155.57 ! [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))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Range__Collect__split,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_rel__compI,axiom,
% 155.55/155.57 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => ( 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))
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_RangeI,axiom,
% 155.55/155.57 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_rel__comp__UNION__distrib2,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_rel__comp__UNION__distrib,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_rel__comp__distrib,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_rel__comp__distrib2,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_O__assoc,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_rel__comp__mono,axiom,
% 155.55/155.57 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => ( 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))
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_rel__comp__empty2,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_rel__comp__empty1,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Range__Id__on,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_union__comp__emptyL,axiom,
% 155.55/155.57 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => ( 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))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_union__comp__emptyR,axiom,
% 155.55/155.57 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => ( 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))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Range__empty,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Range__empty__iff,axiom,
% 155.55/155.57 ! [V_r_2,T_a,T_b] :
% 155.55/155.57 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_rel__comp__subset__Sigma,axiom,
% 155.55/155.57 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => ( 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))))
% 155.55/155.57 => 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)))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Range__Un__eq,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__Range,axiom,
% 155.55/155.57 ! [V_r_2,T_b,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 155.55/155.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_snd__eq__Range,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Range__iff,axiom,
% 155.55/155.57 ! [V_r_2,T_b,V_a_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 155.55/155.57 <=> ? [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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Range__insert,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Range__Int__subset,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Range__Diff__subset,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_max__ext__compat,axiom,
% 155.55/155.57 ! [V_S_2,V_R_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__ext__compat,axiom,
% 155.55/155.57 ! [V_S_2,V_R_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_RangeP__Range__eq,axiom,
% 155.55/155.57 ! [V_x_2,V_r_2,T_b,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_RangeE,axiom,
% 155.55/155.57 ! [V_r_2,T_b,V_b_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 155.55/155.57 => ~ ! [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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_RangeP_Ointros,axiom,
% 155.55/155.57 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 155.55/155.57 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_RangeP_Oequations,axiom,
% 155.55/155.57 ! [V_a2_2,V_r_2,T_b,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2))
% 155.55/155.57 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_pred__comp__rel__comp__eq,axiom,
% 155.55/155.57 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 <=> 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_reduction__pairI,axiom,
% 155.55/155.57 ! [V_S_2,V_R_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_R_2)
% 155.55/155.57 => ( 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))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__less__than,axiom,
% 155.55/155.57 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_pred__comp_Ointros,axiom,
% 155.55/155.57 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
% 155.55/155.57 => c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a_2,V_ca_2) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__empty,axiom,
% 155.55/155.57 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__inv__image,axiom,
% 155.55/155.57 ! [V_f_2,T_b,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__lex__prod,axiom,
% 155.55/155.57 ! [V_rb_2,T_b,V_ra_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_ra_2)
% 155.55/155.57 => ( c_Wellfounded_Owf(T_b,V_rb_2)
% 155.55/155.57 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__measure,axiom,
% 155.55/155.57 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__comp__self,axiom,
% 155.55/155.57 ! [V_R_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_R_2)
% 155.55/155.57 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_min__ext__wf,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__subset,axiom,
% 155.55/155.57 ! [V_p_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => ( 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))
% 155.55/155.57 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__Int2,axiom,
% 155.55/155.57 ! [V_r_H_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__Int1,axiom,
% 155.55/155.57 ! [V_r_H_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_pred__comp_Oequations,axiom,
% 155.55/155.57 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 155.55/155.57 ( c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a1_2,V_a3_2)
% 155.55/155.57 <=> ? [B_b] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 155.55/155.57 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_max__ext__wf,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__pair__less,axiom,
% 155.55/155.57 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__mlex,axiom,
% 155.55/155.57 ! [V_f_2,V_R_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_R_2)
% 155.55/155.57 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__finite__psubset,axiom,
% 155.55/155.57 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__not__refl,axiom,
% 155.55/155.57 ! [V_a_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => ~ 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__not__sym,axiom,
% 155.55/155.57 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => ( 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))
% 155.55/155.57 => ~ 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__asym,axiom,
% 155.55/155.57 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => ( 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))
% 155.55/155.57 => ~ 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__irrefl,axiom,
% 155.55/155.57 ! [V_a_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => ~ 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__int__ge__less__than,axiom,
% 155.55/155.57 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__int__ge__less__than2,axiom,
% 155.55/155.57 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__less,axiom,
% 155.55/155.57 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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_acc__wfD,axiom,
% 155.55/155.57 ! [V_x_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__acc__iff,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__no__loop,axiom,
% 155.55/155.57 ! [V_R_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__union__merge,axiom,
% 155.55/155.57 ! [V_S_2,V_R_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 <=> 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 <=> ~ ? [B_f] :
% 155.55/155.57 ! [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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wfE__pf,axiom,
% 155.55/155.57 ! [V_A_2,V_R_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_R_2)
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__union__compatible,axiom,
% 155.55/155.57 ! [V_S_2,V_R_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_R_2)
% 155.55/155.57 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 155.55/155.57 => ( 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))
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf,axiom,
% 155.55/155.57 ! [T_a] :
% 155.55/155.57 ( class_Orderings_Owellorder(T_a)
% 155.55/155.57 => 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_reduction__pair__def,axiom,
% 155.55/155.57 ! [V_P_2,T_a] :
% 155.55/155.57 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 155.55/155.57 <=> ( 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))
% 155.55/155.57 & 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_reduction__pair__lemma,axiom,
% 155.55/155.57 ! [V_S_2,V_R_2,V_P_2,T_a] :
% 155.55/155.57 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 155.55/155.57 => 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)) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__map__pair__image,axiom,
% 155.55/155.57 ! [V_f_2,T_b,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__lenlex,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__Un,axiom,
% 155.55/155.57 ! [V_s_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => ( c_Wellfounded_Owf(T_a,V_s_2)
% 155.55/155.57 => ( 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))
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_DomainI,axiom,
% 155.55/155.57 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Domain__Id__on,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Domain__empty__iff,axiom,
% 155.55/155.57 ! [V_r_2,T_b,T_a] :
% 155.55/155.57 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.57 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Domain__empty,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Domain__mono,axiom,
% 155.55/155.57 ! [V_s_2,V_r_2,T_b,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Domain__Un__eq,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__Domain,axiom,
% 155.55/155.57 ! [V_r_2,T_b,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 155.55/155.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_fst__eq__Domain,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Domain__iff,axiom,
% 155.55/155.57 ! [V_r_2,T_b,V_a_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 155.55/155.57 <=> ? [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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Domain__insert,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Domain__Int__subset,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Domain__Diff__subset,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Field__def,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Domain__Collect__split,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_pred__nat__def,axiom,
% 155.55/155.57 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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_DomainP__Domain__eq,axiom,
% 155.55/155.57 ! [V_x_2,V_r_2,T_b,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_DomainP_Ointros,axiom,
% 155.55/155.57 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 155.55/155.57 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_DomainP_Oequations,axiom,
% 155.55/155.57 ! [V_a1_2,V_r_2,T_b,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2))
% 155.55/155.57 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__pred__nat,axiom,
% 155.55/155.57 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__lex,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__lexn,axiom,
% 155.55/155.57 ! [V_n_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lex__def,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lexn_Osimps_I1_J,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_DomainE,axiom,
% 155.55/155.57 ! [V_r_2,T_b,V_a_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 155.55/155.57 => ~ ! [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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__same__fst,axiom,
% 155.55/155.57 ! [T_a,V_R_2,T_b,V_P_2] :
% 155.55/155.57 ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(V_P_2,B_x))
% 155.55/155.57 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) )
% 155.55/155.57 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__if__measure,axiom,
% 155.55/155.57 ! [T_a,V_g_2,V_f_2,V_P_2] :
% 155.55/155.57 ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(V_P_2,B_x))
% 155.55/155.57 => 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))) )
% 155.55/155.57 => 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))))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wfP__def,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 155.55/155.57 <=> 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wfP__empty,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_accp__wfPD,axiom,
% 155.55/155.57 ! [V_x_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 155.55/155.57 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wfP__accp__iff,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 155.55/155.57 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wfP__subset,axiom,
% 155.55/155.57 ! [V_p_2,V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 155.55/155.57 => ( 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))
% 155.55/155.57 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__in__rel,axiom,
% 155.55/155.57 ! [V_R_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_R_2)
% 155.55/155.57 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wfP__wf__eq,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wfP__acyclicP,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_pigeonhole__infinite,axiom,
% 155.55/155.57 ! [V_f_2,T_b,V_A_2,T_a] :
% 155.55/155.57 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 155.55/155.57 => ? [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.55/155.57 & ~ 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)))))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__acyclic,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_acyclic__subset,axiom,
% 155.55/155.57 ! [V_r_2,V_s_2,T_a] :
% 155.55/155.57 ( c_Wellfounded_Oacyclic(T_a,V_s_2)
% 155.55/155.57 => ( 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))
% 155.55/155.57 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__acyclic__wf,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 155.55/155.57 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 155.55/155.57 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 155.55/155.57 => ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.55/155.57 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Nitpick_Owf_H__def,axiom,
% 155.55/155.57 ! [V_r_2,T_a] :
% 155.55/155.57 ( c_Nitpick_Owf_H(T_a,V_r_2)
% 155.55/155.57 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 155.55/155.57 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 155.55/155.57 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Abs__Integ__cases,axiom,
% 155.55/155.57 ! [V_x_2] :
% 155.55/155.57 ~ ! [B_y] :
% 155.55/155.57 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 155.55/155.57 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Abs__Integ__induct,axiom,
% 155.55/155.57 ! [V_x_2,V_P_2] :
% 155.55/155.57 ( ! [B_y] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 155.55/155.57 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 155.55/155.57 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__range__map__of__map__add,axiom,
% 155.55/155.57 ! [V_l_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( 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)))))
% 155.55/155.57 => 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))))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__dom__map__of,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__range__map__of,axiom,
% 155.55/155.57 ! [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))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__add__map__of__foldr,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_body__def,axiom,
% 155.55/155.57 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__mapk__SomeI,axiom,
% 155.55/155.57 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] :
% 155.55/155.57 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.57 => ( 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)
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__map,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_inj__mapI,axiom,
% 155.55/155.57 ! [V_f_2,T_b,T_a] :
% 155.55/155.57 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_foldr__map,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__injective,axiom,
% 155.55/155.57 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 155.55/155.57 => V_xs_2 = V_ys_2 ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_inj__mapD,axiom,
% 155.55/155.57 ! [V_f_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_inj__map__eq__map,axiom,
% 155.55/155.57 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.55/155.57 => ( 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)
% 155.55/155.57 <=> V_xs_2 = V_ys_2 ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_inj__map,axiom,
% 155.55/155.57 ! [V_f_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__ident,axiom,
% 155.55/155.57 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__map,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_List_Omap_Ocompositionality,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__comp__map,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_List_Omap_Ocomp,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_List_Omap_Oid,axiom,
% 155.55/155.57 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_List_Omap_Oidentity,axiom,
% 155.55/155.57 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__map__restrict,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__map__keys,axiom,
% 155.55/155.57 ! [V_m_2,T_b,V_xs_2,T_a] :
% 155.55/155.57 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2)
% 155.55/155.57 => 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 ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__set,axiom,
% 155.55/155.57 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__map,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__eq__conv,axiom,
% 155.55/155.57 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] :
% 155.55/155.57 ( 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)
% 155.55/155.57 <=> ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 155.55/155.57 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_infinite__UNIV__listI,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__inj__on,axiom,
% 155.55/155.57 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => V_xs_2 = V_ys_2 ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_inj__on__map__eq__map,axiom,
% 155.55/155.57 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( 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)
% 155.55/155.57 <=> V_xs_2 = V_ys_2 ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__fun__upd,axiom,
% 155.55/155.57 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] :
% 155.55/155.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__eq__dom,axiom,
% 155.55/155.57 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 155.55/155.57 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__is__SomeD,axiom,
% 155.55/155.57 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__SomeD,axiom,
% 155.55/155.57 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_dom__map__of__conv__image__fst,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__eq__None__iff,axiom,
% 155.55/155.57 ! [V_x_2,V_xys_2,T_a,T_b] :
% 155.55/155.57 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a)
% 155.55/155.57 <=> ~ 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_WT__bodies__def,axiom,
% 155.55/155.57 ( c_Com_OWT__bodies
% 155.55/155.57 <=> ! [B_x] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_ran__distinct,axiom,
% 155.55/155.57 ! [V_al_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__map__of__compr,axiom,
% 155.55/155.57 ! [V_xs_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__map,axiom,
% 155.55/155.57 ! [V_xs_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
% 155.55/155.57 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 155.55/155.57 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__inject__set,axiom,
% 155.55/155.57 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 155.55/155.57 <=> 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) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Some__eq__map__of__iff,axiom,
% 155.55/155.57 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( 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)
% 155.55/155.57 <=> 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__eq__Some__iff,axiom,
% 155.55/155.57 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( 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)
% 155.55/155.57 <=> 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__is__SomeI,axiom,
% 155.55/155.57 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_greaterThanLessThan__upto,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_weak__map__of__SomeI,axiom,
% 155.55/155.57 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ? [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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__upto,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_atLeastAtMost__upto,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__upto,axiom,
% 155.55/155.57 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_atLeastLessThan__upto,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_greaterThanAtMost__upto,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nat__list__def,axiom,
% 155.55/155.57 ! [V_l_2] :
% 155.55/155.57 ( c_List_Onat__list(V_l_2)
% 155.55/155.57 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__remove1__eq,axiom,
% 155.55/155.57 ! [V_x_2,V_xs_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.55/155.57 => 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_remove1__commute,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__remove1,axiom,
% 155.55/155.57 ! [V_x,V_xs,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.55/155.57 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_remove1__idem,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_notin__set__remove1,axiom,
% 155.55/155.57 ! [V_y_2,V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => ~ 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_in__set__remove1,axiom,
% 155.55/155.57 ! [V_xs_2,T_a,V_b_2,V_a_2] :
% 155.55/155.57 ( V_a_2 != V_b_2
% 155.55/155.57 => ( 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))))
% 155.55/155.57 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__remove1__subset,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_sorted__list__of__set__remove,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__zip__map,axiom,
% 155.55/155.57 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => 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)) )
% 155.55/155.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__zipI1,axiom,
% 155.55/155.57 ! [V_ys,T_b,V_xs,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.55/155.57 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__zipI2,axiom,
% 155.55/155.57 ! [V_xs,T_b,V_ys,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 155.55/155.57 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_zip__same__conv__map,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_zip__map__fst__snd,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__zip__map,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__zip__map2,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_zip__same,axiom,
% 155.55/155.57 ! [V_xs_2,V_b_2,V_a_2,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 & V_a_2 = V_b_2 ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__zip__leftD,axiom,
% 155.55/155.57 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__zip__rightD,axiom,
% 155.55/155.57 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_in__set__zipE,axiom,
% 155.55/155.57 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_zip__map__map,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_zip__map1,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_zip__map2,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_sorted__list__of__set__insert,axiom,
% 155.55/155.57 ! [V_x_2,V_A_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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)))))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__zip__upd,axiom,
% 155.55/155.57 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => ( 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)
% 155.55/155.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 155.55/155.57 => ( 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))
% 155.55/155.57 => 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)) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_length__zip,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lexn__length,axiom,
% 155.55/155.57 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2
% 155.55/155.57 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_insort__key__left__comm,axiom,
% 155.55/155.57 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_insort__left__comm,axiom,
% 155.55/155.57 ! [V_xs_2,V_y_2,V_x_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_neq__if__length__neq,axiom,
% 155.55/155.57 ! [V_ys,V_xs,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => V_xs != V_ys ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_length__insort,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_b)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_length__map,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__eq__imp__length__eq,axiom,
% 155.55/155.57 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_remove1__insort,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => 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 ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__insort,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_b)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_card__length,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_card__distinct,axiom,
% 155.55/155.57 ! [V_xs_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__card,axiom,
% 155.55/155.57 ! [V_xs_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__zip__inject,axiom,
% 155.55/155.57 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => ( 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)
% 155.55/155.57 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 155.55/155.57 => ( 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))
% 155.55/155.57 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__fst__zip,axiom,
% 155.55/155.57 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => 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 ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__snd__zip,axiom,
% 155.55/155.57 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => 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 ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__insort,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_b)
% 155.55/155.57 => ( 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)))
% 155.55/155.57 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_length__pos__if__in__set,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_zip__eq__conv,axiom,
% 155.55/155.57 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2
% 155.55/155.57 <=> ( 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
% 155.55/155.57 & 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 ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lenlex__conv,axiom,
% 155.55/155.57 ! [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)))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lenlex__def,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__lists__length__eq,axiom,
% 155.55/155.57 ! [V_n_2,V_A_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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))))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__eq__iff__zip__eq,axiom,
% 155.55/155.57 ! [T_a,V_ys_2,V_xs_2] :
% 155.55/155.57 ( V_xs_2 = V_ys_2
% 155.55/155.57 <=> ( 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)
% 155.55/155.57 & ! [B_x] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__zip__is__None,axiom,
% 155.55/155.57 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => ( 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)
% 155.55/155.57 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__zip__is__Some,axiom,
% 155.55/155.57 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 <=> ? [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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_length__remove1,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => 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)) )
% 155.55/155.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_dom__map__of__zip,axiom,
% 155.55/155.57 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_finite__lists__length__le,axiom,
% 155.55/155.57 ! [V_n_2,V_A_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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))))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel__iff__zip,axiom,
% 155.55/155.57 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 <=> ( 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)
% 155.55/155.57 & ! [B_x] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_length__sublist,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel__eq__len,axiom,
% 155.55/155.57 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__sublistI,axiom,
% 155.55/155.57 ! [V_I_2,V_xs_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.55/155.57 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel__mono,axiom,
% 155.55/155.57 ! [V_s_2,V_r_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_notin__set__sublistI,axiom,
% 155.55/155.57 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => ~ 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_in__set__sublistD,axiom,
% 155.55/155.57 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__sublist__subset,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrelp__listrel__eq,axiom,
% 155.55/155.57 ! [V_xa_2,V_x_2,V_r_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 <=> 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lexn_Osimps_I2_J,axiom,
% 155.55/155.57 ! [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)))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_impossible__Cons,axiom,
% 155.55/155.57 ! [V_x,V_ys,V_xs,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__ConsD,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,V_y_2,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => ( V_y_2 = V_x_2
% 155.55/155.57 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_zip__Cons__Cons,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__subset__Cons,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_foldr_Osimps_I2_J,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrelp_OCons,axiom,
% 155.55/155.57 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 155.55/155.57 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2)
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrelp_Oequations_I2_J,axiom,
% 155.55/155.57 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 155.55/155.57 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list_Oinject,axiom,
% 155.55/155.57 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 <=> ( V_a_2 = V_a_H_2
% 155.55/155.57 & V_list_2 = V_list_H_2 ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_not__Cons__self2,axiom,
% 155.55/155.57 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 155.55/155.57
% 155.55/155.57 fof(fact_not__Cons__self,axiom,
% 155.55/155.57 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map_Osimps_I2_J,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_remove1_Osimps_I2_J,axiom,
% 155.55/155.57 ! [V_xs,T_a,V_y,V_x] :
% 155.55/155.57 ( ( V_x = V_y
% 155.55/155.57 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 155.55/155.57 & ( V_x != V_y
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_insort__key_Osimps_I2_J,axiom,
% 155.55/155.57 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( ( 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)))
% 155.55/155.57 => 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)) )
% 155.55/155.57 & ( ~ 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)))
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct_Osimps_I2_J,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))
% 155.55/155.57 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of__Cons__code_I2_J,axiom,
% 155.55/155.57 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 155.55/155.57 ( ( V_l = V_k
% 155.55/155.57 => 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) )
% 155.55/155.57 & ( V_l != V_k
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list_Osize_I4_J,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel_OCons,axiom,
% 155.55/155.57 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__of_Osimps_I2_J,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Cons__in__lex,axiom,
% 155.55/155.57 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 <=> ( ( 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))
% 155.55/155.57 & 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) )
% 155.55/155.57 | ( V_x_2 = V_y_2
% 155.55/155.57 & 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))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel__Cons,axiom,
% 155.55/155.57 ! [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))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__Cons__def,axiom,
% 155.55/155.57 ! [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)))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel__Cons2,axiom,
% 155.55/155.57 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ~ ! [B_x,B_xs] :
% 155.55/155.57 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 155.55/155.57 => ( 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))
% 155.55/155.57 => ~ 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))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel__Cons1,axiom,
% 155.55/155.57 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ~ ! [B_y,B_ys] :
% 155.55/155.57 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys)
% 155.55/155.57 => ( 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))
% 155.55/155.57 => ~ 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))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_insort__insert__insort__key,axiom,
% 155.55/155.57 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( ~ 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))))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lexord__cons__cons,axiom,
% 155.55/155.57 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 <=> ( 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))
% 155.55/155.57 | ( V_a_2 = V_b_2
% 155.55/155.57 & 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))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__insort__insert,axiom,
% 155.55/155.57 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_b)
% 155.55/155.57 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_insort__insert__triv,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__insort__insert,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_insort__insert__key__triv,axiom,
% 155.55/155.57 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( 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))))
% 155.55/155.57 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lexord__lex,axiom,
% 155.55/155.57 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 <=> ( 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)))
% 155.55/155.57 & 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_insort__insert__insort,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( class_Orderings_Olinorder(T_a)
% 155.55/155.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__zip,axiom,
% 155.55/155.57 ! [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)))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list_Osize_I2_J,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__Cons__0,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__Cons__Suc,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__zip,axiom,
% 155.55/155.57 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__eq__iff__nth__eq,axiom,
% 155.55/155.57 ! [T_a,V_ys_2,V_xs_2] :
% 155.55/155.57 ( V_xs_2 = V_ys_2
% 155.55/155.57 <=> ( 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)
% 155.55/155.57 & ! [B_i] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__size__map,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth_Osimps,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_all__set__conv__all__nth,axiom,
% 155.55/155.57 ! [V_P_2,V_xs_2,T_a] :
% 155.55/155.57 ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.57 <=> ! [B_i] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__map,axiom,
% 155.55/155.57 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__conv__nth,axiom,
% 155.55/155.57 ! [V_xs_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.55/155.57 <=> ! [B_i] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ! [B_j] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( B_i != B_j
% 155.55/155.57 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__eq__iff__index__eq,axiom,
% 155.55/155.57 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => ( 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)
% 155.55/155.57 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__mem,axiom,
% 155.55/155.57 ! [V_xs_2,T_a,V_n_2] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_in__set__conv__nth,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 <=> ? [B_i] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__Cons_H,axiom,
% 155.55/155.57 ! [V_xs,V_x,T_a,V_n] :
% 155.55/155.57 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.57 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 155.55/155.57 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__conv__nth,axiom,
% 155.55/155.57 ! [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))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__Cons__number__of,axiom,
% 155.55/155.57 ! [V_xs,V_x,T_a,V_v] :
% 155.55/155.57 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.57 => 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 )
% 155.55/155.57 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__size__estimation,axiom,
% 155.55/155.57 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__size__estimation_H,axiom,
% 155.55/155.57 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__sublist,axiom,
% 155.55/155.57 ! [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))))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel__iff__nth,axiom,
% 155.55/155.57 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 <=> ( 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)
% 155.55/155.57 & ! [B_n] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lexord__take__index__conv,axiom,
% 155.55/155.57 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 <=> ( ( 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)))
% 155.55/155.57 & 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 )
% 155.55/155.57 | ? [B_i] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2)
% 155.55/155.57 & 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)) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__list__update,axiom,
% 155.55/155.57 ! [V_i_2,V_a_2,V_xs_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.55/155.57 => ( ~ 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))))))
% 155.55/155.57 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__take,axiom,
% 155.55/155.57 ! [V_xs,T_a,V_n,V_i] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__list__update__neq,axiom,
% 155.55/155.57 ! [V_x,V_xs,T_a,V_j,V_i] :
% 155.55/155.57 ( V_i != V_j
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__update__id,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__update__beyond,axiom,
% 155.55/155.57 ! [V_x,V_i,V_xs,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_take__all,axiom,
% 155.55/155.57 ! [V_n,V_xs,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__take__subset,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__take,axiom,
% 155.55/155.57 ! [V_i,V_xs,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.55/155.57 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__update,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_take__map,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__update__overwrite,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__update__swap,axiom,
% 155.55/155.57 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 155.55/155.57 ( V_i != V_i_H
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_take__take,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_update__zip,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_take__zip,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_zip__update,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_length__take,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_length__list__update,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_in__set__takeD,axiom,
% 155.55/155.57 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__update_Osimps_I2_J,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__update__code_I3_J,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_take__Suc__Cons,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__update__code_I2_J,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_sublist__upt__eq__take,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__take__subset__set__take,axiom,
% 155.55/155.57 ! [V_xs_2,T_a,V_n_2,V_m_2] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.55/155.57 => 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__update__subsetI,axiom,
% 155.55/155.57 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__update__subset__insert,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__list__update,axiom,
% 155.55/155.57 ! [V_x,V_j,V_xs,T_a,V_i] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( ( V_i = V_j
% 155.55/155.57 => 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 )
% 155.55/155.57 & ( V_i != V_j
% 155.55/155.57 => 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) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__update__same__conv,axiom,
% 155.55/155.57 ! [V_x_2,V_xs_2,T_a,V_i_2] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 155.55/155.57 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__list__update__eq,axiom,
% 155.55/155.57 ! [V_x,V_xs,T_a,V_i] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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 ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_set__update__memI,axiom,
% 155.55/155.57 ! [V_x_2,V_xs_2,T_a,V_n_2] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__upd__upds__conv__if,axiom,
% 155.55/155.57 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] :
% 155.55/155.57 ( ( 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))))
% 155.55/155.57 => 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) )
% 155.55/155.57 & ( ~ 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))))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel__subset,axiom,
% 155.55/155.57 ! [V_A_2,V_r_2,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => 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))))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__le__upds,axiom,
% 155.55/155.57 ! [V_bs_2,V_as_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__add__upds,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lists__mono,axiom,
% 155.55/155.57 ! [V_B_2,V_A_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__upds__apply__nontin,axiom,
% 155.55/155.57 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lists__UNIV,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_equiv__listrel,axiom,
% 155.55/155.57 ! [V_r_2,V_A_2,T_a] :
% 155.55/155.57 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel__refl__on,axiom,
% 155.55/155.57 ! [V_r_2,V_A_2,T_a] :
% 155.55/155.57 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__upds__Cons,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Cons__in__lists__iff,axiom,
% 155.55/155.57 ! [V_A_2,V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.55/155.57 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_in__lists__conv__set,axiom,
% 155.55/155.57 ! [V_A_2,V_xs_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 155.55/155.57 <=> ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__upds__list__update2__drop,axiom,
% 155.55/155.57 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__upds__twist,axiom,
% 155.55/155.57 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] :
% 155.55/155.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2)))
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lists__eq__set,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_restrict__map__upds,axiom,
% 155.55/155.57 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] :
% 155.55/155.57 ( 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)
% 155.55/155.57 => ( 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))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_dom__map__upds,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel1__subset__listrel,axiom,
% 155.55/155.57 ! [V_r_H_2,V_r_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2)
% 155.55/155.57 => 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lexord__irreflexive,axiom,
% 155.55/155.57 ! [V_y_2,V_r_2,T_a] :
% 155.55/155.57 ( ! [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))
% 155.55/155.57 => ~ 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Cons__acc__listrel1I,axiom,
% 155.55/155.57 ! [V_xs_2,V_r_2,V_x_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 155.55/155.57 => ( 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))))
% 155.55/155.57 => 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)))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel1__mono,axiom,
% 155.55/155.57 ! [V_s_2,V_r_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel1I2,axiom,
% 155.55/155.57 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel1__eq__len,axiom,
% 155.55/155.57 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lists__accI,axiom,
% 155.55/155.57 ! [V_r_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lists__accD,axiom,
% 155.55/155.57 ! [V_r_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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))))
% 155.55/155.57 => 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel1I1,axiom,
% 155.55/155.57 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 155.55/155.57 ( 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))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Cons__listrel1__Cons,axiom,
% 155.55/155.57 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 <=> ( ( 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))
% 155.55/155.57 & V_xs_2 = V_ys_2 )
% 155.55/155.57 | ( V_x_2 = V_y_2
% 155.55/155.57 & 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))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listrel1__iff__update,axiom,
% 155.55/155.57 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 <=> ? [B_y,B_n] :
% 155.55/155.57 ( 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))
% 155.55/155.57 & 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)))
% 155.55/155.57 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_lexord__linear,axiom,
% 155.55/155.57 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 155.55/155.57 ( ! [B_a,B_b] :
% 155.55/155.57 ( 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))
% 155.55/155.57 | B_a = B_b
% 155.55/155.57 | 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)) )
% 155.55/155.57 => ( 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)))
% 155.55/155.57 | V_x_2 = V_y_2
% 155.55/155.57 | 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))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__setsum__nth,axiom,
% 155.55/155.57 ! [V_xs_2,T_a] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__size__pointwise,axiom,
% 155.55/155.57 ! [V_g_2,V_f_2,V_xs_2,T_a] :
% 155.55/155.57 ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 155.55/155.57 ! [V_ns_2] :
% 155.55/155.57 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.57 <=> ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 155.55/155.57 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__simps_I2_J,axiom,
% 155.55/155.57 ! [V_xs,V_x,T_a] :
% 155.55/155.57 ( class_Groups_Omonoid__add(T_a)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_elem__le__listsum__nat,axiom,
% 155.55/155.57 ! [V_ns,V_k] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__0,axiom,
% 155.55/155.57 ! [V_xs_2,T_b,T_a] :
% 155.55/155.57 ( class_Groups_Omonoid__add(T_a)
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__addf,axiom,
% 155.55/155.57 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__mult__const,axiom,
% 155.55/155.57 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( class_Rings_Osemiring__0(T_a)
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__const__mult,axiom,
% 155.55/155.57 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] :
% 155.55/155.57 ( class_Rings_Osemiring__0(T_a)
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__subtractf,axiom,
% 155.55/155.57 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__update__nat,axiom,
% 155.55/155.57 ! [V_n,V_ns,V_k] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__abs,axiom,
% 155.55/155.57 ! [V_xs_2,T_a] :
% 155.55/155.57 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 155.55/155.57 => 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)))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_uminus__listsum__map,axiom,
% 155.55/155.57 ! [V_xs_2,V_f_2,T_b,T_a] :
% 155.55/155.57 ( class_Groups_Oab__group__add(T_a)
% 155.55/155.57 => 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)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_list__size__conv__listsum,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 155.55/155.57 ! [V_xs_2,T_a] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.57 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 155.55/155.57 ! [V_f_2,V_xs_2,T_a,T_b] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.57 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.55/155.57 => 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)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 155.55/155.57 ! [V_j_2,V_i_2,V_f_2,T_a] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 155.55/155.57 ! [V_l_2,V_k_2,V_f_2,T_a] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__triv,axiom,
% 155.55/155.57 ! [V_xs_2,V_r_2,T_b,T_a] :
% 155.55/155.57 ( class_Rings_Osemiring__1(T_a)
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__map__remove1,axiom,
% 155.55/155.57 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => 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)))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 155.55/155.57 ! [V_f_2,V_A_2,T_a,T_b] :
% 155.55/155.57 ( class_Groups_Ocomm__monoid__add(T_b)
% 155.55/155.57 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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))))) )
% 155.55/155.57 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_listsum__mono,axiom,
% 155.55/155.57 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] :
% 155.55/155.57 ( ( class_Groups_Omonoid__add(T_b)
% 155.55/155.57 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 155.55/155.57 => ( ! [B_x] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 155.55/155.57 => 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)))) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_someI,axiom,
% 155.55/155.57 ! [T_a,V_x_2,V_P_2] :
% 155.55/155.57 ( hBOOL(hAPP(V_P_2,V_x_2))
% 155.55/155.57 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_tfl__some,axiom,
% 155.55/155.57 ! [T_a,B_P] :
% 155.55/155.57 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 155.55/155.57 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_someI__ex,axiom,
% 155.55/155.57 ! [T_a,V_P_2] :
% 155.55/155.57 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 155.55/155.57 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_some__eq__ex,axiom,
% 155.55/155.57 ! [T_a,V_P_2] :
% 155.55/155.57 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2)))
% 155.55/155.57 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_some__eq__trivial,axiom,
% 155.55/155.57 ! [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 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_some__sym__eq__trivial,axiom,
% 155.55/155.57 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 155.55/155.57
% 155.55/155.57 fof(fact_exE__some,axiom,
% 155.55/155.57 ! [T_a,V_ca_2,V_P_2] :
% 155.55/155.57 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 155.55/155.57 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2)
% 155.55/155.57 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Nitpick_Ocard_H__def,axiom,
% 155.55/155.57 ! [V_A_2,T_a] :
% 155.55/155.57 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => 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)))) )
% 155.55/155.57 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.55/155.57 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_LeastM__def,axiom,
% 155.55/155.57 ! [V_P_2,V_m_2,T_a,T_b] :
% 155.55/155.57 ( class_Orderings_Oord(T_b)
% 155.55/155.57 => 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))))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_LeastM__nat__lemma,axiom,
% 155.55/155.57 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 155.55/155.57 ( hBOOL(hAPP(V_P_2,V_k_2))
% 155.55/155.57 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2)))
% 155.55/155.57 & ! [B_y] :
% 155.55/155.57 ( hBOOL(hAPP(V_P_2,B_y))
% 155.55/155.57 => 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))) ) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_LeastM__nat__le,axiom,
% 155.55/155.57 ! [T_a,V_m_2,V_x_2,V_P_2] :
% 155.55/155.57 ( hBOOL(hAPP(V_P_2,V_x_2))
% 155.55/155.57 => 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))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_split__paired__Eps,axiom,
% 155.55/155.57 ! [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)))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Eps__split__eq,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Eps__split,axiom,
% 155.55/155.57 ! [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))) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_GreatestM__def,axiom,
% 155.55/155.57 ! [V_P_2,V_m_2,T_a,T_b] :
% 155.55/155.57 ( class_Orderings_Oord(T_b)
% 155.55/155.57 => 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))))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_butlast__take,axiom,
% 155.55/155.57 ! [V_xs,T_a,V_n] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_LeastM__natI,axiom,
% 155.55/155.57 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 155.55/155.57 ( hBOOL(hAPP(V_P_2,V_k_2))
% 155.55/155.57 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_map__butlast,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_in__set__butlastD,axiom,
% 155.55/155.57 ! [V_xs_2,V_x_2,T_a] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 155.55/155.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_take__butlast,axiom,
% 155.55/155.57 ! [V_xs,T_a,V_n] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => 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) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_length__butlast,axiom,
% 155.55/155.57 ! [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)) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_butlast__conv__take,axiom,
% 155.55/155.57 ! [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) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_butlast__list__update,axiom,
% 155.55/155.57 ! [V_x,V_xs,T_a,V_k] :
% 155.55/155.57 ( ( 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))
% 155.55/155.57 => 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) )
% 155.55/155.57 & ( 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))
% 155.55/155.57 => 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) ) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_Greatest__def,axiom,
% 155.55/155.57 ! [T_a] :
% 155.55/155.57 ( class_Orderings_Oord(T_a)
% 155.55/155.57 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ).
% 155.55/155.57
% 155.55/155.57 fof(fact_nth__take__lemma,axiom,
% 155.55/155.57 ! [V_ys,V_xs,T_a,V_k] :
% 155.55/155.57 ( 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)))
% 155.55/155.57 => ( 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)))
% 155.55/155.57 => ( ! [B_i] :
% 155.55/155.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 155.55/155.57 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 155.55/155.58 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_take__Cons__number__of,axiom,
% 155.55/155.58 ! [V_xs,V_x,T_a,V_v] :
% 155.55/155.58 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.58 => 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) )
% 155.55/155.58 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.58 => 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)) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_partition__set,axiom,
% 155.55/155.58 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 155.55/155.58 ( 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)
% 155.55/155.58 => 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) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_lists_ONil,axiom,
% 155.55/155.58 ! [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))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listrel__Nil2,axiom,
% 155.55/155.58 ! [V_r_2,V_xs_2,T_a] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listrel__Nil1,axiom,
% 155.55/155.58 ! [V_r_2,V_xs_2,T_a] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_sorted__list__of__set__empty,axiom,
% 155.55/155.58 ! [T_a] :
% 155.55/155.58 ( class_Orderings_Olinorder(T_a)
% 155.55/155.58 => 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) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list_Osimps_I3_J,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list_Osimps_I2_J,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_insort__key_Osimps_I1_J,axiom,
% 155.55/155.58 ! [V_x_2,V_f_2,T_a,T_b] :
% 155.55/155.58 ( class_Orderings_Olinorder(T_b)
% 155.55/155.58 => 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)) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_partition_Osimps_I1_J,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_sublist__nil,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_upto__empty,axiom,
% 155.55/155.58 ! [V_i,V_j] :
% 155.55/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 155.55/155.58 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_zip__Nil,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_zip_Osimps_I1_J,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_foldr_Osimps_I1_J,axiom,
% 155.55/155.58 ! [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 ).
% 155.55/155.58
% 155.55/155.58 fof(fact_map__of__Cons__code_I1_J,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_remove1_Osimps_I1_J,axiom,
% 155.55/155.58 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_distinct_Osimps_I1_J,axiom,
% 155.55/155.58 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_insort__not__Nil,axiom,
% 155.55/155.58 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] :
% 155.55/155.58 ( class_Orderings_Olinorder(T_b)
% 155.55/155.58 => 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) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listrelp_Oequations_I1_J,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listrelp_ONil,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list_Osize_I1_J,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_map__upds__Nil1,axiom,
% 155.55/155.58 ! [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 ).
% 155.55/155.58
% 155.55/155.58 fof(fact_map__upds__Nil2,axiom,
% 155.55/155.58 ! [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 ).
% 155.55/155.58
% 155.55/155.58 fof(fact_take__eq__Nil,axiom,
% 155.55/155.58 ! [V_xs_2,V_n_2,T_a] :
% 155.55/155.58 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 155.55/155.58 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.58 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_take__0,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_take__Nil,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list__update__nonempty,axiom,
% 155.55/155.58 ! [V_x_2,V_k_2,V_xs_2,T_a] :
% 155.55/155.58 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a)
% 155.55/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list__update_Osimps_I1_J,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list__update__code_I1_J,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_map__is__Nil__conv,axiom,
% 155.55/155.58 ! [V_xs_2,V_f_2,T_a,T_b] :
% 155.55/155.58 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 155.55/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_map_Osimps_I1_J,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_Nil__is__map__conv,axiom,
% 155.55/155.58 ! [V_xs_2,V_f_2,T_b,T_a] :
% 155.55/155.58 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)
% 155.55/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list_Osize_I3_J,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_length__0__conv,axiom,
% 155.55/155.58 ! [V_xs_2,T_a] :
% 155.55/155.58 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_set__empty2,axiom,
% 155.55/155.58 ! [V_xs_2,T_a] :
% 155.55/155.58 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2)
% 155.55/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_set__empty,axiom,
% 155.55/155.58 ! [V_xs_2,T_a] :
% 155.55/155.58 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.55/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listsum__simps_I1_J,axiom,
% 155.55/155.58 ! [T_a] :
% 155.55/155.58 ( class_Groups_Omonoid__add(T_a)
% 155.55/155.58 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_distinct__butlast,axiom,
% 155.55/155.58 ! [T_a,V_xs] :
% 155.55/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.55/155.58 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.55/155.58 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_butlast_Osimps_I1_J,axiom,
% 155.55/155.58 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_butlast_Osimps_I2_J,axiom,
% 155.55/155.58 ! [V_x,T_a,V_xs] :
% 155.55/155.58 ( ( V_xs = c_List_Olist_ONil(T_a)
% 155.55/155.58 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 155.55/155.58 & ( V_xs != c_List_Olist_ONil(T_a)
% 155.55/155.58 => 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)) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_sublist__empty,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_map__of_Osimps_I1_J,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_length__greater__0__conv,axiom,
% 155.55/155.58 ! [V_xs_2,T_a] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_take__1__Cons,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_not__listrel1__Nil,axiom,
% 155.55/155.58 ! [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))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_not__Nil__listrel1,axiom,
% 155.55/155.58 ! [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))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listrel_ONil,axiom,
% 155.55/155.58 ! [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))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_lexord__Nil__right,axiom,
% 155.55/155.58 ! [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))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_Nil__notin__lex,axiom,
% 155.55/155.58 ! [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))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_Nil2__notin__lex,axiom,
% 155.55/155.58 ! [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))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_partition__P,axiom,
% 155.55/155.58 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 155.55/155.58 ( 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)
% 155.55/155.58 => ( ! [B_x] :
% 155.55/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2)))
% 155.55/155.58 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.55/155.58 & ! [B_x] :
% 155.55/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2)))
% 155.55/155.58 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_take__Cons,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_upto_Osimps,axiom,
% 155.55/155.58 ! [V_j,V_i] :
% 155.55/155.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 155.55/155.58 => 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)) )
% 155.55/155.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 155.55/155.58 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_sublist__singleton,axiom,
% 155.55/155.58 ! [V_x_2,T_a,V_A_2] :
% 155.55/155.58 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 155.55/155.58 => 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)) )
% 155.55/155.58 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 155.55/155.58 => 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) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_partition_Osimps_I2_J,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_lists__empty,axiom,
% 155.55/155.58 ! [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))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_take__Cons_H,axiom,
% 155.55/155.58 ! [V_xs,V_x,T_a,V_n] :
% 155.55/155.58 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.58 => 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) )
% 155.55/155.58 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.55/155.58 => 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)) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_upto__rec__number__of,axiom,
% 155.55/155.58 ! [V_n,V_m] :
% 155.55/155.58 ( ( 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)))
% 155.55/155.58 => 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))) )
% 155.55/155.58 & ( ~ 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)))
% 155.55/155.58 => 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) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listrel__Nil,axiom,
% 155.55/155.58 ! [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))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_set__Cons__sing__Nil,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_upto_Opsimps,axiom,
% 155.55/155.58 ! [V_j_2,V_i_2] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 155.55/155.58 => 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)) )
% 155.55/155.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 155.55/155.58 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_anamorph_Osimps,axiom,
% 155.55/155.58 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 155.55/155.58 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 155.55/155.58 => 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) )
% 155.55/155.58 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 155.55/155.58 => 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)) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listset_Osimps_I1_J,axiom,
% 155.55/155.58 ! [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))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_zip__Cons,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list_Osimps_I5_J,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list_Osimps_I4_J,axiom,
% 155.55/155.58 ! [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 ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listset_Osimps_I2_J,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_zip__Cons1,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_upto_Opinduct,axiom,
% 155.55/155.58 ! [V_P_2,V_a1_2,V_a0_2] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => ( ! [B_i,B_j] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 155.55/155.58 => 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)) )
% 155.55/155.58 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 155.55/155.58 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_map__upds__append1,axiom,
% 155.55/155.58 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => 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)))) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append1__eq__conv,axiom,
% 155.55/155.58 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 <=> ( V_xs_2 = V_ys_2
% 155.55/155.58 & V_x_2 = V_y_2 ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_Cons__eq__append__conv,axiom,
% 155.55/155.58 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] :
% 155.55/155.58 ( 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)
% 155.55/155.58 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 155.55/155.58 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 )
% 155.55/155.58 | ? [B_ys_H] :
% 155.55/155.58 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2
% 155.55/155.58 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__eq__Cons__conv,axiom,
% 155.55/155.58 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] :
% 155.55/155.58 ( 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)
% 155.55/155.58 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 155.55/155.58 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) )
% 155.55/155.58 | ? [B_ys_H] :
% 155.55/155.58 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H)
% 155.55/155.58 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_eq__Nil__appendI,axiom,
% 155.55/155.58 ! [T_a,V_ys,V_xs] :
% 155.55/155.58 ( V_xs = V_ys
% 155.55/155.58 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__self__conv2,axiom,
% 155.55/155.58 ! [V_ys_2,V_xs_2,T_a] :
% 155.55/155.58 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2
% 155.55/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__self__conv,axiom,
% 155.55/155.58 ! [V_ys_2,V_xs_2,T_a] :
% 155.55/155.58 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2
% 155.55/155.58 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__is__Nil__conv,axiom,
% 155.55/155.58 ! [V_ys_2,V_xs_2,T_a] :
% 155.55/155.58 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a)
% 155.55/155.58 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 155.55/155.58 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_self__append__conv2,axiom,
% 155.55/155.58 ! [V_xs_2,T_a,V_ys_2] :
% 155.55/155.58 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 155.55/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_self__append__conv,axiom,
% 155.55/155.58 ! [V_ys_2,T_a,V_xs_2] :
% 155.55/155.58 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 155.55/155.58 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__Nil2,axiom,
% 155.55/155.58 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 155.55/155.58
% 155.55/155.58 fof(fact_Nil__is__append__conv,axiom,
% 155.55/155.58 ! [V_ys_2,V_xs_2,T_a] :
% 155.55/155.58 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 155.55/155.58 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 155.55/155.58 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__Nil,axiom,
% 155.55/155.58 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 155.55/155.58
% 155.55/155.58 fof(fact_butlast__append,axiom,
% 155.55/155.58 ! [V_xs,T_a,V_ys] :
% 155.55/155.58 ( ( V_ys = c_List_Olist_ONil(T_a)
% 155.55/155.58 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 155.55/155.58 & ( V_ys != c_List_Olist_ONil(T_a)
% 155.55/155.58 => 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)) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listsum__append,axiom,
% 155.55/155.58 ! [V_ys,V_xs,T_a] :
% 155.55/155.58 ( class_Groups_Omonoid__add(T_a)
% 155.55/155.58 => 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)) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_zip__append,axiom,
% 155.55/155.58 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 155.55/155.58 ( 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)
% 155.55/155.58 => ( 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)
% 155.55/155.58 => 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)) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_length__append,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_set__append,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_map__append,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_fun__upds__append2__drop,axiom,
% 155.55/155.58 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 155.55/155.58 ( 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)
% 155.55/155.58 => 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) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_fun__upds__append__drop,axiom,
% 155.55/155.58 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 155.55/155.58 ( 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)
% 155.55/155.58 => 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) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__in__lists__conv,axiom,
% 155.55/155.58 ! [V_A_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 155.55/155.58 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__assoc,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__eq__append__conv2,axiom,
% 155.55/155.58 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.58 ( 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)
% 155.55/155.58 <=> ? [B_us] :
% 155.55/155.58 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us)
% 155.55/155.58 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 )
% 155.55/155.58 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2
% 155.55/155.58 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_same__append__eq,axiom,
% 155.55/155.58 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.58 ( 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)
% 155.55/155.58 <=> V_ys_2 = V_zs_2 ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__same__eq,axiom,
% 155.55/155.58 ! [V_zs_2,V_xs_2,V_ys_2,T_a] :
% 155.55/155.58 ( 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)
% 155.55/155.58 <=> V_ys_2 = V_zs_2 ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__eq__appendI,axiom,
% 155.55/155.58 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 155.55/155.58 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 155.55/155.58 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 155.55/155.58 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_map__of__append,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_foldr__append,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_Cons__eq__appendI,axiom,
% 155.55/155.58 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 155.55/155.58 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 155.55/155.58 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 155.55/155.58 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__Cons,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_nth__append__length,axiom,
% 155.55/155.58 ! [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 ).
% 155.55/155.58
% 155.55/155.58 fof(fact_nth__append__length__plus,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_take__append,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list__update__append1,axiom,
% 155.55/155.58 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => 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) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list__update__length,axiom,
% 155.55/155.58 ! [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)) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_remove1__append,axiom,
% 155.55/155.58 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 155.55/155.58 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.58 => 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) )
% 155.55/155.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.55/155.58 => 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)) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_in__set__butlast__appendI,axiom,
% 155.55/155.58 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 155.55/155.58 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 155.55/155.58 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) )
% 155.55/155.58 => 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))))) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_butlast__snoc,axiom,
% 155.55/155.58 ! [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 ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__listrel1I,axiom,
% 155.55/155.58 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.58 ( ( ( 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)))
% 155.55/155.58 & V_us_2 = V_vs_2 )
% 155.55/155.58 | ( V_xs_2 = V_ys_2
% 155.55/155.58 & 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))) ) )
% 155.55/155.58 => 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))) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_lexord__append__leftI,axiom,
% 155.55/155.58 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => 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))) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_distinct__append,axiom,
% 155.55/155.58 ! [V_ys_2,V_xs_2,T_a] :
% 155.55/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 155.55/155.58 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.55/155.58 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 155.55/155.58 & 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)) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_nth__append,axiom,
% 155.55/155.58 ! [V_ys,V_xs,T_a,V_n] :
% 155.55/155.58 ( ( 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)))
% 155.55/155.58 => 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) )
% 155.55/155.58 & ( ~ 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)))
% 155.55/155.58 => 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))) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_list__update__append,axiom,
% 155.55/155.58 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 155.55/155.58 ( ( 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)))
% 155.55/155.58 => 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) )
% 155.55/155.58 & ( ~ 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)))
% 155.55/155.58 => 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)) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_sublist__append,axiom,
% 155.55/155.58 ! [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)))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listrel1I,axiom,
% 155.55/155.58 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 155.55/155.58 ( 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))
% 155.55/155.58 => ( 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))
% 155.55/155.58 => ( 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))
% 155.55/155.58 => 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))) ) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_lexord__append__left__rightI,axiom,
% 155.55/155.58 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] :
% 155.55/155.58 ( 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))
% 155.55/155.58 => 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))) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_take__Suc__conv__app__nth,axiom,
% 155.55/155.58 ! [V_xs,T_a,V_i] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => 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))) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 155.55/155.58 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 <=> ( ( 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)))
% 155.55/155.58 & V_x_2 = V_y_2 )
% 155.55/155.58 | ( V_xs_2 = V_ys_2
% 155.55/155.58 & 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)) ) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_sublist__Cons,axiom,
% 155.55/155.58 ! [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)))) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_listrel1E,axiom,
% 155.55/155.58 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => ~ ! [B_x,B_y] :
% 155.55/155.58 ( 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))
% 155.55/155.58 => ! [B_us,B_vs] :
% 155.55/155.58 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs))
% 155.55/155.58 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_lexord__append__leftD,axiom,
% 155.55/155.58 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => ( ! [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))
% 155.55/155.58 => 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))) ) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_rotate1__def,axiom,
% 155.55/155.58 ! [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) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_upd__conv__take__nth__drop,axiom,
% 155.55/155.58 ! [V_a,V_xs,T_a,V_i] :
% 155.55/155.58 ( 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)))
% 155.55/155.58 => 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))) ) ).
% 155.55/155.58
% 155.55/155.58 fof(fact_append__take__drop__id,axiom,
% 155.55/155.58 ! [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 ).
% 155.55/155.58
% 155.55/155.58 fof(fact_rotate1__is__Nil__conv,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 155.87/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__Nil,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__butlast,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_butlast__drop,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__drop__subset,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_in__set__dropD,axiom,
% 155.87/155.58 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 155.87/155.58 ( 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))))
% 155.87/155.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__drop,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__rotate1,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__rotate1,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__map,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_take__drop,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__take,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__drop,axiom,
% 155.87/155.58 ! [V_i,V_xs,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.87/155.58 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct1__rotate,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)))
% 155.87/155.58 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__drop,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__0,axiom,
% 155.87/155.58 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__zip,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_nth__via__drop,axiom,
% 155.87/155.58 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 155.87/155.58 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 155.87/155.58 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__1__Cons,axiom,
% 155.87/155.58 ! [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 ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__Suc__Cons,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__drop__subset__set__drop,axiom,
% 155.87/155.58 ! [V_xs_2,T_a,V_m_2,V_n_2] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 155.87/155.58 => 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)))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__all,axiom,
% 155.87/155.58 ! [V_n,V_xs,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__eq__Nil,axiom,
% 155.87/155.58 ! [V_xs_2,V_n_2,T_a] :
% 155.87/155.58 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 155.87/155.58 <=> 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__append,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_append__eq__conv__conj,axiom,
% 155.87/155.58 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 155.87/155.58 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2
% 155.87/155.58 <=> ( 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)
% 155.87/155.58 & 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__Cons,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__Cons_H,axiom,
% 155.87/155.58 ! [V_xs,V_x,T_a,V_n] :
% 155.87/155.58 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.87/155.58 => 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) )
% 155.87/155.58 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_nth__drop,axiom,
% 155.87/155.58 ! [V_xs,T_a,V_i,V_n] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_append__eq__append__conv__if,axiom,
% 155.87/155.58 ! [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] :
% 155.87/155.58 ( 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)
% 155.87/155.58 <=> ( ( 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)))
% 155.87/155.58 => ( 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)
% 155.87/155.58 & 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) ) )
% 155.87/155.58 & ( ~ 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)))
% 155.87/155.58 => ( 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
% 155.87/155.58 & 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 ) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_nth__drop_H,axiom,
% 155.87/155.58 ! [V_xs,T_a,V_i] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate__simps,axiom,
% 155.87/155.58 ! [V_xs,V_x,T_b,T_a] :
% 155.87/155.58 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 155.87/155.58 & 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__Cons__number__of,axiom,
% 155.87/155.58 ! [V_xs,V_x,T_a,V_v] :
% 155.87/155.58 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.87/155.58 => 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) )
% 155.87/155.58 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_take__add,axiom,
% 155.87/155.58 ! [V_xs,T_a,V_j,V_i] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate1__length01,axiom,
% 155.87/155.58 ! [V_xs,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_zip__append2,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_zip__append1,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_id__take__nth__drop,axiom,
% 155.87/155.58 ! [V_xs,T_a,V_i] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_take__hd__drop,axiom,
% 155.87/155.58 ! [V_xs,T_a,V_n] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_hd__drop__conv__nth,axiom,
% 155.87/155.58 ! [V_n,T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => ( 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)))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_hd_Osimps,axiom,
% 155.87/155.58 ! [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 ).
% 155.87/155.58
% 155.87/155.58 fof(fact_hd__map,axiom,
% 155.87/155.58 ! [V_f_2,T_b,T_a,V_xs_2] :
% 155.87/155.58 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_hd__append,axiom,
% 155.87/155.58 ! [V_ys,T_a,V_xs] :
% 155.87/155.58 ( ( V_xs = c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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) )
% 155.87/155.58 & ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_hd__append2,axiom,
% 155.87/155.58 ! [V_ys,T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_hd__in__set,axiom,
% 155.87/155.58 ! [T_a,V_xs_2] :
% 155.87/155.58 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_hd__conv__nth,axiom,
% 155.87/155.58 ! [T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate1__hd__tl,axiom,
% 155.87/155.58 ! [T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_hd__rotate__conv__nth,axiom,
% 155.87/155.58 ! [V_n,T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_tl__drop,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__tl,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate__is__Nil__conv,axiom,
% 155.87/155.58 ! [V_xs_2,V_n_2,T_a] :
% 155.87/155.58 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 155.87/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_tl_Osimps_I1_J,axiom,
% 155.87/155.58 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__rotate,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__rotate,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__tl,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate__map,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__tl,axiom,
% 155.87/155.58 ! [V_xs,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.87/155.58 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__rotate,axiom,
% 155.87/155.58 ! [V_xs_2,V_n_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)))
% 155.87/155.58 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate__rotate,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_tl_Osimps_I2_J,axiom,
% 155.87/155.58 ! [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 ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate1__rotate__swap,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_tl__append2,axiom,
% 155.87/155.58 ! [V_ys,T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_take__tl,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate__conv__mod,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__Suc,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate__Suc,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_tl__append,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate0,axiom,
% 155.87/155.58 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate__add,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate__id,axiom,
% 155.87/155.58 ! [V_xs,T_a,V_n] :
% 155.87/155.58 ( 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)
% 155.87/155.58 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate__length01,axiom,
% 155.87/155.58 ! [V_n,V_xs,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__tl,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_tl__take,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_take__Suc,axiom,
% 155.87/155.58 ! [V_n,T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate__drop__take,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_fold1__set,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 155.87/155.58 => ( V_xs_2 != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_lexord__append__rightI,axiom,
% 155.87/155.58 ! [V_r_2,V_x_2,T_a,V_y_2] :
% 155.87/155.58 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldl__Cons,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_start__le__sum,axiom,
% 155.87/155.58 ! [V_ns_2,V_n_2,V_m_2] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldl__assoc,axiom,
% 155.87/155.58 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 155.87/155.58 ( class_Groups_Osemigroup__add(T_a)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldl__absorb0,axiom,
% 155.87/155.58 ! [V_zs_2,V_x_2,T_a] :
% 155.87/155.58 ( class_Groups_Omonoid__add(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldr__conv__foldl,axiom,
% 155.87/155.58 ! [V_a_2,V_xs_2,T_a] :
% 155.87/155.58 ( class_Groups_Oab__semigroup__add(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldl__map,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldl__Nil,axiom,
% 155.87/155.58 ! [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 ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldl__append,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_listsum__foldl,axiom,
% 155.87/155.58 ! [T_a] :
% 155.87/155.58 ( class_Groups_Omonoid__add(T_a)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldl__foldr1,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( class_Groups_Omonoid__add(T_a)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldl__foldr1__lemma,axiom,
% 155.87/155.58 ! [V_xs_2,V_a_2,T_a] :
% 155.87/155.58 ( class_Groups_Omonoid__add(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sum__eq__0__conv,axiom,
% 155.87/155.58 ! [V_ns_2,V_m_2] :
% 155.87/155.58 ( 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)
% 155.87/155.58 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.87/155.58 & ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 155.87/155.58 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Sup__fin__set__fold,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( class_Lattices_Olattice(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Inf__fin__set__fold,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( class_Lattices_Olattice(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Min__fin__set__fold,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Max__fin__set__fold,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_SUPR__set__fold,axiom,
% 155.87/155.58 ! [V_f_2,V_xs_2,T_b,T_a] :
% 155.87/155.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__upds__fold__map__upd,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_elem__le__sum,axiom,
% 155.87/155.58 ! [V_ns_2,V_n_2] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_lexord__Nil__left,axiom,
% 155.87/155.58 ! [V_r_2,V_y_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__list__update,axiom,
% 155.87/155.58 ! [V_x,V_k,T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => ( ( 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))
% 155.87/155.58 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 155.87/155.58 & ( 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))
% 155.87/155.58 => 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) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__ConsL,axiom,
% 155.87/155.58 ! [V_x,T_a,V_xs] :
% 155.87/155.58 ( V_xs = c_List_Olist_ONil(T_a)
% 155.87/155.58 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__ConsR,axiom,
% 155.87/155.58 ! [V_x,T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last_Osimps,axiom,
% 155.87/155.58 ! [V_x,T_a,V_xs] :
% 155.87/155.58 ( ( V_xs = c_List_Olist_ONil(T_a)
% 155.87/155.58 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 155.87/155.58 & ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__map,axiom,
% 155.87/155.58 ! [V_f_2,T_b,T_a,V_xs_2] :
% 155.87/155.58 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__appendL,axiom,
% 155.87/155.58 ! [V_xs,T_a,V_ys] :
% 155.87/155.58 ( V_ys = c_List_Olist_ONil(T_a)
% 155.87/155.58 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__appendR,axiom,
% 155.87/155.58 ! [V_xs,T_a,V_ys] :
% 155.87/155.58 ( V_ys != c_List_Olist_ONil(T_a)
% 155.87/155.58 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__append,axiom,
% 155.87/155.58 ! [V_xs,T_a,V_ys] :
% 155.87/155.58 ( ( V_ys = c_List_Olist_ONil(T_a)
% 155.87/155.58 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 155.87/155.58 & ( V_ys != c_List_Olist_ONil(T_a)
% 155.87/155.58 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__in__set,axiom,
% 155.87/155.58 ! [T_a,V_as_2] :
% 155.87/155.58 ( V_as_2 != c_List_Olist_ONil(T_a)
% 155.87/155.58 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__snoc,axiom,
% 155.87/155.58 ! [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 ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__drop,axiom,
% 155.87/155.58 ! [V_xs,T_a,V_n] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_snoc__eq__iff__butlast,axiom,
% 155.87/155.58 ! [V_ys_2,V_x_2,V_xs_2,T_a] :
% 155.87/155.58 ( 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
% 155.87/155.58 <=> ( V_ys_2 != c_List_Olist_ONil(T_a)
% 155.87/155.58 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2
% 155.87/155.58 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_append__butlast__last__id,axiom,
% 155.87/155.58 ! [T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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 ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__conv__nth,axiom,
% 155.87/155.58 ! [T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_lists_Osimps,axiom,
% 155.87/155.58 ! [V_A_2,V_a_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2)))
% 155.87/155.58 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 155.87/155.58 | ? [B_a,B_l] :
% 155.87/155.58 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l)
% 155.87/155.58 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 155.87/155.58 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INFI__set__fold,axiom,
% 155.87/155.58 ! [V_f_2,V_xs_2,T_b,T_a] :
% 155.87/155.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF1__E,axiom,
% 155.87/155.58 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 155.87/155.58 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF1__D,axiom,
% 155.87/155.58 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.87/155.58 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__D,axiom,
% 155.87/155.58 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 155.87/155.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__E,axiom,
% 155.87/155.58 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2)))
% 155.87/155.58 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF2__E,axiom,
% 155.87/155.58 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 155.87/155.58 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF2__D,axiom,
% 155.87/155.58 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.87/155.58 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_finite__INT,axiom,
% 155.87/155.58 ! [V_A_2,T_b,V_I_2,T_a] :
% 155.87/155.58 ( ? [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2))
% 155.87/155.58 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) )
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__extend__simps_I10_J,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__simps_I10_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF__INT__eq2,axiom,
% 155.87/155.58 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 <=> 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_le__INF__iff,axiom,
% 155.87/155.58 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] :
% 155.87/155.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.58 => ( 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)))
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.87/155.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__subset__iff,axiom,
% 155.87/155.58 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 155.87/155.58 => 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Image__INT__subset,axiom,
% 155.87/155.58 ! [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)))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__lower,axiom,
% 155.87/155.58 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__absorb,axiom,
% 155.87/155.58 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__insert,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__extend__simps_I1_J,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.87/155.58 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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 )
% 155.87/155.58 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__extend__simps_I2_J,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.87/155.58 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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 )
% 155.87/155.58 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF__const,axiom,
% 155.87/155.58 ! [V_M_2,T_a,V_A_2,T_b] :
% 155.87/155.58 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 155.87/155.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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 ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__simps_I5_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__extend__simps_I5_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__constant,axiom,
% 155.87/155.58 ! [V_ca_2,T_b,T_a,V_A_2] :
% 155.87/155.58 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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)) )
% 155.87/155.58 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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 ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__empty,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF__INT__eq,axiom,
% 155.87/155.58 ! [V_x_2,V_r_2,T_b,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 <=> 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__insert__distrib,axiom,
% 155.87/155.58 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__iff,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.87/155.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Collect__ball__eq,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_a,T_b] :
% 155.87/155.58 ( 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))
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.87/155.58 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_b,T_a] :
% 155.87/155.58 ( 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)
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.87/155.58 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__simps_I7_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__simps_I6_J,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__extend__simps_I7_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Un__INT__distrib,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__extend__simps_I6_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Un__INT__distrib2,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_vimage__INT,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Pow__INT__eq,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INFI__apply,axiom,
% 155.87/155.58 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 155.87/155.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF__commute,axiom,
% 155.87/155.58 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 155.87/155.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF__less__iff,axiom,
% 155.87/155.58 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] :
% 155.87/155.58 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.58 & class_Orderings_Olinorder(T_a) )
% 155.87/155.58 => ( 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))
% 155.87/155.58 <=> ? [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 155.87/155.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_UN__extend__simps_I7_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_UN__simps_I7_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__simps_I9_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__extend__simps_I9_J,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Compl__INT,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Compl__UN,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INFI__bool__eq,axiom,
% 155.87/155.58 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__Int__distrib,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__Un,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF__subset,axiom,
% 155.87/155.58 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 155.87/155.58 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.87/155.58 => 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INTER__def,axiom,
% 155.87/155.58 ! [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)))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__simps_I2_J,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.87/155.58 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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)) )
% 155.87/155.58 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__simps_I1_J,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.87/155.58 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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)) )
% 155.87/155.58 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Collect__all__eq,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__simps_I3_J,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.87/155.58 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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)) )
% 155.87/155.58 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__extend__simps_I3_J,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.87/155.58 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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) )
% 155.87/155.58 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__extend__simps_I4_J,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.87/155.58 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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 )
% 155.87/155.58 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF__leI,axiom,
% 155.87/155.58 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 155.87/155.58 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 155.87/155.58 => 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__greaterThan__UNIV,axiom,
% 155.87/155.58 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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INT__simps_I4_J,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 155.87/155.58 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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)) )
% 155.87/155.58 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose__aux__max,axiom,
% 155.87/155.58 ! [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)))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_lists__IntI,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,V_l_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2)))
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2)))
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_listsp_ONil,axiom,
% 155.87/155.58 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF1__iff,axiom,
% 155.87/155.58 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.87/155.58 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_INF2__iff,axiom,
% 155.87/155.58 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.87/155.58 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__append,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_append__in__listsp__conv,axiom,
% 155.87/155.58 ! [V_ys_2,V_xs_2,V_A_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 155.87/155.58 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 155.87/155.58 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_listsp_Oequations_I1_J,axiom,
% 155.87/155.58 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter_Osimps_I1_J,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__empty__conv,axiom,
% 155.87/155.58 ! [V_xs_2,V_P_2,T_a] :
% 155.87/155.58 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_partition__filter1,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__filter__le,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__is__subset,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__map,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sum__length__filter__compl,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_in__listsp__conv__set,axiom,
% 155.87/155.58 ! [V_xs_2,V_A_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__id__conv,axiom,
% 155.87/155.58 ! [V_xs_2,V_P_2,T_a] :
% 155.87/155.58 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_listsp__inf__eq,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_listsp__infI,axiom,
% 155.87/155.58 ! [V_B_2,V_l_2,V_A_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2))
% 155.87/155.58 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2))
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__insort__triv,axiom,
% 155.87/155.58 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_b)
% 155.87/155.58 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__filter,axiom,
% 155.87/155.58 ! [V_P_2,V_xs_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.87/155.58 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_remove1__filter__not,axiom,
% 155.87/155.58 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 155.87/155.58 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__remove1,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_listsp__conj__eq,axiom,
% 155.87/155.58 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2))
% 155.87/155.58 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__filter,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_listsp_Oequations_I2_J,axiom,
% 155.87/155.58 ! [V_a2_2,V_a1_2,V_A_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2)))
% 155.87/155.58 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 155.87/155.58 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter_Osimps_I2_J,axiom,
% 155.87/155.58 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 155.87/155.58 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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)) )
% 155.87/155.58 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_partition__filter2,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__filter,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__filter__map,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__filter__less,axiom,
% 155.87/155.58 ! [V_P_2,V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_partition__filter__conv,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_listsp__mono,axiom,
% 155.87/155.58 ! [V_B_2,V_A_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__minus__filter__out,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__in__sublist,axiom,
% 155.87/155.58 ! [V_s_2,V_xs_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_listsp__lists__eq,axiom,
% 155.87/155.58 ! [V_x_2,V_A_2,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__filter__conv__card,axiom,
% 155.87/155.58 ! [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))))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_lists__Int__eq,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__filter__def,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose__max__length,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose_Osimps_I2_J,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose__map__map,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__filter__simps_I2_J,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose__empty,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a))
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 155.87/155.58 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose_Osimps_I1_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__of__filter__in,axiom,
% 155.87/155.58 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] :
% 155.87/155.58 ( 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)
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__filter__simps_I1_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sublist__shift__lemma__Suc,axiom,
% 155.87/155.58 ! [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)))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_nth__transpose,axiom,
% 155.87/155.58 ! [V_xs_2,T_a,V_i_2] :
% 155.87/155.58 ( 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))))
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__transpose,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__filter__map__filter,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_insort__key__remove1,axiom,
% 155.87/155.58 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_b)
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 155.87/155.58 => ( 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
% 155.87/155.58 => 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 ) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sublist__def,axiom,
% 155.87/155.58 ! [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))))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted_ONil,axiom,
% 155.87/155.58 ! [T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__single,axiom,
% 155.87/155.58 ! [V_x,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__map__same,axiom,
% 155.87/155.58 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__filter,axiom,
% 155.87/155.58 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 155.87/155.58 => 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__same,axiom,
% 155.87/155.58 ! [V_xs_2,V_g_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_atLeastLessThan__upt,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__upt,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__drop,axiom,
% 155.87/155.58 ! [V_n,V_xs,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_drop__upt,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_hd__upt,axiom,
% 155.87/155.58 ! [V_j,V_i] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.87/155.58 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_upt__Suc__append,axiom,
% 155.87/155.58 ! [V_j,V_i] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_upt__Suc,axiom,
% 155.87/155.58 ! [V_j,V_i] :
% 155.87/155.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.87/155.58 => 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))) )
% 155.87/155.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.87/155.58 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_upt__add__eq__append,axiom,
% 155.87/155.58 ! [V_k,V_j,V_i] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_upt__eq__Nil__conv,axiom,
% 155.87/155.58 ! [V_j_2,V_i_2] :
% 155.87/155.58 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 155.87/155.58 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.87/155.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_upt__conv__Nil,axiom,
% 155.87/155.58 ! [V_i,V_j] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 155.87/155.58 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_upt__0,axiom,
% 155.87/155.58 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted_Oequations_I1_J,axiom,
% 155.87/155.58 ! [T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__butlast,axiom,
% 155.87/155.58 ! [V_xs,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__map__remove1,axiom,
% 155.87/155.58 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 155.87/155.58 => 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__insort__key,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( 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)))
% 155.87/155.58 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__Suc__upt,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__distinct__set__unique,axiom,
% 155.87/155.58 ! [V_ys_2,V_xs_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 155.87/155.58 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 155.87/155.58 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 155.87/155.58 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 155.87/155.58 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__take,axiom,
% 155.87/155.58 ! [V_n,V_xs,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__insort,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( 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))
% 155.87/155.58 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__upt,axiom,
% 155.87/155.58 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__remove1,axiom,
% 155.87/155.58 ! [V_a,V_xs,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__upt,axiom,
% 155.87/155.58 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__upto,axiom,
% 155.87/155.58 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__list__of__set__range,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__insort__insert,axiom,
% 155.87/155.58 ! [V_x_2,V_xs_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_take__upt,axiom,
% 155.87/155.58 ! [V_n,V_m,V_i] :
% 155.87/155.58 ( 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))
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_upt__conv__Cons,axiom,
% 155.87/155.58 ! [V_j,V_i] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__many,axiom,
% 155.87/155.58 ! [V_zs,V_y,V_x,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 155.87/155.58 => 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))) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__many__eq,axiom,
% 155.87/155.58 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( 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)))
% 155.87/155.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 155.87/155.58 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_upt__rec,axiom,
% 155.87/155.58 ! [V_j,V_i] :
% 155.87/155.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.87/155.58 => 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)) )
% 155.87/155.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.87/155.58 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__insort__insert__key,axiom,
% 155.87/155.58 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 155.87/155.58 => 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__tl,axiom,
% 155.87/155.58 ! [V_xs,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__upt,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__Cons,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 155.87/155.58 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 155.87/155.58 & ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__append,axiom,
% 155.87/155.58 ! [V_ys_2,V_xs_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 155.87/155.58 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 155.87/155.58 & c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 155.87/155.58 & ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => ! [B_xa] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2)))
% 155.87/155.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_upt__rec__number__of,axiom,
% 155.87/155.58 ! [V_n,V_m] :
% 155.87/155.58 ( ( 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)))
% 155.87/155.58 => 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))) )
% 155.87/155.58 & ( ~ 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)))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_upt__eq__Cons__conv,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 155.87/155.58 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 155.87/155.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 155.87/155.58 & V_i_2 = V_x_2
% 155.87/155.58 & 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 ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__upt,axiom,
% 155.87/155.58 ! [V_j,V_i] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__insort,axiom,
% 155.87/155.58 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 155.87/155.58 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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)) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__nth,axiom,
% 155.87/155.58 ! [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 ).
% 155.87/155.58
% 155.87/155.58 fof(fact_atLeastAtMost__upt,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_atLeast__upt,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 155.87/155.58 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 155.87/155.58 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 155.87/155.58 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 155.87/155.58 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_nth__upt,axiom,
% 155.87/155.58 ! [V_j,V_k,V_i] :
% 155.87/155.58 ( 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))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_greaterThanAtMost__upt,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted_Oequations_I2_J,axiom,
% 155.87/155.58 ! [V_a1_2,V_a2_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2))
% 155.87/155.58 <=> ( ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2)))
% 155.87/155.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) )
% 155.87/155.58 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_greaterThanLessThan__upt,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_nth__map__upt,axiom,
% 155.87/155.58 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__list__of__set,axiom,
% 155.87/155.58 ! [V_A_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.87/155.58 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2
% 155.87/155.58 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))
% 155.87/155.58 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_atMost__upto,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_insort__remove1,axiom,
% 155.87/155.58 ! [V_xs_2,V_a_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 155.87/155.58 => 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 ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__nth__mono,axiom,
% 155.87/155.58 ! [V_j,V_i,V_xs,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.87/155.58 => ( 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)))
% 155.87/155.58 => 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))) ) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__equals__nth__mono,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 155.87/155.58 <=> ! [B_j] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => ! [B_i] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 155.87/155.58 => 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))) ) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__sorted__distinct__set__unique,axiom,
% 155.87/155.58 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_b)
% 155.87/155.58 => ( 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)))
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 155.87/155.58 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)))
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))
% 155.87/155.58 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)))
% 155.87/155.58 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 155.87/155.58 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sublist__shift__lemma,axiom,
% 155.87/155.58 ! [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))))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose__rectangle,axiom,
% 155.87/155.58 ! [V_n_2,T_a,V_xs_2] :
% 155.87/155.58 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 155.87/155.58 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 155.87/155.58 => ( ! [B_i] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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 )
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose_Opsimps_I2_J,axiom,
% 155.87/155.58 ! [V_xss_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose_Opsimps_I1_J,axiom,
% 155.87/155.58 ! [T_a] :
% 155.87/155.58 ( 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))))
% 155.87/155.58 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose__column,axiom,
% 155.87/155.58 ! [V_i_2,V_xs_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => ( 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)))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose__aux__filter__head,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_inj__on__rev,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__is__Nil__conv,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 155.87/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Nil__is__rev__conv,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2)
% 155.87/155.58 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev_Osimps_I1_J,axiom,
% 155.87/155.58 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__concat,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__map,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__singleton__conv,axiom,
% 155.87/155.58 ! [V_x_2,V_xs_2,T_a] :
% 155.87/155.58 ( 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))
% 155.87/155.58 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_singleton__rev__conv,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( 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)
% 155.87/155.58 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_concat__conv__foldl,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__foldl__cons,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldl__conv__concat,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__rev,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2)))
% 155.87/155.58 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_concat__append,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__append,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldl__foldr,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldr__foldl,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_concat_Osimps_I1_J,axiom,
% 155.87/155.58 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__rev,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_listsum__rev,axiom,
% 155.87/155.58 ! [V_xs,T_a] :
% 155.87/155.58 ( class_Groups_Ocomm__monoid__add(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__rev__ident,axiom,
% 155.87/155.58 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__swap,axiom,
% 155.87/155.58 ! [V_ys_2,V_xs_2,T_a] :
% 155.87/155.58 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2
% 155.87/155.58 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__is__rev__conv,axiom,
% 155.87/155.58 ! [V_ys_2,V_xs_2,T_a] :
% 155.87/155.58 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2)
% 155.87/155.58 <=> V_xs_2 = V_ys_2 ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__rev,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_zip__rev,axiom,
% 155.87/155.58 ! [V_ys,T_b,V_xs,T_a] :
% 155.87/155.58 ( 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)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__filter,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_concat_Osimps_I2_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_concat__eq__Nil__conv,axiom,
% 155.87/155.58 ! [V_xss_2,T_a] :
% 155.87/155.58 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a)
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 155.87/155.58 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Nil__eq__concat__conv,axiom,
% 155.87/155.58 ! [V_xss_2,T_a] :
% 155.87/155.58 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2)
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 155.87/155.58 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__concat,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__concat,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__eq__Cons__iff,axiom,
% 155.87/155.58 ! [V_ys_2,V_y_2,V_xs_2,T_a] :
% 155.87/155.58 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
% 155.87/155.58 <=> 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev_Osimps_I2_J,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__concat,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__concat,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_hd__rev,axiom,
% 155.87/155.58 ! [T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_last__rev,axiom,
% 155.87/155.58 ! [T_a,V_xs] :
% 155.87/155.58 ( V_xs != c_List_Olist_ONil(T_a)
% 155.87/155.58 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__transpose,axiom,
% 155.87/155.58 ! [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)))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__drop,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__take,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rotate__rev,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose_Osimps_I3_J,axiom,
% 155.87/155.58 ! [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))))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__nth,axiom,
% 155.87/155.58 ! [V_xs,T_a,V_n] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_concat__injective,axiom,
% 155.87/155.58 ! [V_ys_2,V_xs_2,T_a] :
% 155.87/155.58 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 155.87/155.58 => ( 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)
% 155.87/155.58 => ( ! [B_x] :
% 155.87/155.58 ( 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))))
% 155.87/155.58 => 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)) )
% 155.87/155.58 => V_xs_2 = V_ys_2 ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_concat__eq__concat__iff,axiom,
% 155.87/155.58 ! [V_ys_2,V_xs_2,T_a] :
% 155.87/155.58 ( ! [B_x] :
% 155.87/155.58 ( 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))))
% 155.87/155.58 => 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)) )
% 155.87/155.58 => ( 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)
% 155.87/155.58 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 155.87/155.58 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_rev__update,axiom,
% 155.87/155.58 ! [V_y,V_xs,T_a,V_k] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_concat__map__singleton,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__rev__nth__mono,axiom,
% 155.87/155.58 ! [V_j,V_i,V_xs,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 155.87/155.58 => ( 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)))
% 155.87/155.58 => 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))) ) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_foldr__max__sorted,axiom,
% 155.87/155.58 ! [V_y_2,V_xs_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2))
% 155.87/155.58 => ( ( V_xs_2 = c_List_Olist_ONil(T_a)
% 155.87/155.58 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 )
% 155.87/155.58 & ( V_xs_2 != c_List_Olist_ONil(T_a)
% 155.87/155.58 => 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) ) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose_Opsimps_I3_J,axiom,
% 155.87/155.58 ! [V_xss_2,V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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))))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__transpose__sorted,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 155.87/155.58 => 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) )
% 155.87/155.58 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a))
% 155.87/155.58 => 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))) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose__column__length,axiom,
% 155.87/155.58 ! [V_i_2,V_xs_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => ( 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)))
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose__aux__filter__tail,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_nth__nth__transpose__sorted,axiom,
% 155.87/155.58 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => ( 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))))
% 155.87/155.58 => ( 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))))
% 155.87/155.58 => 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) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transpose__transpose,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 155.87/155.58 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile__map,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_zip__takeWhile__fst,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_zip__takeWhile__snd,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__takeWhileD,axiom,
% 155.87/155.58 ! [V_xs_2,V_P_2,V_x_2,T_a] :
% 155.87/155.58 ( 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))))
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile__eq__all__conv,axiom,
% 155.87/155.58 ! [V_xs_2,V_P_2,T_a] :
% 155.87/155.58 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__takeWhile__le,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile__eq__take,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__takeWhile,axiom,
% 155.87/155.58 ! [V_P_2,V_xs_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.87/155.58 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 155.87/155.58 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 155.87/155.58 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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)) )
% 155.87/155.58 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__takeWhile,axiom,
% 155.87/155.58 ! [V_P_2,V_xs_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile__tail,axiom,
% 155.87/155.58 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] :
% 155.87/155.58 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_return__list__def,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile__append1,axiom,
% 155.87/155.58 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile__nth,axiom,
% 155.87/155.58 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 155.87/155.58 ( 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))))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_nth__length__takeWhile,axiom,
% 155.87/155.58 ! [V_xs_2,V_P_2,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => ~ 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))))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__upds__def,axiom,
% 155.87/155.58 ! [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)))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile__not__last,axiom,
% 155.87/155.58 ! [T_a,V_xs_2] :
% 155.87/155.58 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 155.87/155.58 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 155.87/155.58 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( 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)))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 155.87/155.58 ! [V_l] :
% 155.87/155.58 ( c_List_Onat__list(V_l)
% 155.87/155.58 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__remdups__concat,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__remdups,axiom,
% 155.87/155.58 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__remdups__leq,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_remdups__map__remdups,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__remdups,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_remove1__remdups,axiom,
% 155.87/155.58 ! [V_x,V_xs,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_remdups__eq__nil__iff,axiom,
% 155.87/155.58 ! [V_x_2,T_a] :
% 155.87/155.58 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a)
% 155.87/155.58 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_remdups__eq__nil__right__iff,axiom,
% 155.87/155.58 ! [V_x_2,T_a] :
% 155.87/155.58 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2)
% 155.87/155.58 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_remdups_Osimps_I1_J,axiom,
% 155.87/155.58 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__remdups,axiom,
% 155.87/155.58 ! [V_l,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_remdups__id__iff__distinct,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2
% 155.87/155.58 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__remdups__id,axiom,
% 155.87/155.58 ! [V_xs,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.87/155.58 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__remdups__eq,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( 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)
% 155.87/155.58 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_remdups__remdups,axiom,
% 155.87/155.58 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_remdups__filter,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_embed__list__def,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_remdups_Osimps_I2_J,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => 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) )
% 155.87/155.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__remdups__card__conv,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile__neq__rev,axiom,
% 155.87/155.58 ! [V_x_2,V_xs_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_dropWhile__neq__rev,axiom,
% 155.87/155.58 ! [V_x_2,V_xs_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__dropWhile__le,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__dropWhile,axiom,
% 155.87/155.58 ! [V_P_2,V_xs_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.87/155.58 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 155.87/155.58 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 155.87/155.58 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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) )
% 155.87/155.58 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__dropWhile,axiom,
% 155.87/155.58 ! [V_P_2,V_xs_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 155.87/155.58 ! [V_xs_2,V_P_2,T_a] :
% 155.87/155.58 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a)
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile__dropWhile__id,axiom,
% 155.87/155.58 ! [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 ).
% 155.87/155.58
% 155.87/155.58 fof(fact_hd__dropWhile,axiom,
% 155.87/155.58 ! [V_xs_2,V_P_2,T_a] :
% 155.87/155.58 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a)
% 155.87/155.58 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_dropWhile__map,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_dropWhile__append1,axiom,
% 155.87/155.58 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.58 => 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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 155.87/155.58 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] :
% 155.87/155.58 ( 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)
% 155.87/155.58 <=> ( 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))
% 155.87/155.58 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_dropWhile__eq__drop,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_dropWhile__nth,axiom,
% 155.87/155.58 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 155.87/155.58 ( 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))))
% 155.87/155.58 => 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)))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_listsum__map__filter,axiom,
% 155.87/155.58 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] :
% 155.87/155.58 ( class_Groups_Omonoid__add(T_b)
% 155.87/155.58 => ( ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.58 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 155.87/155.58 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) )
% 155.87/155.58 => 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)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__nth__monoI,axiom,
% 155.87/155.58 ! [V_xs,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => ( ! [B_i,B_j] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 155.87/155.58 => ( 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)))
% 155.87/155.58 => 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))) ) )
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_n__lists_Osimps_I2_J,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__sublists,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__n__lists,axiom,
% 155.87/155.58 ! [V_n,V_xs,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.87/155.58 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__set__sublists,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 155.87/155.58 => 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)))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__n__lists,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__n__lists__elem,axiom,
% 155.87/155.58 ! [V_xs_2,V_n_2,V_ys_2,T_a] :
% 155.87/155.58 ( 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))))
% 155.87/155.58 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sublists__powset,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sublists_Osimps_I1_J,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_n__lists_Osimps_I1_J,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_n__lists__Nil,axiom,
% 155.87/155.58 ! [T_a,V_n] :
% 155.87/155.58 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.87/155.58 => 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))) )
% 155.87/155.58 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.87/155.58 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sublists_Osimps_I2_J,axiom,
% 155.87/155.58 ! [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))))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__n__lists,axiom,
% 155.87/155.58 ! [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)))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_product_Osimps_I2_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__the__def,axiom,
% 155.87/155.58 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_product_Osimps_I1_J,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__product,axiom,
% 155.87/155.58 ! [V_ys,T_b,V_xs,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.87/155.58 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 155.87/155.58 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_product__list__set,axiom,
% 155.87/155.58 ! [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))) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__of__zip__enum__inject,axiom,
% 155.87/155.58 ! [V_ys_2,V_xs_2,T_a,T_b] :
% 155.87/155.58 ( ( class_Enum_Oenum(T_b)
% 155.87/155.58 & class_Enum_Oenum(T_a) )
% 155.87/155.58 => ( 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))
% 155.87/155.58 => ( 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))
% 155.87/155.58 => ( 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)))
% 155.87/155.58 => V_xs_2 = V_ys_2 ) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sort__foldl__insort,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__prod__def,axiom,
% 155.87/155.58 ! [T_b,T_a] :
% 155.87/155.58 ( ( class_Enum_Oenum(T_a)
% 155.87/155.58 & class_Enum_Oenum(T_b) )
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__distinct,axiom,
% 155.87/155.58 ! [T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__option__def,axiom,
% 155.87/155.58 ! [T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_distinct__sort,axiom,
% 155.87/155.58 ! [V_xs_2,V_f_2,T_a,T_b] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_b)
% 155.87/155.58 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)))
% 155.87/155.58 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_filter__sort,axiom,
% 155.87/155.58 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_b)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_length__sort,axiom,
% 155.87/155.58 ! [V_xs_2,V_f_2,T_a,T_b] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_b)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__sort,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sort__key__simps_I1_J,axiom,
% 155.87/155.58 ! [V_f_2,T_a,T_b] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_b)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_set__sort,axiom,
% 155.87/155.58 ! [V_xs_2,V_f_2,T_a,T_b] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_b)
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_in__enum,axiom,
% 155.87/155.58 ! [V_x_2,T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_UNIV__enum,axiom,
% 155.87/155.58 ! [T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__UNIV,axiom,
% 155.87/155.58 ! [T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__sort__key,axiom,
% 155.87/155.58 ! [V_xs_2,V_f_2,T_b,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sort__key__simps_I2_J,axiom,
% 155.87/155.58 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_b)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__fun__code,axiom,
% 155.87/155.58 ! [T_b,T_a] :
% 155.87/155.58 ( ( class_Enum_Oenum(T_a)
% 155.87/155.58 & class_HOL_Oequal(T_a)
% 155.87/155.58 & class_Enum_Oenum(T_b) )
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__fun__def,axiom,
% 155.87/155.58 ! [T_b,T_a] :
% 155.87/155.58 ( ( class_Enum_Oenum(T_a)
% 155.87/155.58 & class_Enum_Oenum(T_b) )
% 155.87/155.58 => 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))) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 155.87/155.58 ! [V_xs_2,T_a] :
% 155.87/155.58 ( class_Orderings_Olinorder(T_a)
% 155.87/155.58 => 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)) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_all__n__lists__def,axiom,
% 155.87/155.58 ! [V_n_2,V_P_2,T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2)
% 155.87/155.58 <=> ! [B_x] :
% 155.87/155.58 ( 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)))))
% 155.87/155.58 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_ex__n__lists__def,axiom,
% 155.87/155.58 ! [V_n_2,V_P_2,T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2)
% 155.87/155.58 <=> ? [B_x] :
% 155.87/155.58 ( 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)))))
% 155.87/155.58 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__all__fun__def,axiom,
% 155.87/155.58 ! [V_P_2,T_a,T_b] :
% 155.87/155.58 ( ( class_Enum_Oenum(T_b)
% 155.87/155.58 & class_Enum_Oenum(T_a) )
% 155.87/155.58 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 155.87/155.58 <=> 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__ex__fun__def,axiom,
% 155.87/155.58 ! [V_P_2,T_a,T_b] :
% 155.87/155.58 ( ( class_Enum_Oenum(T_b)
% 155.87/155.58 & class_Enum_Oenum(T_a) )
% 155.87/155.58 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 155.87/155.58 <=> 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_all__code,axiom,
% 155.87/155.58 ! [V_P_2,T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 155.87/155.58 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_exists__code,axiom,
% 155.87/155.58 ! [V_P_2,T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 155.87/155.58 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__all,axiom,
% 155.87/155.58 ! [V_P_2,T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2))
% 155.87/155.58 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__ex,axiom,
% 155.87/155.58 ! [V_P_2,T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2))
% 155.87/155.58 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__all__option__def,axiom,
% 155.87/155.58 ! [V_P_2,T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2))
% 155.87/155.58 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 155.87/155.58 & 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)))) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__ex__option__def,axiom,
% 155.87/155.58 ! [V_P_2,T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2))
% 155.87/155.58 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 155.87/155.58 | 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)))) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__ex__prod__def,axiom,
% 155.87/155.58 ! [V_P_2,T_a,T_b] :
% 155.87/155.58 ( ( class_Enum_Oenum(T_b)
% 155.87/155.58 & class_Enum_Oenum(T_a) )
% 155.87/155.58 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2))
% 155.87/155.58 <=> 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))))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__all__prod__def,axiom,
% 155.87/155.58 ! [V_P_2,T_a,T_b] :
% 155.87/155.58 ( ( class_Enum_Oenum(T_b)
% 155.87/155.58 & class_Enum_Oenum(T_a) )
% 155.87/155.58 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2))
% 155.87/155.58 <=> 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))))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_order__fun_I1_J,axiom,
% 155.87/155.58 ! [V_g_2,V_f_2,T_a,T_b] :
% 155.87/155.58 ( ( class_Orderings_Oorder(T_b)
% 155.87/155.58 & class_Enum_Oenum(T_a) )
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 155.87/155.58 <=> 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_order__fun_I2_J,axiom,
% 155.87/155.58 ! [V_g_2,V_f_2,T_a,T_b] :
% 155.87/155.58 ( ( class_Orderings_Oorder(T_b)
% 155.87/155.58 & class_Enum_Oenum(T_a) )
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 155.87/155.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 155.87/155.58 & 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)))) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__ex__fun__code,axiom,
% 155.87/155.58 ! [V_P_2,T_a,T_b] :
% 155.87/155.58 ( ( class_Enum_Oenum(T_b)
% 155.87/155.58 & class_Enum_Oenum(T_a)
% 155.87/155.58 & class_HOL_Oequal(T_a) )
% 155.87/155.58 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 155.87/155.58 <=> 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_enum__all__fun__code,axiom,
% 155.87/155.58 ! [V_P_2,T_a,T_b] :
% 155.87/155.58 ( ( class_Enum_Oenum(T_b)
% 155.87/155.58 & class_Enum_Oenum(T_a)
% 155.87/155.58 & class_HOL_Oequal(T_a) )
% 155.87/155.58 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 155.87/155.58 <=> 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_image__INT,axiom,
% 155.87/155.58 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] :
% 155.87/155.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 155.87/155.58 => ( ! [B_x] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 155.87/155.58 => 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)) )
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2))
% 155.87/155.58 => 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)) ) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_map__of__zip__enum__is__Some,axiom,
% 155.87/155.58 ! [V_x,V_ys,T_b,T_a] :
% 155.87/155.58 ( class_Enum_Oenum(T_a)
% 155.87/155.58 => ( 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))
% 155.87/155.58 => ? [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) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_takeWhile__eq__filter,axiom,
% 155.87/155.58 ! [V_xs_2,V_P_2,T_a] :
% 155.87/155.58 ( ! [B_x] :
% 155.87/155.58 ( 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))))
% 155.87/155.58 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 155.87/155.58 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_inj__on__mapI,axiom,
% 155.87/155.58 ! [V_A_2,V_f_2,T_b,T_a] :
% 155.87/155.58 ( 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)))
% 155.87/155.58 => 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) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_UnionI,axiom,
% 155.87/155.58 ! [V_A_2,V_C_2,V_X_2,T_a] :
% 155.87/155.58 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 155.87/155.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2))
% 155.87/155.58 => 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))) ) ) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_image__Union,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Union__image__eq,axiom,
% 155.87/155.58 ! [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) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_UNION__eq__Union__image,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.58
% 155.87/155.58 fof(fact_Field__Union,axiom,
% 155.87/155.58 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_INT__simps_I8_J,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_INT__extend__simps_I8_J,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sup__upper,axiom,
% 155.87/155.59 ! [V_A_2,V_x_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Union__UNIV,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sup__le__iff,axiom,
% 155.87/155.59 ! [V_b_2,V_A_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => ( 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))
% 155.87/155.59 <=> ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Union__mono,axiom,
% 155.87/155.59 ! [V_B_2,V_A_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Union__quotient,axiom,
% 155.87/155.59 ! [V_r_2,V_A_2,T_a] :
% 155.87/155.59 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.87/155.59 => 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 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Union__upper,axiom,
% 155.87/155.59 ! [V_A_2,V_B_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_subset__Pow__Union,axiom,
% 155.87/155.59 ! [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)))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_finite__UnionD,axiom,
% 155.87/155.59 ! [V_A_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))
% 155.87/155.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Union__empty,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Union__insert,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Union__Pow__eq,axiom,
% 155.87/155.59 ! [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 ).
% 155.87/155.59
% 155.87/155.59 fof(fact_less__Sup__iff,axiom,
% 155.87/155.59 ! [V_S_2,V_a_2,T_a] :
% 155.87/155.59 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 & class_Orderings_Olinorder(T_a) )
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2)))
% 155.87/155.59 <=> ? [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 155.87/155.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Union__Un__distrib,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Union__disjoint,axiom,
% 155.87/155.59 ! [V_A_2,V_C_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 <=> ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2))
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sup__insert,axiom,
% 155.87/155.59 ! [V_A_2,V_a_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sup__singleton,axiom,
% 155.87/155.59 ! [V_a_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sup__empty,axiom,
% 155.87/155.59 ! [T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sup__UNIV,axiom,
% 155.87/155.59 ! [T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Int__Union,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Int__Union2,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sigma__Union,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Domain__Union,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Union__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_UN__extend__simps_I8_J,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_UN__simps_I8_J,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_vimage__Union,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Range__Union,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Un__eq__Union,axiom,
% 155.87/155.59 ! [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))))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Un__Union__image,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Union__Int__subset,axiom,
% 155.87/155.59 ! [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)))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sup__binary,axiom,
% 155.87/155.59 ! [V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sup__fin__Sup,axiom,
% 155.87/155.59 ! [V_A_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.87/155.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.59 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sup__set__fold,axiom,
% 155.87/155.59 ! [V_xs_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_finite__Union,axiom,
% 155.87/155.59 ! [V_A_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2))
% 155.87/155.59 => ( ! [B_M] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2))
% 155.87/155.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) )
% 155.87/155.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_insert__partition,axiom,
% 155.87/155.59 ! [V_F_2,V_x_2,T_a] :
% 155.87/155.59 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))
% 155.87/155.59 => ( ! [B_x] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ! [B_xa] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( B_x != B_xa
% 155.87/155.59 => 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)) ) ) )
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 155.87/155.59 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 155.87/155.59 ( ! [B_i] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) )
% 155.87/155.59 => ( ( 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)))
% 155.87/155.59 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) )
% 155.87/155.59 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_length__takeWhile__less__P__nth,axiom,
% 155.87/155.59 ! [V_xs_2,T_a,V_P_2,V_j_2] :
% 155.87/155.59 ( ! [B_i] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 155.87/155.59 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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)))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sup__Inf,axiom,
% 155.87/155.59 ! [V_A_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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)))))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inf__Sup,axiom,
% 155.87/155.59 ! [V_A_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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))))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_finite__Inter,axiom,
% 155.87/155.59 ! [V_M_2,T_a] :
% 155.87/155.59 ( ? [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2))
% 155.87/155.59 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) )
% 155.87/155.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_InterD,axiom,
% 155.87/155.59 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_InterE,axiom,
% 155.87/155.59 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inter__eq,axiom,
% 155.87/155.59 ! [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)))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inf__singleton,axiom,
% 155.87/155.59 ! [V_a_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inf__empty,axiom,
% 155.87/155.59 ! [T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inf__UNIV,axiom,
% 155.87/155.59 ! [T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inf__insert,axiom,
% 155.87/155.59 ! [V_A_2,V_a_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inter__Un__distrib,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inter__insert,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inter__UNIV,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inf__lower,axiom,
% 155.87/155.59 ! [V_A_2,V_x_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inf__less__iff,axiom,
% 155.87/155.59 ! [V_a_2,V_S_2,T_a] :
% 155.87/155.59 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 & class_Orderings_Olinorder(T_a) )
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2))
% 155.87/155.59 <=> ? [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 155.87/155.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inter__lower,axiom,
% 155.87/155.59 ! [V_A_2,V_B_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_le__Inf__iff,axiom,
% 155.87/155.59 ! [V_A_2,V_b_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => ( 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)))
% 155.87/155.59 <=> ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inter__empty,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inter__anti__mono,axiom,
% 155.87/155.59 ! [V_A_2,V_B_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inter__image__eq,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_INTER__eq__Inter__image,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inter__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Un__Inter,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Int__eq__Inter,axiom,
% 155.87/155.59 ! [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))))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Int__Inter__image,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inter__Un__subset,axiom,
% 155.87/155.59 ! [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)))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inf__binary,axiom,
% 155.87/155.59 ! [V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inf__fin__Inf,axiom,
% 155.87/155.59 ! [V_A_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.87/155.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.59 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inf__set__fold,axiom,
% 155.87/155.59 ! [V_xs_2,T_a] :
% 155.87/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__def,axiom,
% 155.87/155.59 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 155.87/155.59 <=> ( 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)
% 155.87/155.59 & ! [B_x] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_sorted_Osimps,axiom,
% 155.87/155.59 ! [V_a_2,T_a] :
% 155.87/155.59 ( class_Orderings_Olinorder(T_a)
% 155.87/155.59 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2)
% 155.87/155.59 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 155.87/155.59 | ? [B_xs,B_x] :
% 155.87/155.59 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 155.87/155.59 & ! [B_xa] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs)))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) )
% 155.87/155.59 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__Cons,axiom,
% 155.87/155.59 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 155.87/155.59 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__map1,axiom,
% 155.87/155.59 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] :
% 155.87/155.59 ( 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)
% 155.87/155.59 <=> 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__map2,axiom,
% 155.87/155.59 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 <=> 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__eq,axiom,
% 155.87/155.59 ! [T_a,V_ys_2,V_xs_2] :
% 155.87/155.59 ( V_xs_2 = V_ys_2
% 155.87/155.59 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__lengthD,axiom,
% 155.87/155.59 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__dropI,axiom,
% 155.87/155.59 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2)
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__takeI,axiom,
% 155.87/155.59 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__Nil,axiom,
% 155.87/155.59 ! [V_ys_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2)
% 155.87/155.59 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__Nil2,axiom,
% 155.87/155.59 ! [V_xs_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b))
% 155.87/155.59 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__rev,axiom,
% 155.87/155.59 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__rev1,axiom,
% 155.87/155.59 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2)
% 155.87/155.59 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__append,axiom,
% 155.87/155.59 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 155.87/155.59 ( 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)
% 155.87/155.59 => ( 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))
% 155.87/155.59 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 155.87/155.59 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__appendI,axiom,
% 155.87/155.59 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2)
% 155.87/155.59 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2)
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__conv__all__nth,axiom,
% 155.87/155.59 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 155.87/155.59 <=> ( 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)
% 155.87/155.59 & ! [B_i] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => 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))) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__nthD,axiom,
% 155.87/155.59 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__nthD2,axiom,
% 155.87/155.59 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__update__cong,axiom,
% 155.87/155.59 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 155.87/155.59 => 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)) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__update__cong2,axiom,
% 155.87/155.59 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 155.87/155.59 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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)) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2I,axiom,
% 155.87/155.59 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] :
% 155.87/155.59 ( ! [B_x] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) )
% 155.87/155.59 => ( 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)
% 155.87/155.59 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_card__partition,axiom,
% 155.87/155.59 ! [V_k_2,V_C_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2))
% 155.87/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 155.87/155.59 => ( ! [B_c] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2))
% 155.87/155.59 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 )
% 155.87/155.59 => ( ! [B_c1] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2))
% 155.87/155.59 => ! [B_c2] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2))
% 155.87/155.59 => ( B_c1 != B_c2
% 155.87/155.59 => 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)) ) ) )
% 155.87/155.59 => 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)) ) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_all__nth__imp__all__set,axiom,
% 155.87/155.59 ! [V_x_2,V_P_2,V_xs_2,T_a] :
% 155.87/155.59 ( ! [B_i] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_map__removeAll__inj__on,axiom,
% 155.87/155.59 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_removeAll__id,axiom,
% 155.87/155.59 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.59 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_removeAll_Osimps_I2_J,axiom,
% 155.87/155.59 ! [V_xs,T_a,V_y,V_x] :
% 155.87/155.59 ( ( V_x = V_y
% 155.87/155.59 => 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) )
% 155.87/155.59 & ( V_x != V_y
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_distinct__removeAll,axiom,
% 155.87/155.59 ! [V_x,V_xs,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.87/155.59 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_removeAll__filter__not__eq,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_removeAll__filter__not,axiom,
% 155.87/155.59 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 155.87/155.59 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_removeAll_Osimps_I1_J,axiom,
% 155.87/155.59 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_removeAll__append,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_distinct__remove1__removeAll,axiom,
% 155.87/155.59 ! [V_x,V_xs,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.87/155.59 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_map__removeAll__inj,axiom,
% 155.87/155.59 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 155.87/155.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_set__removeAll,axiom,
% 155.87/155.59 ! [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)))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_not__in__set__insert,axiom,
% 155.87/155.59 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.59 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_List_Oinsert__def,axiom,
% 155.87/155.59 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.59 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 )
% 155.87/155.59 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => 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) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_insert__remdups,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_distinct__insert,axiom,
% 155.87/155.59 ! [V_x,V_xs,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 155.87/155.59 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_in__set__insert,axiom,
% 155.87/155.59 ! [V_xs_2,V_x_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_List_Oset__insert,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_insert__Nil,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_concat__map__maps,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_maps__def,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_maps__simps_I2_J,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_maps__simps_I1_J,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_distinct__concat,axiom,
% 155.87/155.59 ! [V_xs_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2))
% 155.87/155.59 => ( ! [B_ys] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 155.87/155.59 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) )
% 155.87/155.59 => ( ! [B_ys] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 155.87/155.59 => ! [B_zs] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 155.87/155.59 => ( B_ys != B_zs
% 155.87/155.59 => 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)) ) ) )
% 155.87/155.59 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_measures__lesseq,axiom,
% 155.87/155.59 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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)))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_wf__measures,axiom,
% 155.87/155.59 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_in__measures_I1_J,axiom,
% 155.87/155.59 ! [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))))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_measures__def,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_measures__less,axiom,
% 155.87/155.59 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_in__measures_I2_J,axiom,
% 155.87/155.59 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 <=> ( 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)))
% 155.87/155.59 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 155.87/155.59 & 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))) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_inj__on__Inter,axiom,
% 155.87/155.59 ! [V_f_2,T_b,T_a,V_S_2] :
% 155.87/155.59 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 155.87/155.59 => ( ! [B_A] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2))
% 155.87/155.59 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) )
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Inter__subset,axiom,
% 155.87/155.59 ! [V_B_2,V_A_2,T_a] :
% 155.87/155.59 ( ! [B_X] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) )
% 155.87/155.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_foldl__apply,axiom,
% 155.87/155.59 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] :
% 155.87/155.59 ( ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => 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)) )
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_inj__on__INTER,axiom,
% 155.87/155.59 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] :
% 155.87/155.59 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.59 => ( ! [B_i] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2))
% 155.87/155.59 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) )
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_zip__obtain__same__length,axiom,
% 155.87/155.59 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 155.87/155.59 ( ( 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))
% 155.87/155.59 => 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)))) )
% 155.87/155.59 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_map__of__eqI,axiom,
% 155.87/155.59 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => ( ! [B_x] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => 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) )
% 155.87/155.59 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_finite__UN__I,axiom,
% 155.87/155.59 ! [V_B_2,T_b,V_A_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.87/155.59 => ( ! [B_a] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 155.87/155.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_wfP__SUP,axiom,
% 155.87/155.59 ! [T_a,V_r_2,T_b] :
% 155.87/155.59 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i))
% 155.87/155.59 => ( ! [B_i,B_j] :
% 155.87/155.59 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 155.87/155.59 => 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)) )
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_dropWhile__append2,axiom,
% 155.87/155.59 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 155.87/155.59 ( ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__all2__all__nthI,axiom,
% 155.87/155.59 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] :
% 155.87/155.59 ( 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)
% 155.87/155.59 => ( ! [B_n] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => 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))) )
% 155.87/155.59 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_finite__map__freshness,axiom,
% 155.87/155.59 ! [V_f_2,T_b,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2)))
% 155.87/155.59 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 155.87/155.59 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_mem__splitI2,axiom,
% 155.87/155.59 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] :
% 155.87/155.59 ( ! [B_a,B_b] :
% 155.87/155.59 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_mem__splitE,axiom,
% 155.87/155.59 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ~ ! [B_x,B_y] :
% 155.87/155.59 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)
% 155.87/155.59 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_finite__sorted__distinct__unique,axiom,
% 155.87/155.59 ! [V_A_2,T_a] :
% 155.87/155.59 ( class_Orderings_Olinorder(T_a)
% 155.87/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.87/155.59 => ? [B_x] :
% 155.87/155.59 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2
% 155.87/155.59 & c_List_Olinorder__class_Osorted(T_a,B_x)
% 155.87/155.59 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x))
% 155.87/155.59 & ! [B_y] :
% 155.87/155.59 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2
% 155.87/155.59 & c_List_Olinorder__class_Osorted(T_a,B_y)
% 155.87/155.59 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) )
% 155.87/155.59 => B_y = B_x ) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_setsum__SucD,axiom,
% 155.87/155.59 ! [V_n_2,V_A_2,V_f_2,T_a] :
% 155.87/155.59 ( 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)
% 155.87/155.59 => ? [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.87/155.59 & 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_nat__mod__eq__lemma,axiom,
% 155.87/155.59 ! [V_y,V_n,V_x] :
% 155.87/155.59 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 155.87/155.59 => ? [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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_takeWhile__append2,axiom,
% 155.87/155.59 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 155.87/155.59 ( ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_insort__is__Cons,axiom,
% 155.87/155.59 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] :
% 155.87/155.59 ( class_Orderings_Olinorder(T_b)
% 155.87/155.59 => ( ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 155.87/155.59 => 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) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_wfI__pf,axiom,
% 155.87/155.59 ! [V_R_2,T_a] :
% 155.87/155.59 ( ! [B_A] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
% 155.87/155.59 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_filter__eq__Cons__iff,axiom,
% 155.87/155.59 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] :
% 155.87/155.59 ( 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)
% 155.87/155.59 <=> ? [B_us,B_vs] :
% 155.87/155.59 ( 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))
% 155.87/155.59 & ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 155.87/155.59 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 155.87/155.59 & hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.59 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Cons__eq__filter__iff,axiom,
% 155.87/155.59 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 155.87/155.59 ( 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)
% 155.87/155.59 <=> ? [B_us,B_vs] :
% 155.87/155.59 ( 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))
% 155.87/155.59 & ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 155.87/155.59 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 155.87/155.59 & hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.59 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Sigma__mono,axiom,
% 155.87/155.59 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 155.87/155.59 => ( ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.87/155.59 => 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))) )
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_not__acc__down,axiom,
% 155.87/155.59 ! [V_R_2,V_x_2,T_a] :
% 155.87/155.59 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2)))
% 155.87/155.59 => ~ ! [B_z] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_acc_OaccI,axiom,
% 155.87/155.59 ! [V_r_2,V_x_2,T_a] :
% 155.87/155.59 ( ! [B_y] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) )
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_fold__image__1,axiom,
% 155.87/155.59 ! [V_f_2,V_S_2,T_a,T_b] :
% 155.87/155.59 ( class_Groups_Ocomm__monoid__mult(T_b)
% 155.87/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 155.87/155.59 => ( ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 155.87/155.59 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 155.87/155.59 => 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) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_card_Oneutral,axiom,
% 155.87/155.59 ! [V_A_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.87/155.59 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.87/155.59 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 155.87/155.59 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_max__ext_Osimps,axiom,
% 155.87/155.59 ! [V_R_2,V_a2_2,V_a1_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 155.87/155.59 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 155.87/155.59 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 155.87/155.59 & ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 155.87/155.59 => ? [B_xa] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 155.87/155.59 & 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)) ) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__ball__nth,axiom,
% 155.87/155.59 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => hBOOL(hAPP(V_P_2,B_x)) )
% 155.87/155.59 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_mod__induct__0,axiom,
% 155.87/155.59 ! [V_i_2,V_P_2,V_p_2] :
% 155.87/155.59 ( ! [B_i] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 155.87/155.59 => ( hBOOL(hAPP(V_P_2,B_i))
% 155.87/155.59 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 155.87/155.59 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 155.87/155.59 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_sorted_OCons,axiom,
% 155.87/155.59 ! [V_x_2,V_xs_2,T_a] :
% 155.87/155.59 ( class_Orderings_Olinorder(T_a)
% 155.87/155.59 => ( ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) )
% 155.87/155.59 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 155.87/155.59 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_InterI,axiom,
% 155.87/155.59 ! [V_A_2,V_C_2,T_a] :
% 155.87/155.59 ( ! [B_X] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) )
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_fold__image__cong,axiom,
% 155.87/155.59 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 155.87/155.59 ( class_Groups_Oab__semigroup__mult(T_b)
% 155.87/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.87/155.59 => ( ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.87/155.59 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 155.87/155.59 => 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) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Min__eqI,axiom,
% 155.87/155.59 ! [V_x_2,V_A_2,T_a] :
% 155.87/155.59 ( class_Orderings_Olinorder(T_a)
% 155.87/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.87/155.59 => ( ! [B_y] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) )
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.87/155.59 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Max__eqI,axiom,
% 155.87/155.59 ! [V_x_2,V_A_2,T_a] :
% 155.87/155.59 ( class_Orderings_Olinorder(T_a)
% 155.87/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.87/155.59 => ( ! [B_y] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) )
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.87/155.59 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_wf__no__infinite__down__chainE,axiom,
% 155.87/155.59 ! [V_f_2,V_r_2,T_a] :
% 155.87/155.59 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.87/155.59 => ~ ! [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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__ex__length,axiom,
% 155.87/155.59 ! [V_xs_2,V_P_2,T_a] :
% 155.87/155.59 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 155.87/155.59 <=> ? [B_n] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__ex__simps_I2_J,axiom,
% 155.87/155.59 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__ex__append,axiom,
% 155.87/155.59 ! [V_ys_2,V_xs_2,V_P_2,T_a] :
% 155.87/155.59 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 155.87/155.59 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 155.87/155.59 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__ex__rev,axiom,
% 155.87/155.59 ! [V_xs_2,V_P_2,T_a] :
% 155.87/155.59 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
% 155.87/155.59 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__ex__iff,axiom,
% 155.87/155.59 ! [V_xs_2,V_P_2,T_a] :
% 155.87/155.59 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 155.87/155.59 <=> ? [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.87/155.59 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_list__ex__simps_I1_J,axiom,
% 155.87/155.59 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 155.87/155.59 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 155.87/155.59 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 155.87/155.59 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_setsum__reindex__cong,axiom,
% 155.87/155.59 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 155.87/155.59 ( class_Groups_Ocomm__monoid__add(T_c)
% 155.87/155.59 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 155.87/155.59 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 155.87/155.59 => ( ! [B_a] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 155.87/155.59 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 155.87/155.59 => 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) ) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_scomp__unfold,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_scomp__def,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_scomp__apply,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Pair__scomp,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_scomp__Pair,axiom,
% 155.87/155.59 ! [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 ).
% 155.87/155.59
% 155.87/155.59 fof(fact_scomp__scomp,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_iterate_Osimps,axiom,
% 155.87/155.59 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 155.87/155.59 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 155.87/155.59 => 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) )
% 155.87/155.59 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_setsum__ivl__cong,axiom,
% 155.87/155.59 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] :
% 155.87/155.59 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 155.87/155.59 & class_Orderings_Oord(T_a) )
% 155.87/155.59 => ( V_a_2 = V_ca_2
% 155.87/155.59 => ( V_b_2 = V_d_2
% 155.87/155.59 => ( ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x))
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2))
% 155.87/155.59 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 155.87/155.59 => 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)) ) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_log_Osimps,axiom,
% 155.87/155.59 ! [V_i,V_b] :
% 155.87/155.59 ( ( ( 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)))
% 155.87/155.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 155.87/155.59 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 155.87/155.59 & ( ~ ( 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)))
% 155.87/155.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_minus__shift__def,axiom,
% 155.87/155.59 ! [V_r,V_l,V_k] :
% 155.87/155.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 155.87/155.59 => 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) )
% 155.87/155.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 155.87/155.59 => 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) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_inc__shift__def,axiom,
% 155.87/155.59 ! [V_k,V_v] :
% 155.87/155.59 ( ( V_v = V_k
% 155.87/155.59 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 155.87/155.59 & ( V_v != V_k
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_select,axiom,
% 155.87/155.59 ! [V_s_2,T_a,V_xs_2] :
% 155.87/155.59 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_select__weight__member,axiom,
% 155.87/155.59 ! [V_s_2,V_xs_2,T_a] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_select__weigth__select,axiom,
% 155.87/155.59 ! [T_a,V_xs_2] :
% 155.87/155.59 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_select__weight__cons__zero,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_select__weigth__drop__zero,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_pick__member,axiom,
% 155.87/155.59 ! [V_xs_2,T_a,V_i_2] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_pick_Osimps,axiom,
% 155.87/155.59 ! [V_xs,V_x,T_a,V_i] :
% 155.87/155.59 ( ( 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)))
% 155.87/155.59 => 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) )
% 155.87/155.59 & ( ~ 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)))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_pick__drop__zero,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_select__weight__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_pick__same,axiom,
% 155.87/155.59 ! [V_xs_2,T_a,V_l_2] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_number__of__code__numeral__def,axiom,
% 155.87/155.59 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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 155.87/155.59 ! [V_y_2,V_x_2] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 155.87/155.59 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 155.87/155.59 <=> V_x_2 = V_y_2 ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_one__code__numeral__def,axiom,
% 155.87/155.59 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_zero__code__numeral__def,axiom,
% 155.87/155.59 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_times__code__numeral__code,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 155.87/155.59 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 155.87/155.59 ! [V_m_2,V_n_2] :
% 155.87/155.59 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 155.87/155.59 <=> V_n_2 = V_m_2 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_less__code__numeral__code,axiom,
% 155.87/155.59 ! [V_m_2,V_n_2] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_plus__code__numeral__code,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_less__eq__code__numeral__code,axiom,
% 155.87/155.59 ! [V_m_2,V_n_2] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_code__numeral__not__eq__zero,axiom,
% 155.87/155.59 ! [V_i_2] :
% 155.87/155.59 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 155.87/155.59 <=> 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_range,axiom,
% 155.87/155.59 ! [V_s,V_k] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_select__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_subtract__code__numeral__code,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_type__definition__code__numeral,axiom,
% 155.87/155.59 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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_nat__of__inverse,axiom,
% 155.87/155.59 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 155.87/155.59
% 155.87/155.59 fof(fact_of__nat__nat__of,axiom,
% 155.87/155.59 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 155.87/155.59
% 155.87/155.59 fof(fact_nat__of__of__nat,axiom,
% 155.87/155.59 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 155.87/155.59
% 155.87/155.59 fof(fact_times__code__numeral__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_nat__of__code,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_less__eq__code__numeral__def,axiom,
% 155.87/155.59 ! [V_m_2,V_n_2] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 155.87/155.59 <=> 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_less__code__numeral__def,axiom,
% 155.87/155.59 ! [V_m_2,V_n_2] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 155.87/155.59 <=> 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_nat__of__number,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_nat__of,axiom,
% 155.87/155.59 ! [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)))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 155.87/155.59 ! [V_l_2,V_k_2] :
% 155.87/155.59 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 155.87/155.59 <=> V_k_2 = V_l_2 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_code__numeral_Onat__of__inject,axiom,
% 155.87/155.59 ! [V_y_2,V_x_2] :
% 155.87/155.59 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 155.87/155.59 <=> V_x_2 = V_y_2 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_int__of__def,axiom,
% 155.87/155.59 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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_nat__of__aux__def,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Suc__code__numeral__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_minus__code__numeral__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_of__nat__inverse,axiom,
% 155.87/155.59 ! [V_y_2] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 155.87/155.59 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_plus__code__numeral__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_div__code__numeral__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_subtract__code__numeral__def,axiom,
% 155.87/155.59 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_minus__code__numeral__code,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_mod__code__numeral__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_code__numeral__decr,axiom,
% 155.87/155.59 ! [V_k] :
% 155.87/155.59 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_less__eq,axiom,
% 155.87/155.59 ! [V_n_2,V_m_2] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_wf__trancl,axiom,
% 155.87/155.59 ! [V_r_2,T_a] :
% 155.87/155.59 ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.87/155.59 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_less__than__def,axiom,
% 155.87/155.59 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_acyclic__def,axiom,
% 155.87/155.59 ! [V_r_2,T_a] :
% 155.87/155.59 ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 155.87/155.59 <=> ! [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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl_Or__into__trancl,axiom,
% 155.87/155.59 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__subset__Field2,axiom,
% 155.87/155.59 ! [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))))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_r__into__trancl_H,axiom,
% 155.87/155.59 ! [V_r_2,V_p_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__empty,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__domain,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__range,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_finite__trancl,axiom,
% 155.87/155.59 ! [V_r_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 155.87/155.59 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_r__r__into__trancl,axiom,
% 155.87/155.59 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => ( 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))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__into__trancl2,axiom,
% 155.87/155.59 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 155.87/155.59 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( 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))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__trans,axiom,
% 155.87/155.59 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__mono,axiom,
% 155.87/155.59 ! [V_s_2,V_r_2,V_p_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 155.87/155.59 => ( 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))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__unfold,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__subset__Sigma,axiom,
% 155.87/155.59 ! [V_A_2,V_r_2,T_a] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__Int__subset,axiom,
% 155.87/155.59 ! [V_s_2,V_r_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => ( 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))
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__insert,axiom,
% 155.87/155.59 ! [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)))))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_reflcl__set__eq,axiom,
% 155.87/155.59 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 <=> 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_r__into__rtrancl,axiom,
% 155.87/155.59 ! [V_r_2,V_p_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_IdI,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__into__rtrancl,axiom,
% 155.87/155.59 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_listrel__rtrancl__refl,axiom,
% 155.87/155.59 ! [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)))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__unfold__left,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__unfold__right,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__reflcl,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_reflcl__trancl,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__trancl__absorb,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__rtrancl__absorb,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__trancl__trancl,axiom,
% 155.87/155.59 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__rtrancl__trancl,axiom,
% 155.87/155.59 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__into__trancl1,axiom,
% 155.87/155.59 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( 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))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtranclD,axiom,
% 155.87/155.59 ! [V_R_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( V_a_2 = V_b_2
% 155.87/155.59 | ( V_a_2 != V_b_2
% 155.87/155.59 & 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))) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__into__trancl2,axiom,
% 155.87/155.59 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__eq__or__trancl,axiom,
% 155.87/155.59 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 <=> ( V_x_2 = V_y_2
% 155.87/155.59 | ( V_x_2 != V_y_2
% 155.87/155.59 & 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))) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 155.87/155.59 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 155.87/155.59 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( 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))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__trans,axiom,
% 155.87/155.59 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__mono,axiom,
% 155.87/155.59 ! [V_s_2,V_r_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__subset,axiom,
% 155.87/155.59 ! [V_S_2,V_R_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__subset__rtrancl,axiom,
% 155.87/155.59 ! [V_s_2,V_r_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__Un__subset,axiom,
% 155.87/155.59 ! [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)))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Image__closed__trancl,axiom,
% 155.87/155.59 ! [V_X_2,V_r_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__Int__subset,axiom,
% 155.87/155.59 ! [V_r_2,V_s_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => ( 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))
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__idemp,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__r__diff__Id,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__reflcl__absorb,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__Un__rtrancl,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__reflcl,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__idemp__self__comp,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_r__comp__rtrancl__eq,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__unfold,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Domain__rtrancl,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Range__rtrancl,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_in__rtrancl__UnI,axiom,
% 155.87/155.59 ! [V_S_2,V_R_2,V_x_2,T_a] :
% 155.87/155.59 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 155.87/155.59 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) )
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__empty,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_refl__rtrancl,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Image__Id,axiom,
% 155.87/155.59 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ).
% 155.87/155.59
% 155.87/155.59 fof(fact_R__O__Id,axiom,
% 155.87/155.59 ! [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 ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Id__O__R,axiom,
% 155.87/155.59 ! [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 ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Range__Id,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Domain__Id,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_refl__Id,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 155.87/155.59 ! [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)))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_pair__in__Id__conv,axiom,
% 155.87/155.59 ! [V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 <=> V_a_2 = V_b_2 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_listrel__rtrancl__trans,axiom,
% 155.87/155.59 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => ( 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))))
% 155.87/155.59 => 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)))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 155.87/155.59 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( 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))))
% 155.87/155.59 => 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)))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 155.87/155.59 ! [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)))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_pair__leq__def,axiom,
% 155.87/155.59 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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Not__Domain__rtrancl,axiom,
% 155.87/155.59 ! [V_y_2,V_R_2,V_x_2,T_a] :
% 155.87/155.59 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2)))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 <=> V_x_2 = V_y_2 ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_acc__downwards__aux,axiom,
% 155.87/155.59 ! [V_r_2,V_a_2,V_b_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_acc__downwards,axiom,
% 155.87/155.59 ! [V_b_2,V_r_2,V_a_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_wf__insert,axiom,
% 155.87/155.59 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 <=> ( c_Wellfounded_Owf(T_a,V_r_2)
% 155.87/155.59 & ~ 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 155.87/155.59 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 155.87/155.59 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => 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) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_acyclic__insert,axiom,
% 155.87/155.59 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 155.87/155.59 & ~ 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))) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 155.87/155.59 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 155.87/155.59 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_refl__reflcl,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Id__def,axiom,
% 155.87/155.59 ! [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))))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_irrefl__diff__Id,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_pred__nat__trancl__eq__le,axiom,
% 155.87/155.59 ! [V_n_2,V_m_2] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__subset__Sigma__aux,axiom,
% 155.87/155.59 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => ( 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))))
% 155.87/155.59 => ( V_a_2 = V_b_2
% 155.87/155.59 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_irrefl__tranclI,axiom,
% 155.87/155.59 ! [V_x_2,V_r_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => ~ 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_sequence__trans,axiom,
% 155.87/155.59 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] :
% 155.87/155.59 ( ! [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)))
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__converseI,axiom,
% 155.87/155.59 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__converseD,axiom,
% 155.87/155.59 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__converse,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__Id,axiom,
% 155.87/155.59 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_in__listrel1__converse,axiom,
% 155.87/155.59 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 <=> 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__iff,axiom,
% 155.87/155.59 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 <=> 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converseI,axiom,
% 155.87/155.59 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converseD,axiom,
% 155.87/155.59 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__inv__image,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__Int,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Range__converse,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Domain__converse,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Range__def,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_finite__converse,axiom,
% 155.87/155.59 ! [V_r_2,T_b,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 155.87/155.59 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_acyclic__converse,axiom,
% 155.87/155.59 ! [V_r_2,T_a] :
% 155.87/155.59 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 155.87/155.59 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__Id__on,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__converse,axiom,
% 155.87/155.59 ! [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 ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Field__converse,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__Un,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__rel__comp,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_equiv__comp__eq,axiom,
% 155.87/155.59 ! [V_r_2,V_A_2,T_a] :
% 155.87/155.59 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 155.87/155.59 => 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 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_refl__on__converse,axiom,
% 155.87/155.59 ! [V_r_2,V_A_2,T_a] :
% 155.87/155.59 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 155.87/155.59 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_listrel1__converse,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__INTER,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__UNION,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Image__subset__eq,axiom,
% 155.87/155.59 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 <=> 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))))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__converseI,axiom,
% 155.87/155.59 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__converseD,axiom,
% 155.87/155.59 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 155.87/155.59 ( 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))))
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_trancl__converse,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_wf__converse__trancl,axiom,
% 155.87/155.59 ! [V_r_2,T_a] :
% 155.87/155.59 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 155.87/155.59 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_refl__on__comp__subset,axiom,
% 155.87/155.59 ! [V_r_2,V_A_2,T_a] :
% 155.87/155.59 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 155.87/155.59 => 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))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_comp__equivI,axiom,
% 155.87/155.59 ! [V_A_2,V_r_2,T_a] :
% 155.87/155.59 ( 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
% 155.87/155.59 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2
% 155.87/155.59 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_finite__acyclic__wf__converse,axiom,
% 155.87/155.59 ! [V_r_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 155.87/155.59 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 155.87/155.59 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_converse__def,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Image__INT__eq,axiom,
% 155.87/155.59 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] :
% 155.87/155.59 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))
% 155.87/155.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_total__on__diff__Id,axiom,
% 155.87/155.59 ! [V_r_2,V_A_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_single__valued__Id,axiom,
% 155.87/155.59 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_total__on__converse,axiom,
% 155.87/155.59 ! [V_r_2,V_A_2,T_a] :
% 155.87/155.59 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 155.87/155.59 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_single__valuedD,axiom,
% 155.87/155.59 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] :
% 155.87/155.59 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 155.87/155.59 => ( 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))
% 155.87/155.59 => ( 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))
% 155.87/155.59 => V_y_2 = V_z_2 ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_single__valued__def,axiom,
% 155.87/155.59 ! [V_r_2,T_b,T_a] :
% 155.87/155.59 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 155.87/155.59 <=> ! [B_x,B_y] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => ! [B_z] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => B_y = B_z ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_single__valued__Id__on,axiom,
% 155.87/155.59 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_single__valued__rel__comp,axiom,
% 155.87/155.59 ! [V_s_2,T_c,V_r_2,T_b,T_a] :
% 155.87/155.59 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 155.87/155.59 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 155.87/155.59 => 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)) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_total__on__empty,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_single__valued__subset,axiom,
% 155.87/155.59 ! [V_s_2,V_r_2,T_b,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2)
% 155.87/155.59 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_total__on__def,axiom,
% 155.87/155.59 ! [V_r_2,V_A_2,T_a] :
% 155.87/155.59 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
% 155.87/155.59 <=> ! [B_x] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 155.87/155.59 => ! [B_xa] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 155.87/155.59 => ( B_x != B_xa
% 155.87/155.59 => ( 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))
% 155.87/155.59 | 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)) ) ) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_single__valued__confluent,axiom,
% 155.87/155.59 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
% 155.87/155.59 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2)
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 => ( 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)))
% 155.87/155.59 | 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))) ) ) ) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_Image__Int__eq,axiom,
% 155.87/155.59 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] :
% 155.87/155.59 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2))
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 155.87/155.59 ! [V_R_2,V_p_2,T_a] :
% 155.87/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 155.87/155.59 => 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)))) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_acyclicI,axiom,
% 155.87/155.59 ! [V_r_2,T_a] :
% 155.87/155.59 ( ! [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)))
% 155.87/155.59 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_single__valued__rel__pow,axiom,
% 155.87/155.59 ! [V_n_2,V_R_2,T_a] :
% 155.87/155.59 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2)
% 155.87/155.59 => 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)) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_comp__funpow,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_funpow_Osimps_I2_J,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_funpow__add,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_funpow__swap1,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_wf__exp,axiom,
% 155.87/155.59 ! [V_R_2,V_n_2,T_a] :
% 155.87/155.59 ( 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))
% 155.87/155.59 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_funpow__mult,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_relpow_Osimps_I2_J,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rel__pow__commute,axiom,
% 155.87/155.59 ! [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) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rel__pow__1,axiom,
% 155.87/155.59 ! [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 ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rel__pow__add,axiom,
% 155.87/155.59 ! [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)) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rel__pow__0__E,axiom,
% 155.87/155.59 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 155.87/155.59 ( 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)))
% 155.87/155.59 => V_x_2 = V_y_2 ) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rel__pow__0__I,axiom,
% 155.87/155.59 ! [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))) ).
% 155.87/155.59
% 155.87/155.59 fof(fact_rel__pow__Suc__I2,axiom,
% 155.87/155.59 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] :
% 155.87/155.59 ( 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))
% 155.90/155.59 => ( 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)))
% 155.90/155.59 => 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))) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rel__pow__Suc__I,axiom,
% 155.90/155.59 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => ( 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))
% 155.90/155.59 => 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))) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_funpow_Osimps_I1_J,axiom,
% 155.90/155.59 ! [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) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rtrancl__power,axiom,
% 155.90/155.59 ! [V_R_2,V_p_2,T_a] :
% 155.90/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 155.90/155.59 <=> ? [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))) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rel__pow__imp__rtrancl,axiom,
% 155.90/155.59 ! [V_R_2,V_n_2,V_p_2,T_a] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_relpow_Osimps_I1_J,axiom,
% 155.90/155.59 ! [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) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_trancl__power,axiom,
% 155.90/155.59 ! [V_R_2,V_p_2,T_a] :
% 155.90/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 155.90/155.59 <=> ? [B_n] :
% 155.90/155.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 155.90/155.59 & 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))) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 155.90/155.59 ! [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)) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_funpow__code__def,axiom,
% 155.90/155.59 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rel__pow__E2,axiom,
% 155.90/155.59 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.90/155.59 => V_x_2 != V_z_2 )
% 155.90/155.59 => ~ ! [B_y,B_m] :
% 155.90/155.59 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 155.90/155.59 => ( 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))
% 155.90/155.59 => ~ 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))) ) ) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rotate__def,axiom,
% 155.90/155.59 ! [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)) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rel__pow__E,axiom,
% 155.90/155.59 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 155.90/155.59 => V_x_2 != V_z_2 )
% 155.90/155.59 => ~ ! [B_y,B_m] :
% 155.90/155.59 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 155.90/155.59 => ( 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)))
% 155.90/155.59 => ~ 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)) ) ) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_pos__not__random__dseq__def,axiom,
% 155.90/155.59 ! [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)) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 155.90/155.59 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 155.90/155.59 ( 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))))
% 155.90/155.59 => ( ! [B_x] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => ! [B_y] :
% 155.90/155.59 ( 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))
% 155.90/155.59 => B_y = B_x ) )
% 155.90/155.59 => 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))) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rtrancl__Un__separatorE,axiom,
% 155.90/155.59 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 155.90/155.59 ( 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))))
% 155.90/155.59 => ( ! [B_x] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => ! [B_y] :
% 155.90/155.59 ( 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))
% 155.90/155.59 => B_x = B_y ) )
% 155.90/155.59 => 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))) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rel__pow__Suc__E,axiom,
% 155.90/155.59 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => ~ ! [B_y] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => ~ 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)) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rel__pow__Suc__E2,axiom,
% 155.90/155.59 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => ~ ! [B_y] :
% 155.90/155.59 ( 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))
% 155.90/155.59 => ~ 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))) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_rel__pow__Suc__D2,axiom,
% 155.90/155.59 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => ? [B_y] :
% 155.90/155.59 ( 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))
% 155.90/155.59 & 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))) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_tranclD,axiom,
% 155.90/155.59 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => ? [B_z] :
% 155.90/155.59 ( 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))
% 155.90/155.59 & 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))) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_tranclD2,axiom,
% 155.90/155.59 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 => ? [B_z] :
% 155.90/155.59 ( 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)))
% 155.90/155.59 & 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)) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_IdE,axiom,
% 155.90/155.59 ! [V_p_2,T_a] :
% 155.90/155.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a)))
% 155.90/155.59 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_in__set__conv__decomp,axiom,
% 155.90/155.59 ! [V_xs_2,V_x_2,T_a] :
% 155.90/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.90/155.59 <=> ? [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)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_in__set__conv__decomp__last,axiom,
% 155.90/155.59 ! [V_xs_2,V_x_2,T_a] :
% 155.90/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.90/155.59 <=> ? [B_ys,B_zs] :
% 155.90/155.59 ( 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))
% 155.90/155.59 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_in__set__conv__decomp__first,axiom,
% 155.90/155.59 ! [V_xs_2,V_x_2,T_a] :
% 155.90/155.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 155.90/155.59 <=> ? [B_ys] :
% 155.90/155.59 ( ? [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))
% 155.90/155.59 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 155.90/155.59 ! [V_x_2,V_A_2,T_a] :
% 155.90/155.59 ( class_Orderings_Olinorder(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 155.90/155.59 => 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) ) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_inf__INFI__fold__inf,axiom,
% 155.90/155.59 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 155.90/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 155.90/155.59 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 155.90/155.59 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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)) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 155.90/155.59 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 155.90/155.59 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_inf__Inf__fold__inf,axiom,
% 155.90/155.59 ! [V_B_2,V_A_2,T_a] :
% 155.90/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_min__max_Ofold__inf__insert,axiom,
% 155.90/155.59 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 155.90/155.59 ( class_Orderings_Olinorder(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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)) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_min__max_Ofold__sup__insert,axiom,
% 155.90/155.59 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 155.90/155.59 ( class_Orderings_Olinorder(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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)) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_fold__inf__insert,axiom,
% 155.90/155.59 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 155.90/155.59 ( class_Lattices_Osemilattice__inf(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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)) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_folding_Oeq__fold,axiom,
% 155.90/155.59 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 155.90/155.59 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_fold__image__def,axiom,
% 155.90/155.59 ! [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)) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_fold__empty,axiom,
% 155.90/155.59 ! [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 ).
% 155.90/155.59
% 155.90/155.59 fof(fact_fold__def,axiom,
% 155.90/155.59 ! [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)) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 155.90/155.59 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] :
% 155.90/155.59 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_sup__Sup__fold__sup,axiom,
% 155.90/155.59 ! [V_B_2,V_A_2,T_a] :
% 155.90/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_fold__sup__insert,axiom,
% 155.90/155.59 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 155.90/155.59 ( class_Lattices_Osemilattice__sup(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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)) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_union__fold__insert,axiom,
% 155.90/155.59 ! [V_B_2,V_A_2,T_a] :
% 155.90/155.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_sup__SUPR__fold__sup,axiom,
% 155.90/155.59 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 155.90/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 155.90/155.59 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
% 155.90/155.59 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 155.90/155.59 => 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) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_sup__le__fold__sup,axiom,
% 155.90/155.59 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 155.90/155.59 ( class_Lattices_Osemilattice__sup(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.90/155.59 => 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))) ) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_fold__inf__le__inf,axiom,
% 155.90/155.59 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 155.90/155.59 ( class_Lattices_Osemilattice__inf(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.90/155.59 => 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))) ) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 155.90/155.59 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 155.90/155.59 ( class_Orderings_Olinorder(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.90/155.59 => 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))) ) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 155.90/155.59 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 155.90/155.59 ( class_Orderings_Olinorder(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 155.90/155.59 => 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))) ) ) ) ).
% 155.90/155.59
% 155.90/155.59 fof(fact_Sup__fold__sup,axiom,
% 155.90/155.59 ! [V_A_2,T_a] :
% 155.90/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 155.90/155.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 155.90/155.59 => 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) ) ) ).
% 155.90/155.59
% 155.90/155.59 %----Arity declarations (220)
% 155.90/155.59 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 155.90/155.59 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Lattices_Obounded__lattice(T_1)
% 155.90/155.59 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 155.90/155.59 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Lattices_Obounded__lattice(T_1)
% 155.90/155.59 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Lattices_Obounded__lattice(T_1)
% 155.90/155.59 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Lattices_Olattice(T_1)
% 155.90/155.59 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Lattices_Olattice(T_1)
% 155.90/155.59 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Lattices_Odistrib__lattice(T_1)
% 155.90/155.59 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Lattices_Oboolean__algebra(T_1)
% 155.90/155.59 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Orderings_Opreorder,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Orderings_Opreorder(T_1)
% 155.90/155.59 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 155.90/155.59 ! [T_1,T_2] :
% 155.90/155.59 ( ( class_Finite__Set_Ofinite(T_2)
% 155.90/155.59 & class_Finite__Set_Ofinite(T_1) )
% 155.90/155.59 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Lattices_Olattice,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Lattices_Olattice(T_1)
% 155.90/155.59 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Orderings_Oorder,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Orderings_Oorder(T_1)
% 155.90/155.59 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Orderings_Otop,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Orderings_Otop(T_1)
% 155.90/155.59 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Orderings_Oord,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Orderings_Oord(T_1)
% 155.90/155.59 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Orderings_Obot,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Orderings_Obot(T_1)
% 155.90/155.59 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Groups_Ouminus,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Groups_Ouminus(T_1)
% 155.90/155.59 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Groups_Ominus,axiom,
% 155.90/155.59 ! [T_2,T_1] :
% 155.90/155.59 ( class_Groups_Ominus(T_1)
% 155.90/155.59 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__HOL_Oequal,axiom,
% 155.90/155.59 ! [T_1,T_2] :
% 155.90/155.59 ( ( class_Enum_Oenum(T_2)
% 155.90/155.59 & class_HOL_Oequal(T_1) )
% 155.90/155.59 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_fun__Enum_Oenum,axiom,
% 155.90/155.59 ! [T_1,T_2] :
% 155.90/155.59 ( ( class_Enum_Oenum(T_2)
% 155.90/155.59 & class_Enum_Oenum(T_1) )
% 155.90/155.59 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Com__Ocom__HOL_Oequal,axiom,
% 155.90/155.59 class_HOL_Oequal(tc_Com_Ocom) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 155.90/155.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 155.90/155.59 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 155.90/155.59 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 155.90/155.59 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 155.90/155.59 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 155.90/155.59 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 155.90/155.59 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 155.90/155.59 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 155.90/155.59 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 155.90/155.59 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 155.90/155.59 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 155.90/155.59 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 155.90/155.59 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 155.90/155.59 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 155.90/155.59 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 155.90/155.59 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 155.90/155.59 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 155.90/155.59 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 155.90/155.59 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 155.90/155.59 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 155.90/155.59 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 155.90/155.59 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 155.90/155.59 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 155.90/155.59 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 155.90/155.59 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 155.90/155.59 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 155.90/155.59 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 155.90/155.59 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 155.90/155.59 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 155.90/155.59 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 155.90/155.59 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 155.90/155.59 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 155.90/155.59 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 155.90/155.59 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 155.90/155.59 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 155.90/155.59 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 155.90/155.59 class_Orderings_Opreorder(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 155.90/155.59 class_Orderings_Olinorder(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 155.90/155.59 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 155.90/155.59 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 155.90/155.59 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 155.90/155.59 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 155.90/155.59 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 155.90/155.59 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 155.90/155.59 class_Lattices_Olattice(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 155.90/155.59 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 155.90/155.59 class_Divides_Oring__div(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 155.90/155.59 class_Rings_Omult__zero(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 155.90/155.59 class_Orderings_Oorder(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 155.90/155.59 class_Int_Oring__char__0(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 155.90/155.59 class_Int_Onumber__ring(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 155.90/155.59 class_Rings_Osemiring(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 155.90/155.59 class_Orderings_Oord(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 155.90/155.59 class_Groups_Ouminus(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 155.90/155.59 class_Groups_Osgn__if(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 155.90/155.59 class_Groups_Oabs__if(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 155.90/155.59 class_Rings_Oring__1(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 155.90/155.59 class_Groups_Ominus(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Power_Opower,axiom,
% 155.90/155.59 class_Power_Opower(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 155.90/155.59 class_Groups_Ozero(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Oring,axiom,
% 155.90/155.59 class_Rings_Oring(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 155.90/155.59 class_Rings_Oidom(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Int_Onumber,axiom,
% 155.90/155.59 class_Int_Onumber(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__Groups_Oone,axiom,
% 155.90/155.59 class_Groups_Oone(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Int__Oint__HOL_Oequal,axiom,
% 155.90/155.59 class_HOL_Oequal(tc_Int_Oint) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 155.90/155.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 155.90/155.59 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 155.90/155.59 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 155.90/155.59 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 155.90/155.59 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 155.90/155.59 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 155.90/155.59 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 155.90/155.59 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 155.90/155.59 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 155.90/155.59 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 155.90/155.59 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 155.90/155.59 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 155.90/155.59 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 155.90/155.59 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 155.90/155.59 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 155.90/155.59 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 155.90/155.59 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 155.90/155.59 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 155.90/155.59 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 155.90/155.59 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 155.90/155.59 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 155.90/155.59 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 155.90/155.59 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 155.90/155.59 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 155.90/155.59 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 155.90/155.59 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 155.90/155.59 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 155.90/155.59 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 155.90/155.59 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 155.90/155.59 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 155.90/155.59 class_Lattices_Olattice(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 155.90/155.59 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 155.90/155.59 class_Orderings_Oorder(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 155.90/155.59 class_Rings_Osemiring(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 155.90/155.59 class_Orderings_Oord(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 155.90/155.59 class_Orderings_Obot(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 155.90/155.59 class_Groups_Ominus(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Power_Opower,axiom,
% 155.90/155.59 class_Power_Opower(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 155.90/155.59 class_Groups_Ozero(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 155.90/155.59 class_Int_Onumber(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 155.90/155.59 class_Groups_Oone(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nat__Onat__HOL_Oequal,axiom,
% 155.90/155.59 class_HOL_Oequal(tc_Nat_Onat) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 155.90/155.59 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 155.90/155.59 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 155.90/155.59 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 155.90/155.59 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 155.90/155.59 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 155.90/155.59 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 155.90/155.59 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 155.90/155.59 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 155.90/155.59 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 155.90/155.59 class_Lattices_Olattice(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 155.90/155.59 class_Orderings_Oorder(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 155.90/155.59 class_Orderings_Otop(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 155.90/155.59 class_Orderings_Oord(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 155.90/155.59 class_Orderings_Obot(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 155.90/155.59 class_Groups_Ouminus(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 155.90/155.59 class_Groups_Ominus(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__HOL_Oequal,axiom,
% 155.90/155.59 class_HOL_Oequal(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 155.90/155.59 class_Enum_Oenum(tc_HOL_Obool) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Com__Ostate__HOL_Oequal,axiom,
% 155.90/155.59 class_HOL_Oequal(tc_Com_Ostate) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Com__Ovname__HOL_Oequal,axiom,
% 155.90/155.59 class_HOL_Oequal(tc_Com_Ovname) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_List__Olist__HOL_Oequal,axiom,
% 155.90/155.59 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 155.90/155.59 ! [T_1,T_2] :
% 155.90/155.59 ( ( class_Finite__Set_Ofinite(T_2)
% 155.90/155.59 & class_Finite__Set_Ofinite(T_1) )
% 155.90/155.59 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_sum__HOL_Oequal,axiom,
% 155.90/155.59 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_sum__Enum_Oenum,axiom,
% 155.90/155.59 ! [T_1,T_2] :
% 155.90/155.59 ( ( class_Enum_Oenum(T_2)
% 155.90/155.59 & class_Enum_Oenum(T_1) )
% 155.90/155.59 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 155.90/155.59 ! [T_1] :
% 155.90/155.59 ( class_Finite__Set_Ofinite(T_1)
% 155.90/155.59 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Option__Ooption__HOL_Oequal,axiom,
% 155.90/155.59 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 155.90/155.59 ! [T_1] :
% 155.90/155.59 ( class_Enum_Oenum(T_1)
% 155.90/155.59 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Nitpick__Opair____box__HOL_Oequal,axiom,
% 155.90/155.59 ! [T_1,T_2] : class_HOL_Oequal(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 155.90/155.59 ! [T_1,T_2] :
% 155.90/155.59 ( ( class_Finite__Set_Ofinite(T_2)
% 155.90/155.59 & class_Finite__Set_Ofinite(T_1) )
% 155.90/155.59 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_prod__Smallcheck_Osmall,axiom,
% 155.90/155.59 ! [T_1,T_2] :
% 155.90/155.59 ( ( class_Smallcheck_Osmall(T_2)
% 155.90/155.59 & class_Smallcheck_Osmall(T_1) )
% 155.90/155.59 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_prod__HOL_Oequal,axiom,
% 155.90/155.59 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_prod__Enum_Oenum,axiom,
% 155.90/155.59 ! [T_1,T_2] :
% 155.90/155.59 ( ( class_Enum_Oenum(T_2)
% 155.90/155.59 & class_Enum_Oenum(T_1) )
% 155.90/155.59 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 155.90/155.59 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 155.90/155.59 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
% 155.90/155.59 class_HOL_Oequal(tc_Product__Type_Ounit) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 155.90/155.59 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
% 155.90/155.59 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
% 155.90/155.59 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 155.90/155.59 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 155.90/155.59 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 155.90/155.59 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 155.90/155.59 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 155.90/155.59 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 155.90/155.59 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 155.90/155.59 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 155.90/155.59 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 155.90/155.59 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 155.90/155.59 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 155.90/155.59 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 155.90/155.59 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 155.90/155.59 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 155.90/155.59 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 155.90/155.59 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 155.90/155.59 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 155.90/155.59 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 155.90/155.59 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 155.90/155.59 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 155.90/155.59 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 155.90/155.59 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 155.90/155.59 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 155.90/155.59 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 155.90/155.59 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 155.90/155.59 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 155.90/155.59 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 155.90/155.59 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 155.90/155.59 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 155.90/155.59 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 155.90/155.59 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 155.90/155.59 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 155.90/155.59 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 155.90/155.59 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 155.90/155.59 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 155.90/155.59 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
% 155.90/155.59 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ).
% 155.90/155.59
% 155.90/155.59 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
% 155.90/155.59 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 155.90/155.59
% 155.90/155.59 %----Helper facts (20)
% 155.90/155.59 fof(help_c__COMBI__1,axiom,
% 155.90/155.59 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__COMBK__1,axiom,
% 155.90/155.59 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__COMBB__1,axiom,
% 155.90/155.59 ! [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)) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__COMBC__1,axiom,
% 155.90/155.59 ! [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) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__COMBS__1,axiom,
% 155.90/155.59 ! [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)) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fequal__1,axiom,
% 155.90/155.59 ! [V_y_2,V_x_2] :
% 155.90/155.59 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 155.90/155.59 | V_x_2 = V_y_2 ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fequal__2,axiom,
% 155.90/155.59 ! [V_y_2,V_x_2] :
% 155.90/155.59 ( V_x_2 != V_y_2
% 155.90/155.59 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fFalse__1,axiom,
% 155.90/155.59 ~ hBOOL(c_fFalse) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fTrue__1,axiom,
% 155.90/155.59 hBOOL(c_fTrue) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fNot__1,axiom,
% 155.90/155.59 ! [V_P_2] :
% 155.90/155.59 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 155.90/155.59 | ~ hBOOL(V_P_2) ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fNot__2,axiom,
% 155.90/155.59 ! [V_P_2] :
% 155.90/155.59 ( ~ ~ hBOOL(V_P_2)
% 155.90/155.59 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fconj__1,axiom,
% 155.90/155.59 ! [V_Q_2,V_P_2] :
% 155.90/155.59 ( ~ hBOOL(V_P_2)
% 155.90/155.59 | ~ hBOOL(V_Q_2)
% 155.90/155.59 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fconj__2,axiom,
% 155.90/155.59 ! [V_Q_2,V_P_2] :
% 155.90/155.59 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 155.90/155.59 | hBOOL(V_P_2) ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fconj__3,axiom,
% 155.90/155.59 ! [V_Q_2,V_P_2] :
% 155.90/155.59 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 155.90/155.59 | hBOOL(V_Q_2) ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fdisj__1,axiom,
% 155.90/155.59 ! [V_Q_2,V_P_2] :
% 155.90/155.59 ( ~ hBOOL(V_P_2)
% 155.90/155.59 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fdisj__2,axiom,
% 155.90/155.59 ! [V_P_2,V_Q_2] :
% 155.90/155.59 ( ~ hBOOL(V_Q_2)
% 155.90/155.59 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fdisj__3,axiom,
% 155.90/155.59 ! [V_Q_2,V_P_2] :
% 155.90/155.59 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 155.90/155.59 | hBOOL(V_P_2)
% 155.90/155.59 | hBOOL(V_Q_2) ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fimplies__1,axiom,
% 155.90/155.59 ! [V_Q_2,V_P_2] :
% 155.90/155.59 ( hBOOL(V_P_2)
% 155.90/155.59 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fimplies__2,axiom,
% 155.90/155.59 ! [V_P_2,V_Q_2] :
% 155.90/155.59 ( ~ hBOOL(V_Q_2)
% 155.90/155.59 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 155.90/155.59
% 155.90/155.59 fof(help_c__fimplies__3,axiom,
% 155.90/155.59 ! [V_Q_2,V_P_2] :
% 155.90/155.59 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 155.90/155.59 | ~ hBOOL(V_P_2)
% 155.90/155.59 | hBOOL(V_Q_2) ) ).
% 155.90/155.59
% 155.90/155.59 %----Conjectures (4)
% 155.90/155.59 fof(conj_0,hypothesis,
% 155.90/155.59 c_Hoare__Mirabelle_Ostate__not__singleton ).
% 155.90/155.59
% 155.90/155.59 fof(conj_1,hypothesis,
% 155.90/155.59 ! [B_Z_H] :
% 155.90/155.59 ( ! [B_s1] :
% 155.90/155.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),B_s1))
% 155.90/155.59 => B_Z_H = B_s1 )
% 155.90/155.59 => B_Z_H = v_s_H ) ).
% 155.90/155.59
% 155.90/155.59 fof(conj_2,hypothesis,
% 155.90/155.59 ? [B_x1] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Sledgehammer_058s__2(v_Z,v_s_H)),B_x1)) ).
% 155.90/155.59
% 155.90/155.59 fof(conj_3,conjecture,
% 155.90/155.59 hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)) ).
% 155.90/155.59
% 155.90/155.59 %------------------------------------------------------------------------------
% 155.90/155.59 %-------------------------------------------
% 155.90/155.59 % Proof found
% 155.90/155.59 % SZS status Theorem for theBenchmark
% 155.90/155.59 % SZS output start Proof
% 155.90/155.60 %ClaNum:10099(EqnAxiom:2805)
% 155.90/155.60 %VarNum:70177(SingletonVarNum:20591)
% 155.90/155.60 %MaxLitNum:8
% 155.90/155.60 %MaxfuncDepth:15
% 155.90/155.60 %SharedTerms:1107
% 155.90/155.60 %goalClause: 4463
% 155.90/155.60 %singleGoalClaCount:1
% 155.90/155.60 [2806]P1(a5000)
% 155.90/155.60 [2810]P22(a188)
% 155.90/155.60 [2811]P23(a853)
% 155.90/155.60 [2812]P23(a1)
% 155.90/155.60 [2813]P23(a113)
% 155.90/155.60 [2814]P24(a853)
% 155.90/155.60 [2815]P24(a846)
% 155.90/155.60 [2816]P101(a853)
% 155.90/155.60 [2817]P25(a853)
% 155.90/155.60 [2818]P25(a1)
% 155.90/155.60 [2819]P25(a113)
% 155.90/155.60 [2820]P107(a853)
% 155.90/155.60 [2821]P107(a1)
% 155.90/155.60 [2822]P107(a113)
% 155.90/155.60 [2823]P26(a853)
% 155.90/155.60 [2824]P26(a1)
% 155.90/155.60 [2825]P26(a113)
% 155.90/155.60 [2826]P70(a1)
% 155.90/155.60 [2827]P136(a853)
% 155.90/155.60 [2828]P136(a1)
% 155.90/155.60 [2829]P75(a853)
% 155.90/155.60 [2830]P75(a1)
% 155.90/155.60 [2831]P75(a113)
% 155.90/155.60 [2832]P27(a853)
% 155.90/155.60 [2833]P27(a1)
% 155.90/155.60 [2834]P27(a113)
% 155.90/155.60 [2835]P28(a853)
% 155.90/155.60 [2836]P28(a1)
% 155.90/155.60 [2837]P28(a113)
% 155.90/155.60 [2838]P29(a853)
% 155.90/155.60 [2839]P29(a1)
% 155.90/155.60 [2840]P29(a113)
% 155.90/155.60 [2841]P30(a1)
% 155.90/155.60 [2842]P71(a1)
% 155.90/155.60 [2843]P73(a853)
% 155.90/155.60 [2844]P73(a846)
% 155.90/155.60 [2845]P73(a1)
% 155.90/155.60 [2846]P73(a113)
% 155.90/155.60 [2847]P76(a1)
% 155.90/155.60 [2848]P79(a846)
% 155.90/155.60 [2849]P79(a1)
% 155.90/155.60 [2850]P87(a853)
% 155.90/155.60 [2851]P87(a846)
% 155.90/155.60 [2852]P87(a1)
% 155.90/155.60 [2853]P88(a846)
% 155.90/155.60 [2854]P98(a853)
% 155.90/155.60 [2855]P98(a846)
% 155.90/155.60 [2856]P98(a1)
% 155.90/155.60 [2857]P94(a846)
% 155.90/155.60 [2858]P108(a1)
% 155.90/155.60 [2859]P89(a1)
% 155.90/155.60 [2860]P77(a853)
% 155.90/155.60 [2861]P77(a1)
% 155.90/155.60 [2862]P77(a113)
% 155.90/155.60 [2863]P99(a853)
% 155.90/155.60 [2864]P99(a846)
% 155.90/155.60 [2865]P99(a1)
% 155.90/155.60 [2866]P111(a1)
% 155.90/155.60 [2867]P96(a853)
% 155.90/155.60 [2868]P96(a846)
% 155.90/155.60 [2869]P96(a1)
% 155.90/155.60 [2870]P137(a853)
% 155.90/155.60 [2871]P137(a1)
% 155.90/155.60 [2872]P137(a113)
% 155.90/155.60 [2873]P112(a1)
% 155.90/155.60 [2874]P102(a853)
% 155.90/155.60 [2875]P102(a846)
% 155.90/155.60 [2876]P102(a1)
% 155.90/155.60 [2877]P102(a113)
% 155.90/155.60 [2878]P117(a853)
% 155.90/155.60 [2879]P117(a1)
% 155.90/155.60 [2880]P117(a113)
% 155.90/155.60 [2881]P110(a853)
% 155.90/155.60 [2882]P110(a1)
% 155.90/155.60 [2883]P110(a113)
% 155.90/155.60 [2884]P132(a853)
% 155.90/155.60 [2885]P132(a1)
% 155.90/155.60 [2886]P132(a113)
% 155.90/155.60 [2887]P120(a1)
% 155.90/155.60 [2888]P113(a1)
% 155.90/155.60 [2889]P106(a846)
% 155.90/155.60 [2890]P103(a853)
% 155.90/155.60 [2891]P103(a1)
% 155.90/155.60 [2892]P103(a113)
% 155.90/155.60 [2893]P104(a853)
% 155.90/155.60 [2894]P104(a846)
% 155.90/155.60 [2895]P104(a1)
% 155.90/155.60 [2896]P104(a113)
% 155.90/155.60 [2897]P105(a853)
% 155.90/155.60 [2898]P105(a846)
% 155.90/155.60 [2899]P105(a1)
% 155.90/155.60 [2900]P105(a113)
% 155.90/155.60 [2901]P100(a853)
% 155.90/155.60 [2902]P100(a1)
% 155.90/155.60 [2903]P100(a113)
% 155.90/155.60 [2904]P121(a853)
% 155.90/155.60 [2905]P121(a1)
% 155.90/155.60 [2906]P121(a113)
% 155.90/155.60 [2907]P128(a1)
% 155.90/155.60 [2908]P122(a853)
% 155.90/155.60 [2909]P122(a1)
% 155.90/155.60 [2910]P122(a113)
% 155.90/155.60 [2911]P123(a853)
% 155.90/155.60 [2912]P123(a1)
% 155.90/155.60 [2913]P123(a113)
% 155.90/155.60 [2914]P130(a853)
% 155.90/155.60 [2915]P130(a1)
% 155.90/155.60 [2916]P130(a113)
% 155.90/155.60 [2917]P118(a1)
% 155.90/155.60 [2918]P129(a853)
% 155.90/155.60 [2919]P129(a1)
% 155.90/155.60 [2920]P129(a113)
% 155.90/155.60 [2921]P116(a853)
% 155.90/155.60 [2922]P116(a1)
% 155.90/155.60 [2923]P116(a113)
% 155.90/155.60 [2924]P119(a1)
% 155.90/155.60 [2925]P68(a853)
% 155.90/155.60 [2926]P68(a1)
% 155.90/155.60 [2927]P68(a113)
% 155.90/155.60 [2928]P80(a853)
% 155.90/155.60 [2929]P80(a1)
% 155.90/155.60 [2930]P80(a113)
% 155.90/155.60 [2931]P126(a853)
% 155.90/155.60 [2932]P126(a1)
% 155.90/155.60 [2933]P126(a113)
% 155.90/155.60 [2934]P133(a1)
% 155.90/155.60 [2935]P127(a853)
% 155.90/155.60 [2936]P127(a1)
% 155.90/155.60 [2937]P127(a113)
% 155.90/155.60 [2938]P124(a1)
% 155.90/155.60 [2939]P84(a853)
% 155.90/155.60 [2940]P84(a1)
% 155.90/155.60 [2941]P84(a113)
% 155.90/155.60 [2942]P125(a1)
% 155.90/155.60 [2943]P81(a853)
% 155.90/155.60 [2944]P81(a1)
% 155.90/155.60 [2945]P81(a113)
% 155.90/155.60 [2946]P82(a853)
% 155.90/155.60 [2947]P82(a1)
% 155.90/155.60 [2948]P82(a113)
% 155.90/155.60 [2949]P78(a853)
% 155.90/155.60 [2950]P78(a1)
% 155.90/155.60 [2951]P78(a113)
% 155.90/155.60 [2952]P72(a853)
% 155.90/155.60 [2953]P72(a1)
% 155.90/155.60 [2954]P72(a113)
% 155.90/155.60 [2955]P134(a1)
% 155.90/155.60 [2956]P97(a846)
% 155.90/155.60 [2957]P85(a1)
% 155.90/155.60 [2958]P83(a1)
% 155.90/155.60 [2959]P131(a1)
% 155.90/155.60 [2960]P69(a1)
% 155.90/155.60 [2961]P90(a1)
% 155.90/155.60 [2962]P91(a853)
% 155.90/155.60 [2963]P91(a1)
% 155.90/155.60 [2964]P91(a113)
% 155.90/155.60 [2965]P31(a846)
% 155.90/155.60 [2966]P109(a853)
% 155.90/155.60 [2967]P109(a1)
% 155.90/155.60 [2968]P109(a113)
% 155.90/155.60 [2969]P135(a853)
% 155.90/155.60 [2970]P135(a1)
% 155.90/155.60 [2971]P135(a113)
% 155.90/155.60 [2972]P60(a853)
% 155.90/155.60 [2973]P60(a1)
% 155.90/155.60 [2974]P60(a113)
% 155.90/155.60 [2975]P61(a1)
% 155.90/155.60 [2976]P138(a1)
% 155.90/155.60 [2977]P138(a856)
% 155.90/155.60 [2978]P62(a846)
% 155.90/155.60 [2979]P62(a856)
% 155.90/155.60 [2980]P74(a853)
% 155.90/155.60 [2981]P74(a1)
% 155.90/155.60 [2982]P74(a113)
% 155.90/155.60 [2983]P86(a853)
% 155.90/155.60 [2984]P86(a1)
% 155.90/155.60 [2985]P86(a113)
% 155.90/155.60 [2986]P63(a846)
% 155.90/155.60 [2987]P63(a856)
% 155.90/155.60 [2988]P92(a847)
% 155.90/155.60 [2989]P92(a853)
% 155.90/155.60 [2990]P92(a848)
% 155.90/155.60 [2991]P92(a846)
% 155.90/155.60 [2992]P92(a851)
% 155.90/155.60 [2993]P92(a1)
% 155.90/155.60 [2994]P92(a308)
% 155.90/155.60 [2995]P92(a113)
% 155.90/155.60 [2996]P92(a856)
% 155.90/155.60 [2997]P95(a846)
% 155.90/155.60 [3013]P41(a853,a232)
% 155.90/155.60 [3014]P41(a853,a302)
% 155.90/155.60 [3100]P49(a853,a853,a126)
% 155.90/155.60 [4381]~E(a111,a92)
% 155.90/155.60 [4382]~P22(a224)
% 155.90/155.60 [2807]E(f2(a1),a92)
% 155.90/155.60 [2808]E(f114(a113),a3)
% 155.90/155.60 [2809]E(f21(a113),a22)
% 155.90/155.60 [2998]E(f189(a853),f2(a853))
% 155.90/155.60 [2999]E(f34(a23),f2(a853))
% 155.90/155.60 [3000]E(f93(a224),f2(a853))
% 155.90/155.60 [3001]E(f93(a188),f2(a853))
% 155.90/155.60 [3002]E(f115(a853),f225(a853))
% 155.90/155.60 [3003]E(f124(a853),f226(a853))
% 155.90/155.60 [3004]E(f116(a1),f39(a1))
% 155.90/155.60 [3005]P32(f2(a1))
% 155.90/155.60 [3006]P32(f87(a1))
% 155.90/155.60 [3053]P22(f312(a24,a23))
% 155.90/155.60 [3068]P41(f860(a853,a853),a45)
% 155.90/155.60 [3417]E(f304(a853,a853,a232,a232),a45)
% 155.90/155.60 [4383]~E(f87(a1),f2(a1))
% 155.90/155.60 [3007]E(f125(f2(a853)),f2(a853))
% 155.90/155.60 [3008]E(f4(f2(a113)),f2(a853))
% 155.90/155.60 [3018]E(f312(f88(a1),a92),a92)
% 155.90/155.60 [3022]E(f312(a3,f2(a853)),f2(a113))
% 155.90/155.60 [3023]E(f312(a126,f2(a853)),f87(a853))
% 155.90/155.60 [3024]E(f312(a118,f87(a1)),f87(a853))
% 155.90/155.60 [3025]E(f312(a3,f87(a853)),f87(a113))
% 155.90/155.60 [3027]E(f312(f117(a1),a92),f2(a1))
% 155.90/155.60 [3028]E(f312(f117(a113),a92),f2(a113))
% 155.90/155.60 [3029]E(f312(a118,f2(a1)),f2(a853))
% 155.90/155.60 [3030]E(f312(f190(a847),a23),f2(a853))
% 155.90/155.60 [3031]E(f312(f190(a846),a224),f2(a853))
% 155.90/155.60 [3032]E(f312(f190(a846),a188),f2(a853))
% 155.90/155.60 [3033]E(f312(f117(a853),a92),f2(a853))
% 155.90/155.60 [3038]E(f312(f88(a1),f87(a1)),a111)
% 155.90/155.60 [3046]E(f312(f190(a113),f2(a113)),f2(a853))
% 155.90/155.60 [3047]E(f312(f88(a1),f2(a1)),f2(a1))
% 155.90/155.60 [3048]E(f312(f114(a1),f2(a853)),f2(a1))
% 155.90/155.60 [3049]E(f312(f114(a1),f87(a853)),f87(a1))
% 155.90/155.60 [3063]E(f312(a118,f87(a1)),f312(a126,f2(a853)))
% 155.90/155.60 [3065]E(f312(f173(a849,a847),a29),a30)
% 155.90/155.60 [3066]E(f303(f860(a853,a853),a45),a46)
% 155.90/155.60 [3067]E(f305(f860(a853,a853),a45),a77)
% 155.90/155.60 [3090]E(f312(f234(a853),f2(a853)),f235(f861(a853,a846)))
% 155.90/155.60 [3091]E(f312(f279(a853),f2(a853)),f189(f861(a853,a846)))
% 155.90/155.60 [3102]P43(f189(f861(a1,a846)))
% 155.90/155.60 [3134]E(f312(f312(f21(a113),f2(a113)),f87(a113)),f2(a113))
% 155.90/155.60 [3207]P22(f312(f312(f228(a1),a111),f2(a1)))
% 155.90/155.60 [3232]P22(f312(f312(f228(a1),f2(a1)),f87(a1)))
% 155.90/155.60 [3234]P22(f312(f312(f227(a1),f2(a1)),f87(a1)))
% 155.90/155.60 [3410]P22(f312(f70(a849),f179(a849,a847,a30)))
% 155.90/155.60 [3447]E(f312(f312(f267(a853,a853,a853),a302),f287(a853,a302)),a232)
% 155.90/155.60 [3489]P44(a1,a853,a118,f312(f227(a1),f2(a1)))
% 155.90/155.60 [3493]E(f312(f312(f50(a853,f861(a853,a846)),f235(f861(a853,a846))),f281(a853)),f235(f861(a853,a846)))
% 155.90/155.60 [3494]E(f312(f312(f50(a853,f861(a853,a846)),f235(f861(a853,a846))),f234(a853)),f235(f861(a853,a846)))
% 155.90/155.60 [3495]E(f312(f312(f50(a853,f861(a853,a846)),f235(f861(a853,a846))),f279(a853)),f235(f861(a853,a846)))
% 155.90/155.60 [3496]E(f312(f312(f51(a853,f861(a853,a846)),f235(f861(a853,a846))),f280(a853)),f189(f861(a853,a846)))
% 155.90/155.60 [3510]P19(a853,a1,f114(a1),f235(f861(a853,a846)))
% 155.90/155.60 [3651]E(f312(f82(a853,a113,a1,a3),a118),f117(a113))
% 155.90/155.60 [3876]P56(a113,a853,a19,a3,f235(f861(a853,a846)))
% 155.90/155.60 [3885]P56(a1,f861(f860(a853,a853),a846),a121,a98,a112)
% 155.90/155.60 [4146]E(f250(a1,a1,a1,a1,f39(a1),f88(a1)),a59)
% 155.90/155.60 [4416]~E(f312(f117(a1),a111),f312(f117(a1),a92))
% 155.90/155.60 [4417]~P22(f312(a194,f2(a1)))
% 155.90/155.60 [4418]~P22(f312(a194,f87(a1)))
% 155.90/155.60 [4472]~P22(f312(f312(f228(a1),a92),f2(a1)))
% 155.90/155.60 [3083]E(f312(f312(f21(a1),a111),a111),a92)
% 155.90/155.60 [3099]E(f312(f114(a1),f312(a126,f2(a853))),f87(a1))
% 155.90/155.60 [3158]E(f312(f53(a856),f235(f861(a856,a846))),f87(a853))
% 155.90/155.60 [3182]P22(f312(a194,f312(f117(a1),a111)))
% 155.90/155.60 [3183]P22(f312(f312(f228(a1),a111),a92))
% 155.90/155.60 [3185]P22(f312(f312(f227(a1),a111),a92))
% 155.90/155.60 [3244]E(f312(f312(f289(a853),f2(a853)),f189(f861(a853,a846))),f312(f281(a853),f2(a853)))
% 155.90/155.60 [3299]P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),a92)))
% 155.90/155.60 [3306]P22(f312(f312(f195(a862),f864(a863,a865)),a579))
% 155.90/155.60 [3314]E(f312(f290(a853,a853,a126),f235(f861(a853,a846))),f312(f280(a853),f2(a853)))
% 155.90/155.60 [3352]P3(f860(a853,a853),f235(f861(f860(a853,a853),a846)),a122)
% 155.90/155.60 [3659]E(f312(f82(a853,a1,a113,f114(a1)),a19),a20)
% 155.90/155.60 [3717]P41(a853,f312(f233(f860(a853,a853)),f312(f249(a853,a853,a846),f228(a853))))
% 155.90/155.60 [4462]~P22(f312(a194,f312(f117(a1),a92)))
% 155.90/155.60 [4463]~P22(f312(f312(f195(a862),a863),a865))
% 155.90/155.60 [4464]~P22(f312(f312(f228(a1),a92),a92))
% 155.90/155.60 [4465]~P22(f312(f312(f228(a1),a92),a111))
% 155.90/155.60 [4466]~P22(f312(f312(f228(a1),a111),a111))
% 155.90/155.60 [4467]~P22(f312(f312(f227(a1),a92),a111))
% 155.90/155.60 [4482]~P22(f312(f70(a853),f235(f861(a853,a846))))
% 155.90/155.60 [4483]~P22(f312(f70(a1),f235(f861(a1,a846))))
% 155.90/155.60 [4314]E(f312(f249(a1,a1,a846),f312(f312(f8(f861(a1,a846),f861(a1,a846),a1),f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f228(a1),f2(a1))))),f312(f312(f7(a1,a1,f861(a1,a846)),f312(f312(f8(f861(a1,f861(a1,a846)),f861(a1,f861(a1,a846)),a1),f7(a1,a1,a846)),f312(f312(f8(f861(a1,a1),f861(a1,f861(a1,a846)),a1),f312(f8(a1,f861(a1,a846),a1),a309)),a200))),f87(a1)))),a205)
% 155.90/155.60 [3390]E(f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111),f312(f88(a1),a111))
% 155.90/155.60 [3432]E(f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111),f312(f312(f21(a1),a92),a111))
% 155.90/155.60 [3587]E(f312(f312(f69(f860(a853,a853)),f235(f861(f860(a853,a853),a846))),a122),a112)
% 155.90/155.60 [3615]E(f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f87(a1))
% 155.90/155.60 [3616]E(f312(f117(a113),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f87(a113))
% 155.90/155.60 [3617]E(f312(f117(a853),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f87(a853))
% 155.90/155.60 [3621]E(f312(f117(a853),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(a126,f2(a853)))
% 155.90/155.60 [4010]E(f312(f312(f124(f861(f860(f860(a853,a853),f860(a853,a853)),a846)),a45),f287(f860(a853,a853),f189(f861(f860(f860(a853,a853),f860(a853,a853)),a846)))),a79)
% 155.90/155.60 [4080]E(f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),f2(a853)),f2(a853))),f189(f861(f860(a853,a853),a846))))),f2(a1))
% 155.90/155.60 [4081]E(f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),f87(a853)),f2(a853))),f189(f861(f860(a853,a853),a846))))),f87(a1))
% 155.90/155.60 [4097]E(f312(f233(f860(a853,a853)),f312(f249(a853,a853,a846),f312(f312(f8(a853,f861(a853,a846),a853),f312(f7(a853,a853,a846),a309)),a126))),a302)
% 155.90/155.60 [4066]E(f312(f117(a853),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(a853))))
% 155.90/155.60 [4069]E(f312(f117(a853),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(a853),f87(a853)),f87(a853)))
% 155.90/155.60 [4070]E(f312(f117(a853),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(a846),f235(f861(a846,a846))))
% 155.90/155.60 [4132]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))))
% 155.90/155.60 [4206]P20(f861(f860(a853,a853),a846),f312(f312(f239(f861(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),a846),f861(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),a846)),a46),a78))
% 155.90/155.60 [4207]P20(f861(f860(a853,a853),a846),f312(f312(f239(f861(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),a846),f861(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),a846)),a77),a80))
% 155.90/155.60 [4246]E(f312(f312(f124(f861(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),a846)),f305(f860(a853,a853),a79)),f312(f312(f289(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),f189(f861(f860(a853,a853),a846))),f189(f861(f860(a853,a853),a846)))),f189(f861(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),a846)))),a80)
% 155.90/155.60 [4247]E(f312(f312(f124(f861(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),a846)),f303(f860(a853,a853),a79)),f312(f312(f289(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),f189(f861(f860(a853,a853),a846))),f189(f861(f860(a853,a853),a846)))),f189(f861(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),a846)))),a78)
% 155.90/155.60 [4134]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(a853))))
% 155.90/155.60 [4183]E(f312(f114(a1),f312(f117(a853),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))))
% 155.90/155.60 [4218]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)))))
% 155.90/155.60 [4219]E(f312(f117(a853),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(a853)))))
% 155.90/155.60 [4260]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)))
% 155.90/155.60 [4286]E(f312(f114(a1),f312(f117(a853),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)))
% 155.90/155.60 [4301]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))))
% 155.90/155.60 [3015]P2(x30151,a309)
% 155.90/155.60 [3418]P19(a853,a853,a126,x34181)
% 155.90/155.60 [3009]P92(f852(x30091))
% 155.90/155.60 [3010]P92(f857(x30101))
% 155.90/155.60 [3011]P92(f854(x30111))
% 155.90/155.60 [3012]P92(f855(x30121))
% 155.90/155.60 [3034]P41(a1,f119(x30341))
% 155.90/155.60 [3035]P41(a1,f120(x30351))
% 155.90/155.60 [3037]P42(x30371,f192(x30371))
% 155.90/155.60 [3087]P41(f861(x30871,a846),f286(x30871))
% 155.90/155.60 [3125]E(f54(a1,x31251,x31251),f2(a1))
% 155.90/155.60 [3179]P11(x31791,f861(x31791,a846),f289(x31791))
% 155.90/155.60 [4387]~E(f312(a27,x43871),a23)
% 155.90/155.60 [4389]~E(f312(a126,x43891),x43891)
% 155.90/155.60 [4401]~E(f312(a126,x44011),f2(a853))
% 155.90/155.60 [3016]E(f42(f40(x30161)),f2(a853))
% 155.90/155.60 [3017]E(f42(f41(x30171)),f2(a853))
% 155.90/155.60 [3019]E(f312(f190(a853),x30191),x30191)
% 155.90/155.60 [3020]E(f312(f117(a1),x30201),x30201)
% 155.90/155.60 [3036]E(f312(a98,f313(x30361)),x30361)
% 155.90/155.60 [3050]E(f128(x30501,f127(x30501)),f127(x30501))
% 155.90/155.60 [3051]E(f148(x30511,f127(x30511)),f127(x30511))
% 155.90/155.60 [3054]E(f312(f190(a851),f40(x30541)),f2(a853))
% 155.90/155.60 [3055]E(f312(f190(a851),f41(x30551)),f2(a853))
% 155.90/155.60 [3056]E(f34(f312(a27,x30561)),f2(a853))
% 155.90/155.60 [3060]E(f312(f164(x30601),f127(x30601)),f127(x30601))
% 155.90/155.60 [3061]E(f312(f167(x30611),f127(x30611)),f127(x30611))
% 155.90/155.60 [3062]E(f312(f165(x30621),f127(x30621)),f127(x30621))
% 155.90/155.60 [3069]E(f312(f117(a1),x30691),f312(f116(a1),x30691))
% 155.90/155.60 [3070]E(f312(a98,f312(a121,x30701)),x30701)
% 155.90/155.60 [3072]E(f312(a3,f312(a19,x30721)),x30721)
% 155.90/155.60 [3073]E(f312(a19,f312(a3,x30731)),x30731)
% 155.90/155.60 [3074]P32(f312(f114(a1),x30741))
% 155.90/155.60 [3079]E(f312(f190(f857(x30791)),f192(x30791)),f2(a853))
% 155.90/155.60 [3080]E(f312(f190(f854(x30801)),f127(x30801)),f2(a853))
% 155.90/155.60 [3085]E(f312(f190(a847),f312(a27,x30851)),f2(a853))
% 155.90/155.60 [3086]E(f312(f47(a1,x30861),f2(a1)),f2(a1))
% 155.90/155.60 [3097]E(f218(x30971,f192(x30971)),f189(f861(x30971,a846)))
% 155.90/155.60 [3105]E(f312(f312(f89(a853),x31051),f2(a853)),x31051)
% 155.90/155.60 [3106]E(f312(f312(f89(a1),x31061),f2(a1)),x31061)
% 155.90/155.60 [3107]E(f312(f312(f21(a853),x31071),f2(a853)),x31071)
% 155.90/155.60 [3108]E(f312(f312(f90(a853),x31081),f87(a853)),x31081)
% 155.90/155.60 [3109]E(f312(f312(f90(a1),x31091),f87(a1)),x31091)
% 155.90/155.60 [3110]E(f312(f312(f226(a853),x31101),f2(a853)),x31101)
% 155.90/155.60 [3111]E(f312(f312(f90(a853),x31111),f2(a853)),f2(a853))
% 155.90/155.60 [3112]E(f312(f312(f225(a853),x31121),f2(a853)),f2(a853))
% 155.90/155.60 [3118]E(f312(f168(x31181),f127(x31181)),f189(f861(x31181,a846)))
% 155.90/155.60 [3121]P22(f312(f133(x31211),f127(x31211)))
% 155.90/155.60 [3126]E(f312(f193(x31261,x31261),f5(x31261)),f39(f857(x31261)))
% 155.90/155.60 [3127]E(f312(f193(x31271,x31271),f39(x31271)),f39(f857(x31271)))
% 155.90/155.60 [3128]E(f312(f150(x31281,x31281),f5(x31281)),f39(f854(x31281)))
% 155.90/155.60 [3129]E(f312(f150(x31291,x31291),f39(x31291)),f39(f854(x31291)))
% 155.90/155.60 [3130]E(f54(a1,x31301,f2(a1)),x31301)
% 155.90/155.60 [3131]E(f312(f227(a853),f312(a126,x31311)),f312(f228(a853),x31311))
% 155.90/155.60 [3132]E(f312(f234(a853),f312(a126,x31321)),f312(f280(a853),x31321))
% 155.90/155.60 [3133]E(f312(f279(a853),f312(a126,x31331)),f312(f281(a853),x31331))
% 155.90/155.60 [3135]E(f54(a1,f2(a1),x31351),f2(a1))
% 155.90/155.60 [3142]E(f312(f312(f89(a853),x31421),f87(a853)),f312(a126,x31421))
% 155.90/155.60 [3152]E(f312(f282(a853,x31521),f2(a853)),f189(f861(a853,a846)))
% 155.90/155.60 [3165]E(f283(a853,f2(a853),x31651),f312(f281(a853),x31651))
% 155.90/155.60 [3210]E(f312(f312(f21(a853),f312(a126,x32101)),f87(a853)),x32101)
% 155.90/155.60 [3223]E(f55(f2(a1),x32231),f312(f312(f239(a1,a1),f2(a1)),f2(a1)))
% 155.90/155.60 [3274]P22(f312(f312(f228(a853),x32741),f312(a126,x32741)))
% 155.90/155.60 [3286]P22(f312(f312(f228(a853),f2(a853)),f312(a126,x32861)))
% 155.90/155.60 [3575]E(f312(f312(f21(a113),f312(a3,f312(a126,f312(a19,x35751)))),f87(a113)),x35751)
% 155.90/155.60 [3643]P22(f312(f312(f227(a1),f312(f88(a1),f312(f114(a1),x36431))),f2(a1)))
% 155.90/155.60 [3793]P22(f312(f312(f228(a1),f312(f88(a1),f312(f114(a1),f312(a126,x37931)))),f2(a1)))
% 155.90/155.60 [4424]~E(f235(f861(x44241,a846)),f189(f861(x44241,a846)))
% 155.90/155.60 [4475]~P22(f312(f312(f228(a853),x44751),f2(a853)))
% 155.90/155.60 [4491]~P22(f312(f312(f228(a1),f312(f114(a1),x44911)),f2(a1)))
% 155.90/155.60 [3084]E(f175(x30841,f127(f854(x30841))),f127(f854(x30841)))
% 155.90/155.60 [3088]E(f312(f312(f90(a1),a92),x30881),a92)
% 155.90/155.60 [3089]E(f312(f312(f89(a1),a92),x30891),x30891)
% 155.90/155.60 [3092]E(f312(a118,f312(f114(a1),x30921)),x30921)
% 155.90/155.60 [3093]E(f312(f312(f89(a1),x30931),a92),x30931)
% 155.90/155.60 [3094]E(f312(f312(f21(a1),x30941),a92),x30941)
% 155.90/155.60 [3096]E(f312(f47(a1,f2(a1)),x30961),f2(a1))
% 155.90/155.60 [3098]E(f312(f312(f21(a853),x30981),x30981),f2(a853))
% 155.90/155.60 [3103]E(f312(f88(a1),f312(f88(a1),x31031)),x31031)
% 155.90/155.60 [3104]E(f312(f53(a853),f312(f279(a853),x31041)),x31041)
% 155.90/155.60 [3113]E(f312(f312(f89(a853),f2(a853)),x31131),x31131)
% 155.90/155.60 [3114]E(f312(f312(f89(a1),f2(a1)),x31141),x31141)
% 155.90/155.60 [3115]E(f312(f312(f90(a853),f87(a853)),x31151),x31151)
% 155.90/155.60 [3116]E(f312(f312(f90(a1),f87(a1)),x31161),x31161)
% 155.90/155.60 [3117]E(f312(f312(f226(a853),f2(a853)),x31171),x31171)
% 155.90/155.60 [3122]E(f312(f312(f21(a853),f2(a853)),x31221),f2(a853))
% 155.90/155.60 [3123]E(f312(f312(f90(a853),f2(a853)),x31231),f2(a853))
% 155.90/155.60 [3124]E(f312(f312(f225(a853),f2(a853)),x31241),f2(a853))
% 155.90/155.60 [3140]E(f312(f282(a853,f2(a853)),x31401),f312(f279(a853),x31401))
% 155.90/155.60 [3141]E(f312(f312(f90(a1),a111),x31411),f312(f88(a1),x31411))
% 155.90/155.60 [3144]E(f312(a118,f312(f117(a1),x31441)),f312(f117(a853),x31441))
% 155.90/155.60 [3145]E(f312(a19,f312(f117(a113),x31451)),f312(f117(a853),x31451))
% 155.90/155.60 [3146]E(f312(f53(a853),f312(f281(a853),x31461)),f312(a126,x31461))
% 155.90/155.60 [3156]E(f312(f312(f89(a853),f87(a853)),x31561),f312(a126,x31561))
% 155.90/155.60 [3160]E(f312(f84(a1),f312(f114(a1),x31601)),f312(f114(a1),x31601))
% 155.90/155.60 [3161]E(f312(f116(a1),f312(f114(a1),x31611)),f312(f114(a1),x31611))
% 155.90/155.60 [3164]E(f312(f47(a853,x31641),f312(a126,f2(a853))),x31641)
% 155.90/155.60 [3167]E(f312(f53(x31671),f189(f861(x31671,a846))),f2(a853))
% 155.90/155.60 [3178]E(f312(f47(a1,x31781),f312(f117(a1),a111)),f312(f88(a1),x31781))
% 155.90/155.60 [3180]E(f54(a853,x31801,f312(a126,f2(a853))),f2(a853))
% 155.90/155.60 [3181]E(f54(a1,x31811,f312(f117(a1),a111)),f2(a1))
% 155.90/155.60 [3197]E(f135(a853,f312(f282(a853,x31971),f2(a853))),f127(a853))
% 155.90/155.60 [3198]E(f312(f312(f21(a1),x31981),f87(a1)),f312(f312(f89(a1),x31981),a111))
% 155.90/155.60 [3199]E(f312(f312(f89(a1),x31991),f87(a1)),f312(f312(f21(a1),x31991),a111))
% 155.90/155.60 [3204]P22(f312(f312(f195(a23),x32041),x32041))
% 155.90/155.60 [3205]P22(f312(f312(f227(a853),x32051),x32051))
% 155.90/155.60 [3206]P22(f312(f312(f227(a1),x32061),x32061))
% 155.90/155.60 [3211]E(f312(f88(a1),f312(f117(a1),x32111)),f312(f117(a1),f312(f88(a1),x32111)))
% 155.90/155.60 [3213]P22(f312(f70(a853),f312(f281(a853),x32131)))
% 155.90/155.60 [3214]P22(f312(f70(a853),f312(f279(a853),x32141)))
% 155.90/155.60 [3222]E(f157(x32221,f235(f861(x32221,a846))),f235(f861(f854(x32221),a846)))
% 155.90/155.60 [3226]P22(f312(f312(f227(a853),f2(a853)),x32261))
% 155.90/155.60 [3237]E(f312(f312(f89(a853),f125(x32371)),f312(a126,f2(a853))),f125(f312(a126,x32371)))
% 155.90/155.60 [3238]E(f312(f233(x32381),f312(f16(a846,x32381),a224)),f189(f861(x32381,a846)))
% 155.90/155.60 [3239]E(f312(f233(x32391),f312(f16(a846,x32391),a188)),f235(f861(x32391,a846)))
% 155.90/155.60 [3243]E(f312(f312(f289(a853),x32431),f312(f279(a853),x32431)),f312(f279(a853),f312(a126,x32431)))
% 155.90/155.60 [3255]E(f312(f312(f89(a1),f87(a1)),f312(f114(a1),x32551)),f312(f114(a1),f312(a126,x32551)))
% 155.90/155.60 [3258]E(f312(f312(f147(f854(x32581)),f127(x32581)),f127(f854(x32581))),f62(x32581,f127(x32581)))
% 155.90/155.60 [3277]E(f189(f861(f860(x32771,x32771),a846)),f237(x32771,f189(f861(x32771,a846))))
% 155.90/155.60 [3278]E(f312(f288(x32781),f235(f861(x32781,a846))),f235(f861(f861(x32781,a846),a846)))
% 155.90/155.60 [3279]E(f312(f88(f861(x32791,a846)),f189(f861(x32791,a846))),f235(f861(x32791,a846)))
% 155.90/155.60 [3280]E(f312(f88(f861(x32801,a846)),f235(f861(x32801,a846))),f189(f861(x32801,a846)))
% 155.90/155.60 [3282]P22(f312(f70(x32821),f189(f861(x32821,a846))))
% 155.90/155.60 [3284]E(f312(f282(a853,x32841),f312(a126,x32841)),f312(f312(f289(a853),x32841),f189(f861(a853,a846))))
% 155.90/155.60 [3285]E(f94(f860(a853,a853),f56(x32851,f2(a853))),f312(f312(f239(a853,a853),f2(a853)),x32851))
% 155.90/155.60 [3298]E(f312(f312(f289(a853),f312(a126,x32981)),f312(f281(a853),x32981)),f312(f281(a853),f312(a126,x32981)))
% 155.90/155.60 [3302]P41(x33021,f189(f861(f860(x33021,x33021),a846)))
% 155.90/155.60 [3308]P22(f312(f312(f227(a1),f2(a1)),f312(f114(a1),x33081)))
% 155.90/155.60 [3316]E(f312(f312(f89(a853),f312(f190(a853),x33161)),f312(a126,f2(a853))),f312(f190(a853),f312(a126,x33161)))
% 155.90/155.60 [3425]P43(f312(f290(a853,a1,f114(a1)),x34251))
% 155.90/155.60 [3461]P50(x34611,f189(f861(x34611,a846)),f189(f861(f860(x34611,x34611),a846)))
% 155.90/155.60 [3486]E(f312(f312(f239(a1,a1),f312(f117(a1),a111)),f312(f312(f21(a1),x34861),f87(a1))),f58(f312(f117(a1),a111),x34861))
% 155.90/155.60 [3532]P59(x35321,f312(f16(f861(x35321,a846),x35321),f312(f16(a846,x35321),a224)))
% 155.90/155.60 [3729]P22(f312(f312(f314(f861(f860(a853,a853),a846)),f313(x37291)),a112))
% 155.90/155.60 [3753]P22(f312(f312(f314(f861(f860(a853,a853),a846)),f312(a121,x37531)),a112))
% 155.90/155.60 [3894]P19(x38941,f861(x38941,a846),f312(f312(f7(x38941,f861(x38941,a846),f861(x38941,a846)),f289(x38941)),f189(f861(x38941,a846))),f235(f861(x38941,a846)))
% 155.90/155.60 [4420]~E(f312(f312(f89(a1),x44201),x44201),a111)
% 155.90/155.60 [4461]~E(f312(a3,f312(a126,f312(a19,x44611))),f2(a113))
% 155.90/155.60 [4468]~P22(f312(a194,f312(f114(a1),x44681)))
% 155.90/155.60 [4471]~P22(f312(f312(f228(a853),x44711),x44711))
% 155.90/155.60 [4484]~P22(f312(f312(f227(a853),f312(a126,x44841)),x44841))
% 155.90/155.60 [3229]E(f312(a118,f312(f88(a1),f312(f114(a1),x32291))),f2(a853))
% 155.90/155.60 [3231]E(f312(f312(f89(a1),f312(f88(a1),x32311)),x32311),f2(a1))
% 155.90/155.60 [3236]E(f312(f53(a1),f312(f282(a1,f2(a1)),x32361)),f312(a118,x32361))
% 155.90/155.60 [3248]E(f312(f312(f240(a853),f312(a126,f2(a853))),x32481),f312(a126,f2(a853)))
% 155.90/155.60 [3349]E(f312(f263(x33491),f189(f861(f860(x33491,x33491),a846))),f189(f861(x33491,a846)))
% 155.90/155.60 [3357]E(f48(f861(x33571,a846),f189(f861(f861(x33571,a846),a846))),f189(f861(x33571,a846)))
% 155.90/155.60 [3358]E(f48(f861(x33581,a846),f235(f861(f861(x33581,a846),a846))),f235(f861(x33581,a846)))
% 155.90/155.60 [3359]E(f49(f861(x33591,a846),f189(f861(f861(x33591,a846),a846))),f235(f861(x33591,a846)))
% 155.90/155.60 [3360]E(f49(f861(x33601,a846),f235(f861(f861(x33601,a846),a846))),f189(f861(x33601,a846)))
% 155.90/155.60 [3408]E(f312(f312(f289(f854(x34081)),f127(x34081)),f189(f861(f854(x34081),a846))),f157(x34081,f189(f861(x34081,a846))))
% 155.90/155.60 [3409]E(f312(f312(f289(f854(x34091)),f127(x34091)),f189(f861(f854(x34091),a846))),f158(x34091,f127(f861(x34091,a846))))
% 155.90/155.60 [3446]E(f312(f312(f89(a853),f4(x34461)),f312(a126,f2(a853))),f4(f312(a3,f312(a126,f312(a19,x34461)))))
% 155.90/155.60 [3478]E(f312(f53(a1),f312(f290(a853,a1,f114(a1)),x34781)),f312(f53(a853),x34781))
% 155.90/155.60 [3481]P22(f312(f312(f227(a853),x34811),f312(f312(f90(a853),x34811),x34811)))
% 155.90/155.60 [3504]E(f312(f47(a853,f312(a126,f2(a853))),f312(f117(a853),x35041)),f312(a118,f312(f47(a1,f87(a1)),f312(f117(a1),x35041))))
% 155.90/155.60 [3514]E(f312(f290(a1,a853,a118),f283(a1,f2(a1),f312(f114(a1),x35141))),f312(f281(a853),x35141))
% 155.90/155.60 [3529]E(f312(f168(a853),f135(a853,f312(f282(a853,f2(a853)),f312(a126,x35291)))),f312(f281(a853),x35291))
% 155.90/155.60 [3530]E(f312(f312(f89(a853),f312(f190(a113),x35301)),f312(a126,f2(a853))),f312(f190(a113),f312(a3,f312(a126,f312(a19,x35301)))))
% 155.90/155.60 [3549]E(f312(f290(a1,a853,a118),f312(f290(a853,a1,f114(a1)),x35491)),x35491)
% 155.90/155.60 [3577]E(f312(f312(f289(a853),f2(a853)),f312(f290(a853,a853,a126),f312(f279(a853),x35771))),f312(f279(a853),f312(a126,x35771)))
% 155.90/155.60 [3586]P54(x35861,x35861,f287(x35861,f189(f861(f860(x35861,x35861),a846))))
% 155.90/155.60 [3592]P22(f312(a194,f312(f88(a1),f312(f114(a1),f312(a126,x35921)))))
% 155.90/155.60 [3603]E(f312(f312(f21(f861(a853,a846)),f312(f234(a853),x36031)),f312(f312(f289(a853),x36031),f189(f861(a853,a846)))),f312(f234(a853),f312(a126,x36031)))
% 155.90/155.60 [3618]E(f312(f312(f89(a1),f312(f312(f21(a1),a92),x36181)),f312(f312(f21(a1),a92),x36181)),f312(f312(f21(a1),a92),f312(f312(f89(a1),x36181),x36181)))
% 155.90/155.60 [3632]E(f312(f312(f289(f861(x36321,a846)),f189(f861(x36321,a846))),f189(f861(f861(x36321,a846),a846))),f312(f288(x36321),f189(f861(x36321,a846))))
% 155.90/155.60 [3660]E(f312(f312(f21(f861(a853,a846)),f312(f280(a853),x36601)),f312(f312(f289(a853),f312(a126,x36601)),f189(f861(a853,a846)))),f312(f280(a853),f312(a126,x36601)))
% 155.90/155.60 [3668]E(f312(f312(f289(f857(x36681)),f192(x36681)),f312(f290(x36681,f857(x36681),f219(x36681)),f235(f861(x36681,a846)))),f235(f861(f857(x36681),a846)))
% 155.90/155.60 [3766]E(f312(f117(a853),f312(f312(f89(a1),x37661),x37661)),f312(f312(f95(a853,a853),f312(f117(a853),x37661)),f312(f312(f18(a853,a853,a853),f89(a853)),f5(a853))))
% 155.90/155.60 [4155]P11(x41551,f861(x41551,a846),f312(f312(f8(f861(x41551,a846),f861(f861(x41551,a846),f861(x41551,a846)),x41551),f312(f7(f861(x41551,a846),f861(x41551,a846),f861(x41551,a846)),f21(f861(x41551,a846)))),f312(f312(f7(x41551,f861(x41551,a846),f861(x41551,a846)),f289(x41551)),f189(f861(x41551,a846)))))
% 155.90/155.60 [4245]E(f312(f233(f860(a1,a1)),f312(f249(a1,a1,a846),f312(f312(f8(f861(a1,a846),f861(a1,a846),a1),f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f227(a1),x42451)))),f228(a1)))),f119(x42451))
% 155.90/155.60 [4277]E(f312(f233(f860(a1,a1)),f312(f249(a1,a1,a846),f312(f312(f18(a1,f861(a1,a846),f861(a1,a846)),f312(f312(f8(f861(a846,a846),f861(f861(a1,a846),f861(a1,a846)),a1),f8(a846,a846,a1)),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f227(a1),x42771)))),f228(a1)))),f120(x42771))
% 155.90/155.60 [4326]E(f312(f233(f860(f861(x43261,a846),f861(x43261,a846))),f312(f249(f861(x43261,a846),f861(x43261,a846),a846),f312(f312(f7(f861(x43261,a846),f861(f861(x43261,a846),a846),f861(f861(x43261,a846),a846)),f312(f312(f8(f861(f861(x43261,a846),f861(a846,a846)),f861(f861(f861(x43261,a846),a846),f861(f861(x43261,a846),a846)),f861(x43261,a846)),f18(f861(x43261,a846),a846,a846)),f312(f312(f8(f861(f861(x43261,a846),a846),f861(f861(x43261,a846),f861(a846,a846)),f861(x43261,a846)),f312(f8(a846,f861(a846,a846),f861(x43261,a846)),a310)),f228(f861(x43261,a846))))),f70(x43261)))),f286(x43261))
% 155.90/155.60 [4488]~P22(f312(f70(f854(x44881)),f235(f861(f854(x44881),a846))))
% 155.90/155.60 [4501]~P22(f312(f312(f227(a1),f2(a1)),f312(f88(a1),f312(f114(a1),f312(a126,x45011)))))
% 155.90/155.60 [3384]E(f312(f312(f21(a1),f312(f312(f89(a1),x33841),a111)),a111),x33841)
% 155.90/155.60 [3402]E(f312(f168(a853),f135(a853,f312(f282(a853,f2(a853)),x34021))),f312(f279(a853),x34021))
% 155.90/155.60 [3637]E(f312(f312(f89(a1),f312(f312(f89(a1),f87(a1)),x36371)),x36371),f312(f312(f21(a1),f312(f312(f89(a1),x36371),x36371)),a111))
% 155.90/155.60 [3685]E(f312(f265(x36851,x36851),f287(x36851,f189(f861(f860(x36851,x36851),a846)))),f287(x36851,f189(f861(f860(x36851,x36851),a846))))
% 155.90/155.60 [3732]P22(f312(f312(f227(a853),x37321),f312(f312(f90(a853),x37321),f312(f312(f90(a853),x37321),x37321))))
% 155.90/155.60 [4014]P22(f312(f70(a853),f312(f233(a853),f312(f312(f7(a853,a853,a846),f228(a853)),x40141))))
% 155.90/155.60 [4015]P22(f312(f70(a853),f312(f233(a853),f312(f312(f7(a853,a853,a846),f227(a853)),x40151))))
% 155.90/155.60 [4296]E(f312(f233(f860(x42961,x42961)),f312(f312(f8(f861(x42961,a846),a846,f860(x42961,x42961)),f96(x42961)),f312(f312(f7(f860(x42961,x42961),f861(x42961,f860(x42961,x42961)),f861(x42961,a846)),f312(f312(f8(f861(f860(x42961,x42961),a846),f861(f861(x42961,f860(x42961,x42961)),f861(x42961,a846)),f860(x42961,x42961)),f8(f860(x42961,x42961),a846,x42961)),a309)),f312(f312(f18(x42961,x42961,f860(x42961,x42961)),f239(x42961,x42961)),f5(x42961))))),f287(x42961,f189(f861(f860(x42961,x42961),a846))))
% 155.90/155.60 [4490]~E(f312(f312(f21(a1),f312(f312(f89(a1),x44901),x44901)),a111),a92)
% 155.90/155.60 [4492]~E(f312(f312(f89(a1),f312(f312(f89(a1),f87(a1)),x44921)),x44921),f2(a1))
% 155.90/155.60 [3782]E(f312(f312(f89(a1),f312(f312(f21(a1),a111),x37821)),f312(f312(f21(a1),a111),x37821)),f312(f312(f21(a1),a111),f312(f312(f21(a1),f312(f312(f89(a1),x37821),x37821)),a111)))
% 155.90/155.60 [3902]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),a111),x39021)),f312(f312(f21(a1),a111),x39021))),a111),f312(f312(f21(a1),a111),f312(f312(f89(a1),x39021),x39021)))
% 155.90/155.60 [3936]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f89(a1),x39361),a111)),f312(f312(f89(a1),x39361),a111))),a111),f312(f312(f89(a1),f312(f312(f89(a1),x39361),x39361)),a111))
% 155.90/155.60 [3972]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),a111),x39721)),f312(f312(f21(a1),a111),x39721))),a111),f312(f312(f21(a1),a92),f312(f312(f21(a1),f312(f312(f89(a1),x39721),x39721)),a111)))
% 155.90/155.60 [4077]E(f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x40771),f2(a853))),f189(f861(f860(a853,a853),a846))))),f312(f114(a1),x40771))
% 155.90/155.60 [4086]E(f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),f317(x40861)),f362(x40861))),f189(f861(f860(a853,a853),a846))))),x40861)
% 155.90/155.60 [4120]E(f312(f233(a1),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f227(a1),f2(a1)))),x41201)),f312(f290(a853,a1,f114(a1)),f312(f233(a853),f312(f312(f8(a1,a846,a853),x41201),f114(a1)))))
% 155.90/155.60 [4163]P43(f312(f233(a1),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f227(a1),f2(a1)))),x41631)))
% 155.90/155.60 [4186]P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),x41861),f189(f861(f860(a853,a853),a846)))),a80))
% 155.90/155.60 [4192]E(f312(f290(a1,a853,a118),f312(f233(a1),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f227(a1),f2(a1)))),f312(f312(f8(a853,a846,a1),x41921),a118)))),f312(f233(a853),x41921))
% 155.90/155.60 [4340]E(f292(a853,f312(f312(f50(f860(a853,a853),f861(a853,a846)),f312(a121,x43401)),f312(f249(a853,a853,f861(a853,a846)),f312(f312(f7(a853,f861(a853,a846),f861(a853,f861(a853,a846))),f312(f312(f8(f861(a853,f861(f861(a853,a846),f861(a853,a846))),f861(f861(a853,a846),f861(a853,f861(a853,a846))),a853),f7(a853,f861(a853,a846),f861(a853,a846))),f312(f312(f8(f861(a853,a853),f861(a853,f861(f861(a853,a846),f861(a853,a846))),a853),f312(f8(a853,f861(f861(a853,a846),f861(a853,a846)),a853),f289(a853))),f21(a853)))),f189(f861(a853,a846)))))),f312(a118,x43401))
% 155.90/155.60 [3825]E(f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),x38251),x38251)),a111)),a111),f312(f312(f89(a1),x38251),x38251))
% 155.90/155.60 [3877]E(f312(f312(f21(a1),f312(f312(f21(a1),f312(f312(f89(a1),x38771),x38771)),a111)),a111),f312(f312(f89(a1),f312(f312(f21(a1),x38771),a111)),f312(f312(f21(a1),x38771),a111)))
% 155.90/155.60 [4094]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f89(a1),f312(f88(a1),x40941)),a111)),f312(f312(f89(a1),f312(f88(a1),x40941)),a111))),a111),f312(f88(a1),f312(f312(f21(a1),f312(f312(f89(a1),x40941),x40941)),a111)))
% 155.90/155.60 [4135]E(f312(f312(f89(a853),x41351),f312(f117(a853),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,x41351)))
% 155.90/155.60 [4136]E(f312(f312(f90(a853),x41361),f312(f117(a853),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(a853),x41361),x41361))
% 155.90/155.60 [4137]E(f312(f47(a853,f312(f312(f89(a853),x41371),x41371)),f312(f117(a853),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)))),x41371)
% 155.90/155.60 [4221]E(f54(a853,f312(a126,f312(a126,x42211)),f312(f117(a853),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(a853,x42211,f312(f117(a853),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)))))
% 155.90/155.60 [4357]E(f312(a98,f312(f312(f50(f860(a853,a853),f861(f860(a853,a853),a846)),f312(a121,x43571)),f312(f249(a853,a853,f861(f860(a853,a853),a846)),f312(f312(f8(f861(a853,f861(f860(a853,a853),a846)),f861(a853,f861(f860(a853,a853),a846)),a853),f312(f8(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846),a853),f264(f860(a853,a853),f860(a853,a853),a122))),f312(f312(f7(a853,f861(f860(a853,a853),a846),f861(a853,f861(f860(a853,a853),a846))),f312(f312(f8(f861(a853,f861(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f861(f861(f860(a853,a853),a846),f861(a853,f861(f860(a853,a853),a846))),a853),f7(a853,f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f8(f861(a853,f860(a853,a853)),f861(a853,f861(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),a853),f312(f8(f860(a853,a853),f861(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),a853),f289(f860(a853,a853)))),f312(f7(a853,a853,f860(a853,a853)),f239(a853,a853))))),f189(f861(f860(a853,a853),a846))))))),f312(f88(a1),x43571))
% 155.90/155.60 [4216]E(f312(f312(f89(a853),f312(f117(a853),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)))),x42161),f312(a126,f312(a126,x42161)))
% 155.90/155.60 [4217]E(f312(f312(f90(a853),f312(f117(a853),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)))),x42171),f312(f312(f89(a853),x42171),x42171))
% 155.90/155.60 [4250]E(f312(f47(a853,f312(a126,f312(a126,x42501))),f312(f117(a853),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(a853,x42501),f312(f117(a853),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))))))
% 155.90/155.60 [4302]E(f312(f312(f89(a853),f312(f117(a853),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))),x43021),f312(a126,f312(a126,f312(a126,x43021))))
% 155.90/155.60 [4377]E(f312(f249(a1,a1,f860(a1,a1)),f312(f312(f18(a1,f861(a1,f860(a1,a1)),f861(a1,f860(a1,a1))),f312(f312(f8(f861(a1,f861(f860(a1,a1),f860(a1,a1))),f861(f861(a1,f860(a1,a1)),f861(a1,f860(a1,a1))),a1),f18(a1,f860(a1,a1),f860(a1,a1))),f312(f312(f8(f861(a1,f860(a1,a1)),f861(a1,f861(f860(a1,a1),f860(a1,a1))),a1),f312(f18(a1,f860(a1,a1),f861(f860(a1,a1),f860(a1,a1))),f312(f312(f8(a846,f861(f860(a1,a1),f861(f860(a1,a1),f860(a1,a1))),a1),f108(f860(a1,a1))),f312(f312(f8(a1,a846,a1),f312(f227(a1),f2(a1))),f312(f312(f7(a1,a1,a1),f21(a1)),x43771))))),f312(f312(f7(a1,f861(a1,a1),f861(a1,f860(a1,a1))),f312(f312(f8(f861(a1,f860(a1,a1)),f861(f861(a1,a1),f861(a1,f860(a1,a1))),a1),f8(a1,f860(a1,a1),a1)),f312(f312(f8(a1,f861(a1,f860(a1,a1)),a1),f239(a1,a1)),f312(f312(f7(a1,a1,a1),f312(f312(f8(a1,f861(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)),x43771))))),f312(f312(f8(a1,f861(a1,f860(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(x43771))
% 155.90/155.60 [3057]P92(f859(x30571,x30572))
% 155.90/155.60 [3058]P92(f858(x30581,x30582))
% 155.90/155.60 [3059]P92(f860(x30591,x30592))
% 155.90/155.60 [3077]P33(a1,f174(x30771,x30772))
% 155.90/155.60 [3078]P41(x30781,f149(x30781,x30782))
% 155.90/155.60 [3174]P50(x31741,x31742,f237(x31741,x31742))
% 155.90/155.60 [3175]P54(x31751,x31751,f237(x31751,x31752))
% 155.90/155.60 [3449]P19(x34491,x34491,f5(x34491),x34492)
% 155.90/155.60 [3450]P19(x34501,x34501,f39(x34501),x34502)
% 155.90/155.60 [3456]P37(x34561,x34562,f127(x34561),f127(x34561))
% 155.90/155.60 [3457]P19(x34571,f857(x34571),f219(x34571),x34572)
% 155.90/155.60 [3466]P19(f854(x34661),f854(x34661),f165(x34661),x34662)
% 155.90/155.60 [4385]~E(f41(x43851),f40(x43852))
% 155.90/155.60 [4393]~E(f36(x43931,x43932),a23)
% 155.90/155.60 [4394]~E(f35(x43941,x43942),a23)
% 155.90/155.60 [4395]~E(f28(x43951,x43952),a23)
% 155.90/155.60 [4433]~P38(x44331,x44332,f127(x44331))
% 155.90/155.60 [3039]E(f312(f5(x30391),x30392),x30392)
% 155.90/155.60 [3040]E(f312(f233(x30401),x30402),x30402)
% 155.90/155.60 [3042]E(f312(f39(x30421),x30422),x30422)
% 155.90/155.60 [3064]E(f34(f28(x30641,x30642)),f2(a853))
% 155.90/155.60 [3075]E(f94(x30751,f312(a309,x30752)),x30752)
% 155.90/155.60 [3076]E(f99(x30761,f312(a309,x30762)),x30762)
% 155.90/155.60 [3095]E(f312(f190(a847),f28(x30951,x30952)),f2(a853))
% 155.90/155.60 [3101]E(f312(f132(x31011,x31012),f127(x31011)),f127(x31011))
% 155.90/155.60 [3119]E(f148(x31191,f148(x31191,x31192)),f148(x31191,x31192))
% 155.90/155.60 [3120]E(f287(x31201,f287(x31201,x31202)),f287(x31201,x31202))
% 155.90/155.60 [3138]E(f312(f312(f129(x31381),x31382),f127(x31381)),x31382)
% 155.90/155.60 [3147]E(f312(f312(f169(x31471),x31472),f127(x31471)),f127(x31471))
% 155.90/155.60 [3148]E(f312(f312(f134(x31481),x31482),f127(x31481)),f127(x31481))
% 155.90/155.60 [3150]E(f220(x31501,x31502,f192(x31501)),f2(a853))
% 155.90/155.60 [3151]E(f151(x31511,x31512,f127(x31511)),f2(a853))
% 155.90/155.60 [3153]E(f166(x31531,x31532,f127(x31531)),f127(x31531))
% 155.90/155.60 [3154]E(f172(x31541,x31542,f127(x31541)),f127(x31541))
% 155.90/155.60 [3155]E(f170(x31551,f127(x31551),x31552),f127(x31551))
% 155.90/155.60 [3159]E(f312(f168(x31591),f148(x31591,x31592)),f312(f168(x31591),x31592))
% 155.90/155.60 [3162]E(f312(f236(x31621,x31621),f237(x31621,x31622)),x31622)
% 155.90/155.60 [3163]E(f312(f238(x31631,x31631),f237(x31631,x31632)),x31632)
% 155.90/155.60 [3172]P22(f312(a24,f28(x31721,x31722)))
% 155.90/155.60 [3173]E(f312(f265(x31731,x31731),f237(x31731,x31732)),f237(x31731,x31732))
% 155.90/155.60 [3187]E(f287(f854(x31871),f153(x31871,x31872)),f154(x31871,f287(x31871,x31872)))
% 155.90/155.60 [3189]P22(f312(f133(a1),f174(x31891,x31892)))
% 155.90/155.60 [3195]E(f312(f236(x31951,x31951),f287(x31951,x31952)),f235(f861(x31951,a846)))
% 155.90/155.60 [3196]E(f312(f238(x31961,x31961),f287(x31961,x31962)),f235(f861(x31961,a846)))
% 155.90/155.60 [3200]P22(f312(f133(x32001),f148(x32001,x32002)))
% 155.90/155.60 [3202]P22(f312(f156(x32021,x32022),f127(x32021)))
% 155.90/155.60 [3209]E(f312(f168(a1),f174(x32091,x32092)),f283(a1,x32091,x32092))
% 155.90/155.60 [3212]E(f312(f312(f197(x32121,x32121),x32122),f219(x32121)),x32122)
% 155.90/155.60 [3224]P55(x32241,f189(f861(x32241,a846)),x32242)
% 155.90/155.60 [3230]E(f312(f282(a853,x32301),f312(a126,x32302)),f283(a853,x32301,x32302))
% 155.90/155.60 [3247]E(f312(f312(f147(x32471),x32472),f127(x32471)),f136(x32471,x32472,f127(x32471)))
% 155.90/155.60 [3260]E(f283(a853,f312(a126,x32601),x32602),f284(a853,x32601,x32602))
% 155.90/155.60 [3263]P50(x32631,f235(f861(x32631,a846)),f287(x32631,x32632))
% 155.90/155.60 [3327]E(f312(f312(f21(a853),x33271),f312(a126,x33272)),f312(f53(a853),f285(a853,x33272,x33271)))
% 155.90/155.60 [3385]E(f163(x33851,x33852,f127(x33851)),f312(f312(f239(f854(x33851),f854(x33851)),f127(x33851)),f127(x33851)))
% 155.90/155.60 [3406]E(f312(f249(x34061,x34062,f860(x34061,x34062)),f239(x34061,x34062)),f39(f860(x34061,x34062)))
% 155.90/155.60 [3411]P22(f312(f312(f314(f854(x34111)),f127(x34111)),f157(x34111,x34112)))
% 155.90/155.60 [3412]E(f312(f190(f854(x34121)),f128(x34121,x34122)),f312(f312(f21(a853),f312(f190(f854(x34121)),x34122)),f87(a853)))
% 155.90/155.60 [3419]P22(f312(f70(a853),f285(a853,x34191,x34192)))
% 155.90/155.60 [3420]P22(f312(f70(a853),f284(a853,x34201,x34202)))
% 155.90/155.60 [3421]P22(f312(f70(a853),f283(a853,x34211,x34212)))
% 155.90/155.60 [3422]P22(f312(f70(a1),f285(a1,x34221,x34222)))
% 155.90/155.60 [3423]P22(f312(f70(a1),f284(a1,x34231,x34232)))
% 155.90/155.60 [3424]P22(f312(f70(a1),f283(a1,x34241,x34242)))
% 155.90/155.60 [3527]E(f312(f290(a853,a853,a126),f283(a853,x35271,x35272)),f283(a853,f312(a126,x35271),f312(a126,x35272)))
% 155.90/155.60 [3546]E(f312(f312(f267(x35461,x35461,x35461),f287(x35461,x35462)),f287(x35461,x35462)),f287(x35461,x35462))
% 155.90/155.60 [3585]E(f312(f312(f239(a853,a853),f312(f47(a853,x35851),x35852)),f54(a853,x35851,x35852)),f94(f860(a853,a853),f56(x35851,x35852)))
% 155.90/155.60 [3656]P22(f312(f312(f228(a853),f312(f312(f21(a853),x36561),x36562)),f312(a126,x36561)))
% 155.90/155.60 [3725]E(f312(f312(f89(a1),f312(f312(f90(a1),x37251),f312(f47(a1,x37252),x37251))),f54(a1,x37252,x37251)),x37252)
% 155.90/155.60 [3756]E(f312(f312(f50(a853,f861(f860(f854(x37561),f854(x37561)),a846)),f235(f861(a853,a846))),f139(x37561,x37562)),f141(x37561,x37562))
% 155.90/155.60 [3987]P22(f312(f312(f314(f860(f854(x39871),f854(x39871))),f312(f312(f239(f854(x39871),f854(x39871)),f127(x39871)),f127(x39871))),f154(x39871,x39872)))
% 155.90/155.60 [4148]E(f250(x41481,x41481,x41482,x41482,f5(x41481),f5(x41482)),f39(f860(x41481,x41482)))
% 155.90/155.60 [4150]E(f250(x41501,x41501,x41502,x41502,f39(x41501),f39(x41502)),f39(f860(x41501,x41502)))
% 155.90/155.60 [4403]~E(f312(f219(x44031),x44032),f192(x44031))
% 155.90/155.60 [4421]~P42(x44211,f312(f219(x44211),x44212))
% 155.90/155.60 [3136]E(f312(f223(x31361),f312(f219(x31361),x31362)),x31362)
% 155.90/155.60 [3137]E(f312(f165(x31371),f312(f165(x31371),x31372)),x31372)
% 155.90/155.60 [3139]E(f312(f312(f134(x31391),f2(a853)),x31392),x31392)
% 155.90/155.60 [3149]E(f312(f312(f169(x31491),f2(a853)),x31492),f127(x31491))
% 155.90/155.60 [3157]E(f312(f312(f129(x31571),f127(x31571)),x31572),x31572)
% 155.90/155.60 [3166]E(f312(f190(f857(x31661)),f312(f219(x31661),x31662)),f2(a853))
% 155.90/155.60 [3168]E(f48(f861(x31681,a846),f312(f288(x31681),x31682)),x31682)
% 155.90/155.60 [3169]E(f312(f168(x31691),f312(f164(x31691),x31692)),f312(f168(x31691),x31692))
% 155.90/155.60 [3170]E(f312(f168(x31701),f312(f165(x31701),x31702)),f312(f168(x31701),x31702))
% 155.90/155.60 [3177]E(f312(f312(f21(a113),x31771),x31772),f312(f312(a22,x31771),x31772))
% 155.90/155.60 [3190]E(f312(f312(f89(a853),x31901),x31902),f312(f312(f89(a853),x31902),x31901))
% 155.90/155.60 [3191]E(f312(f312(f89(a1),x31911),x31912),f312(f312(f89(a1),x31912),x31911))
% 155.90/155.60 [3192]E(f312(f312(f90(a853),x31921),x31922),f312(f312(f90(a853),x31922),x31921))
% 155.90/155.60 [3193]E(f312(f312(f90(a1),x31931),x31932),f312(f312(f90(a1),x31932),x31931))
% 155.90/155.60 [3217]E(f312(f312(f184(x32171,x32171),f2(a853)),x32172),f39(x32171))
% 155.90/155.60 [3218]E(f312(f190(f854(x32181)),f312(f164(x32181),x32182)),f312(f190(f854(x32181)),x32182))
% 155.90/155.60 [3219]E(f312(f190(f854(x32191)),f312(f165(x32191),x32192)),f312(f190(f854(x32191)),x32192))
% 155.90/155.60 [3220]E(f170(x32201,x32202,f189(f861(a853,a846))),f127(x32201))
% 155.90/155.60 [3221]E(f312(f312(f150(x32211,x32211),f5(x32211)),x32212),x32212)
% 155.90/155.60 [3240]E(f312(f190(f854(x32401)),f148(x32401,x32402)),f312(f53(x32401),f312(f168(x32401),x32402)))
% 155.90/155.60 [3241]E(f34(f35(x32411,x32412)),f312(f312(f89(a853),f34(x32412)),f312(a126,f2(a853))))
% 155.90/155.60 [3242]E(f312(f263(x32421),f312(f265(x32421,x32421),x32422)),f312(f263(x32421),x32422))
% 155.90/155.60 [3246]P22(f312(f70(x32461),f312(f168(x32461),x32462)))
% 155.90/155.60 [3254]E(f312(f312(f89(a1),x32541),f312(f88(a1),x32542)),f312(f312(f21(a1),x32541),x32542))
% 155.90/155.60 [3262]P18(x32621,x32622,f189(f861(f852(x32621),a846)))
% 155.90/155.60 [3264]E(f312(f290(x32641,x32641,f5(x32641)),x32642),x32642)
% 155.90/155.60 [3265]E(f312(f290(x32651,x32651,f39(x32651)),x32652),x32652)
% 155.90/155.60 [3266]E(f312(f291(x32661,x32661,f5(x32661)),x32662),x32662)
% 155.90/155.60 [3267]E(f312(f291(x32671,x32671,f39(x32671)),x32672),x32672)
% 155.90/155.60 [3268]P22(f312(f235(f861(x32681,a846)),x32682))
% 155.90/155.60 [3270]E(f312(f53(a853),f312(f282(a853,x32701),x32702)),f312(f312(f21(a853),x32702),x32701))
% 155.90/155.60 [3271]E(f312(f282(a853,f312(a126,x32711)),x32712),f285(a853,x32711,x32712))
% 155.90/155.60 [3283]E(f312(f312(f289(x32831),x32832),f189(f861(x32831,a846))),f312(f233(x32831),f312(a309,x32832)))
% 155.90/155.60 [3287]E(f312(f312(f289(x32871),x32872),f189(f861(x32871,a846))),f218(x32871,f312(f219(x32871),x32872)))
% 155.90/155.60 [3290]E(f287(x32901,f312(f265(x32901,x32901),x32902)),f312(f265(x32901,x32901),f287(x32901,x32902)))
% 155.90/155.60 [3294]E(f312(f312(f89(a853),f312(a126,x32941)),x32942),f312(f312(f89(a853),x32941),f312(a126,x32942)))
% 155.90/155.60 [3295]E(f312(f312(f21(a853),f312(a126,x32951)),f312(a126,x32952)),f312(f312(f21(a853),x32951),x32952))
% 155.90/155.60 [3300]E(f63(x33001,f2(a853),x33002),f312(f312(f147(f854(x33001)),f127(x33001)),f127(f854(x33001))))
% 155.90/155.60 [3301]E(f312(f53(a853),f284(a853,x33011,x33012)),f312(f312(f21(a853),x33012),x33011))
% 155.90/155.60 [3304]E(f312(f47(a1,f312(f88(a1),x33041)),f312(f88(a1),x33042)),f312(f47(a1,x33041),x33042))
% 155.90/155.60 [3313]P41(x33131,f312(f312(f266(a853,x33131),a232),x33132))
% 155.90/155.60 [3315]P33(a853,f135(a853,f312(f282(a853,x33151),x33152)))
% 155.90/155.60 [3317]P22(f312(f70(a853),f312(f282(a853,x33171),x33172)))
% 155.90/155.60 [3318]P22(f312(f70(a1),f312(f282(a1,x33181),x33182)))
% 155.90/155.60 [3321]E(f312(f265(f854(x33211),f854(x33211)),f153(x33211,x33212)),f153(x33211,f312(f265(x33211,x33211),x33212)))
% 155.90/155.60 [3322]E(f312(f190(a847),f35(x33221,x33222)),f312(f312(f89(a853),f312(f190(a847),x33222)),f312(a126,f2(a853))))
% 155.90/155.60 [3324]E(f312(f282(a1,x33241),f312(f312(f89(a1),x33242),f87(a1))),f283(a1,x33241,x33242))
% 155.90/155.60 [3326]E(f312(f246(a853,a853),f94(f860(a853,a853),f56(x33261,x33262))),f312(f47(a853,x33261),x33262))
% 155.90/155.60 [3334]E(f181(x33341,x33342,f312(f16(f857(x33342),x33341),f192(x33342))),f189(f861(x33342,a846)))
% 155.90/155.60 [3335]E(f179(x33351,x33352,f312(f16(f857(x33352),x33351),f192(x33352))),f189(f861(x33351,a846)))
% 155.90/155.60 [3336]E(f312(f312(f184(f860(x33361,x33361),a846),f87(a853)),x33362),x33362)
% 155.90/155.60 [3338]E(f312(f312(f21(f861(x33381,a846)),x33382),f189(f861(x33381,a846))),x33382)
% 155.90/155.60 [3339]E(f312(f312(f124(f861(x33391,a846)),x33392),f189(f861(x33391,a846))),x33392)
% 155.90/155.60 [3340]E(f312(f312(f115(f861(x33401,a846)),x33402),f235(f861(x33401,a846))),x33402)
% 155.90/155.60 [3347]E(f293(x33471,f312(a20,x33472),f312(f88(a1),f312(a20,x33472))),f312(f312(f296(a1),x33471),x33472))
% 155.90/155.60 [3348]E(f283(a1,f312(f312(f89(a1),x33481),f87(a1)),x33482),f284(a1,x33481,x33482))
% 155.90/155.60 [3353]E(f312(f248(a853,a853),f94(f860(a853,a853),f56(x33531,x33532))),f54(a853,x33531,x33532))
% 155.90/155.60 [3361]E(f294(x33611,f312(a20,x33612),f312(f88(a1),f312(a20,x33612))),f295(a1,x33611,x33612))
% 155.90/155.60 [3364]P22(f312(f312(f314(x33641),x33642),f235(f861(x33641,a846))))
% 155.90/155.60 [3370]E(f312(f312(f21(a853),f312(a126,x33701)),x33702),f312(f53(a853),f283(a853,x33702,x33701)))
% 155.90/155.60 [3392]E(f312(f47(a1,f312(f114(a1),x33921)),f312(f114(a1),x33922)),f312(f114(a1),f312(f47(a853,x33921),x33922)))
% 155.90/155.60 [3398]E(f312(f312(f21(f861(x33981,a846)),x33982),f235(f861(x33981,a846))),f189(f861(x33981,a846)))
% 155.90/155.60 [3399]E(f312(f312(f124(f861(x33991,a846)),x33992),f235(f861(x33991,a846))),f235(f861(x33991,a846)))
% 155.90/155.60 [3400]E(f312(f312(f115(f861(x34001,a846)),x34002),f189(f861(x34001,a846))),f189(f861(x34001,a846)))
% 155.90/155.60 [3414]E(f54(a1,f312(f88(a1),x34141),f312(f88(a1),x34142)),f312(f88(a1),f54(a1,x34141,x34142)))
% 155.90/155.60 [3415]E(f54(a1,f312(f114(a1),x34151),f312(f114(a1),x34152)),f312(f114(a1),f54(a853,x34151,x34152)))
% 155.90/155.60 [3426]E(f312(f190(f854(x34261)),f312(f167(x34261),x34262)),f312(f312(f21(a853),f312(f190(f854(x34261)),x34262)),f87(a853)))
% 155.90/155.60 [3429]E(f312(f47(a1,f54(a1,x34291,x34292)),x34292),f2(a1))
% 155.90/155.60 [3454]E(f312(a3,f312(f47(a853,f312(a19,x34541)),f312(a19,x34542))),f312(f47(a113,x34541),x34542))
% 155.90/155.60 [3459]E(f312(a3,f54(a853,f312(a19,x34591),f312(a19,x34592))),f54(a113,x34591,x34592))
% 155.90/155.60 [3471]E(f312(f312(f90(a853),x34711),f312(f47(a853,x34712),x34711)),f312(f312(f21(a853),x34712),f54(a853,x34712,x34711)))
% 155.90/155.60 [3472]E(f312(f312(f90(a1),x34721),f312(f47(a1,x34722),x34721)),f312(f312(f21(a1),x34722),f54(a1,x34722,x34721)))
% 155.90/155.60 [3498]E(f312(a3,f312(f312(f89(a853),f312(a19,x34981)),f312(a19,x34982))),f312(f312(f89(a113),x34981),x34982))
% 155.90/155.60 [3499]E(f312(a3,f312(f312(f21(a853),f312(a19,x34991)),f312(a19,x34992))),f312(f312(f21(a113),x34991),x34992))
% 155.90/155.60 [3500]E(f312(a3,f312(f312(f90(a853),f312(a19,x35001)),f312(a19,x35002))),f312(f312(f90(a113),x35001),x35002))
% 155.90/155.60 [3508]E(f312(f290(a853,a853,a126),f312(f282(a853,x35081),x35082)),f312(f282(a853,f312(a126,x35081)),f312(a126,x35082)))
% 155.90/155.60 [3531]P22(f312(f56(x35311,x35312),f94(f860(a853,a853),f56(x35311,x35312))))
% 155.90/155.60 [3552]E(f312(f312(f89(a853),f312(f312(f89(a853),f34(x35521)),f34(x35522))),f312(a126,f2(a853))),f34(f36(x35521,x35522)))
% 155.90/155.60 [3553]E(f54(a853,f312(a126,f54(a853,x35531,x35532)),x35532),f54(a853,f312(a126,x35531),x35532))
% 155.90/155.60 [3567]E(f312(f312(f50(f861(x35671,a846),f861(x35671,a846)),x35672),f5(f861(x35671,a846))),f48(f861(x35671,a846),x35672))
% 155.90/155.60 [3568]E(f312(f312(f51(f861(x35681,a846),f861(x35681,a846)),x35682),f5(f861(x35681,a846))),f49(f861(x35681,a846),x35682))
% 155.90/155.60 [3569]E(f312(f290(f854(x35691),f861(x35691,a846),f168(x35691)),f312(f168(f854(x35691)),f62(x35691,x35692))),f312(f288(x35691),f312(f168(x35691),x35692)))
% 155.90/155.60 [3572]P22(f312(f312(f314(f861(x35721,a846)),x35722),f312(f288(x35721),x35722)))
% 155.90/155.60 [3576]E(f54(a1,f312(f88(a1),f54(a1,x35761,x35762)),x35762),f54(a1,f312(f88(a1),x35761),x35762))
% 155.90/155.60 [3588]P22(f312(f312(f227(f861(x35881,a846)),x35882),f235(f861(x35881,a846))))
% 155.90/155.60 [3590]E(f312(f312(f267(x35901,x35901,x35901),f287(x35901,x35902)),f287(x35901,f287(x35901,x35902))),f287(x35901,x35902))
% 155.90/155.60 [3591]E(f312(f312(f124(f861(x35911,a846)),f312(f238(x35911,x35911),x35912)),f312(f236(x35911,x35911),x35912)),f312(f263(x35911),x35912))
% 155.90/155.60 [3611]E(f298(x36111,x36112,f235(f861(x36111,a846)),f235(f861(x36112,a846))),f235(f861(f859(x36111,x36112),a846)))
% 155.90/155.60 [3661]P22(f312(f312(f227(a853),f54(a853,x36611,x36612)),x36611))
% 155.90/155.60 [3683]P22(f312(f312(f227(a1),f312(f88(a1),f312(f114(a1),x36831))),f312(f114(a1),x36832)))
% 155.90/155.60 [3708]P22(f312(f312(f314(f861(x37081,a846)),f189(f861(x37081,a846))),f312(f288(x37081),x37082)))
% 155.90/155.60 [3713]E(f287(x37131,f312(f312(f267(x37131,x37131,x37131),x37132),f287(x37131,x37132))),f287(x37131,x37132))
% 155.90/155.60 [3716]E(f312(f312(f267(x37161,x37161,x37161),f287(x37161,x37162)),x37162),f312(f312(f267(x37161,x37161,x37161),x37162),f287(x37161,x37162)))
% 155.90/155.60 [3718]E(f312(a118,f312(f312(f89(a1),f312(f312(f21(a1),x37181),x37182)),f87(a1))),f312(f53(a1),f283(a1,x37182,x37181)))
% 155.90/155.60 [3733]E(f312(f236(x37331,x37331),f312(f312(f267(x37331,x37331,x37331),x37332),f287(x37331,x37332))),f312(f236(x37331,x37331),x37332))
% 155.90/155.60 [3734]E(f312(f238(x37341,x37341),f312(f312(f267(x37341,x37341,x37341),x37342),f287(x37341,x37342))),f312(f238(x37341,x37341),x37342))
% 155.90/155.60 [3750]E(f312(f312(f89(a853),f312(f312(f89(a853),f312(f190(a847),x37501)),f312(f190(a847),x37502))),f312(a126,f2(a853))),f312(f190(a847),f36(x37501,x37502)))
% 155.90/155.60 [3761]P19(a853,a853,f312(f312(f7(a853,a853,a853),f89(a853)),x37611),x37612)
% 155.90/155.60 [3763]P33(a853,f312(f165(a853),f312(f312(f150(f854(x37631),a853),f190(f854(x37631))),f175(x37631,x37632))))
% 155.90/155.60 [3813]P22(f312(f312(f228(a1),f312(f88(a1),f312(f114(a1),f312(a126,x38131)))),f312(f114(a1),x38132)))
% 155.90/155.60 [3857]E(f312(f138(f854(x38571),x38571,f312(f7(x38571,f854(x38571),f854(x38571)),f147(x38571)),f127(x38571)),x38572),f312(f165(x38571),x38572))
% 155.90/155.60 [3909]P22(f312(f312(f227(f861(f860(f854(x39091),f854(x39091)),a846)),f154(x39091,x39092)),f287(f854(x39091),f153(x39091,x39092))))
% 155.90/155.60 [3910]P22(f312(f56(x39101,x39102),f312(f312(f239(a853,a853),f312(f47(a853,x39101),x39102)),f54(a853,x39101,x39102))))
% 155.90/155.60 [3950]P22(f312(f312(f227(f861(f860(f854(x39501),f854(x39501)),a846)),f153(x39501,f287(x39501,x39502))),f287(f854(x39501),f153(x39501,x39502))))
% 155.90/155.60 [4175]E(f312(f312(f251(f860(a113,a113),a113,f860(a113,a113),f860(x41751,f860(a113,a113))),f255(f312(f162(a113),f312(f312(f150(f860(a113,x41751),a113),f246(a113,x41751)),x41752)))),f312(f312(f8(x41751,f861(f860(a113,a113),f860(x41751,f860(a113,a113))),a113),f239(x41751,f860(a113,a113))),f256(x41751,x41752))),f254(x41751,x41752))
% 155.90/155.60 [4356]E(f312(f249(f861(f860(x43561,x43561),a846),f861(f860(x43561,x43561),a846),f861(f861(x43562,x43561),f860(f861(f860(x43562,x43562),a846),f861(f860(x43562,x43562),a846)))),f312(f312(f7(f861(f860(x43561,x43561),a846),f861(f861(f860(x43561,x43561),a846),f861(f861(x43562,x43561),f861(f860(x43562,x43562),a846))),f861(f861(f860(x43561,x43561),a846),f861(f861(x43562,x43561),f860(f861(f860(x43562,x43562),a846),f861(f860(x43562,x43562),a846))))),f312(f312(f8(f861(f861(f861(x43562,x43561),f861(f860(x43562,x43562),a846)),f861(f861(x43562,x43561),f860(f861(f860(x43562,x43562),a846),f861(f860(x43562,x43562),a846)))),f861(f861(f861(f860(x43561,x43561),a846),f861(f861(x43562,x43561),f861(f860(x43562,x43562),a846))),f861(f861(f860(x43561,x43561),a846),f861(f861(x43562,x43561),f860(f861(f860(x43562,x43562),a846),f861(f860(x43562,x43562),a846))))),f861(f860(x43561,x43561),a846)),f8(f861(f861(x43562,x43561),f861(f860(x43562,x43562),a846)),f861(f861(x43562,x43561),f860(f861(f860(x43562,x43562),a846),f861(f860(x43562,x43562),a846))),f861(f860(x43561,x43561),a846))),f312(f312(f8(f861(f861(x43562,x43561),f861(f861(f860(x43562,x43562),a846),f860(f861(f860(x43562,x43562),a846),f861(f860(x43562,x43562),a846)))),f861(f861(f861(x43562,x43561),f861(f860(x43562,x43562),a846)),f861(f861(x43562,x43561),f860(f861(f860(x43562,x43562),a846),f861(f860(x43562,x43562),a846)))),f861(f860(x43561,x43561),a846)),f18(f861(x43562,x43561),f861(f860(x43562,x43562),a846),f860(f861(f860(x43562,x43562),a846),f861(f860(x43562,x43562),a846)))),f312(f312(f8(f861(f861(x43562,x43561),f861(f860(x43562,x43562),a846)),f861(f861(x43562,x43561),f861(f861(f860(x43562,x43562),a846),f860(f861(f860(x43562,x43562),a846),f861(f860(x43562,x43562),a846)))),f861(f860(x43561,x43561),a846)),f312(f8(f861(f860(x43562,x43562),a846),f861(f861(f860(x43562,x43562),a846),f860(f861(f860(x43562,x43562),a846),f861(f860(x43562,x43562),a846))),f861(x43562,x43561)),f239(f861(f860(x43562,x43562),a846),f861(f860(x43562,x43562),a846)))),f266(x43561,x43562))))),f266(x43561,x43562))),f83(x43561,x43562))
% 155.90/155.60 [4469]~E(f312(f288(x44691),x44692),f189(f861(f861(x44691,a846),a846)))
% 155.90/155.60 [4487]~P22(f312(f312(f314(x44871),x44872),f189(f861(x44871,a846))))
% 155.90/155.60 [4496]~P22(f312(f312(f228(f861(x44961,a846)),x44962),f189(f861(x44961,a846))))
% 155.90/155.60 [3273]E(f312(f312(f21(a853),x32731),f312(f312(f89(a853),x32731),x32732)),f2(a853))
% 155.90/155.60 [3275]E(f312(f312(f124(f861(x32751,a846)),x32752),x32752),x32752)
% 155.90/155.60 [3276]E(f312(f312(f115(f861(x32761,a846)),x32762),x32762),x32762)
% 155.90/155.60 [3303]E(f312(f47(a1,f312(f88(a1),x33031)),x33032),f312(f47(a1,x33031),f312(f88(a1),x33032)))
% 155.90/155.60 [3305]E(f312(f312(f21(f861(x33051,a846)),x33052),x33052),f189(f861(x33051,a846)))
% 155.90/155.60 [3309]E(f312(f139(x33091,x33092),f2(a853)),f189(f861(f860(f854(x33091),f854(x33091)),a846)))
% 155.90/155.60 [3310]E(f312(f312(f89(a853),x33101),f312(a126,x33102)),f312(a126,f312(f312(f89(a853),x33101),x33102)))
% 155.90/155.60 [3323]E(f196(f312(f114(a1),x33231),f312(f114(a1),x33232)),f312(f114(a1),f312(f312(f21(a853),x33231),x33232)))
% 155.90/155.60 [3329]E(f312(f53(a1),f312(f282(a1,x33291),x33292)),f312(a118,f312(f312(f21(a1),x33292),x33291)))
% 155.90/155.60 [3332]E(f312(f312(f89(a853),f312(a126,x33321)),x33322),f312(a126,f312(f312(f89(a853),x33321),x33322)))
% 155.90/155.60 [3337]E(f312(f88(f861(x33371,a846)),f312(f88(f861(x33371,a846)),x33372)),x33372)
% 155.90/155.60 [3350]E(f175(x33501,f312(f312(f147(f854(x33501)),f127(x33501)),x33502)),f175(x33501,x33502))
% 155.90/155.60 [3354]E(f312(f312(f89(a853),x33541),f312(f312(f90(a853),x33541),x33542)),f312(f312(f90(a853),x33541),f312(a126,x33542)))
% 155.90/155.60 [3362]E(f312(f312(a22,f312(a3,x33621)),f312(a3,x33622)),f312(a3,f312(f312(f21(a853),x33621),x33622)))
% 155.90/155.60 [3376]E(f312(f312(f90(a1),f312(f88(a1),x33761)),x33762),f312(f88(a1),f312(f312(f90(a1),x33761),x33762)))
% 155.90/155.60 [3378]E(f312(f312(f240(a1),f312(f114(a1),x33781)),x33782),f312(f114(a1),f312(f312(f240(a853),x33781),x33782)))
% 155.90/155.60 [3379]E(f312(f312(f89(a113),f312(a3,x33791)),f312(a3,x33792)),f312(a3,f312(f312(f89(a853),x33791),x33792)))
% 155.90/155.60 [3380]E(f312(f312(f90(a113),f312(a3,x33801)),f312(a3,x33802)),f312(a3,f312(f312(f90(a853),x33801),x33802)))
% 155.90/155.60 [3381]E(f312(f312(f225(a853),f312(a126,x33811)),f312(a126,x33812)),f312(a126,f312(f312(f225(a853),x33811),x33812)))
% 155.90/155.60 [3382]E(f312(f312(f226(a853),f312(a126,x33821)),f312(a126,x33822)),f312(a126,f312(f312(f226(a853),x33821),x33822)))
% 155.90/155.60 [3388]E(f312(f168(a853),f135(a853,f312(f282(a853,x33881),x33882))),f312(f282(a853,x33881),x33882))
% 155.90/155.60 [3389]E(f292(x33891,f312(f312(f289(x33891),x33892),f189(f861(x33891,a846)))),x33892)
% 155.90/155.60 [3396]E(f312(f236(x33961,x33962),f189(f861(f860(x33961,x33962),a846))),f189(f861(x33962,a846)))
% 155.90/155.60 [3397]E(f312(f238(x33971,x33972),f189(f861(f860(x33971,x33972),a846))),f189(f861(x33971,a846)))
% 155.90/155.60 [3401]E(f312(a118,f312(f312(f21(a1),x34011),x34012)),f312(f53(a1),f284(a1,x34012,x34011)))
% 155.90/155.60 [3405]E(f312(f312(f89(a853),x34051),f312(f312(f90(a853),x34052),x34051)),f312(f312(f90(a853),f312(a126,x34052)),x34051))
% 155.90/155.60 [3407]E(f312(f312(f69(x34071),f189(f861(x34071,a846))),x34072),f189(f861(f861(x34071,a846),a846)))
% 155.90/155.60 [3416]E(f312(f190(f854(a853)),f135(a853,f312(f282(a853,x34161),x34162))),f312(f312(f21(a853),x34162),x34161))
% 155.90/155.60 [3433]E(f312(f312(f124(f861(x34331,a846)),f189(f861(x34331,a846))),x34332),x34332)
% 155.90/155.60 [3434]E(f312(f312(f115(f861(x34341,a846)),f235(f861(x34341,a846))),x34342),x34342)
% 155.90/155.60 [3435]E(f312(f312(f89(a1),f312(f88(a1),x34351)),f312(f88(a1),x34352)),f312(f88(a1),f312(f312(f89(a1),x34351),x34352)))
% 155.90/155.60 [3439]E(f312(f312(f89(a1),f312(f114(a1),x34391)),f312(f114(a1),x34392)),f312(f114(a1),f312(f312(f89(a853),x34391),x34392)))
% 155.90/155.60 [3440]E(f312(f312(f89(a1),f312(f117(a1),x34401)),f312(f117(a1),x34402)),f312(f117(a1),f312(f312(f89(a1),x34401),x34402)))
% 155.90/155.60 [3442]E(f312(f312(f90(a1),f312(f114(a1),x34421)),f312(f114(a1),x34422)),f312(f114(a1),f312(f312(f90(a853),x34421),x34422)))
% 155.90/155.60 [3443]E(f312(f312(f90(a1),f312(f117(a1),x34431)),f312(f117(a1),x34432)),f312(f117(a1),f312(f312(f90(a1),x34431),x34432)))
% 155.90/155.60 [3460]E(f312(f312(f6(x34601,a853),f312(f16(a853,x34601),f87(a853))),x34602),f312(f53(x34601),x34602))
% 155.90/155.60 [3473]E(f312(f88(a1),f54(a1,f312(f88(a1),x34731),x34732)),f54(a1,x34731,f312(f88(a1),x34732)))
% 155.90/155.60 [3475]E(f312(f168(a1),f174(x34751,f312(f312(f21(a1),x34752),f87(a1)))),f312(f282(a1,x34751),x34752))
% 155.90/155.60 [3479]P22(f312(f312(f227(a853),x34791),f312(f312(f89(a853),x34792),x34791)))
% 155.90/155.60 [3480]P22(f312(f312(f227(a853),x34801),f312(f312(f89(a853),x34801),x34802)))
% 155.90/155.60 [3483]E(f312(f312(f21(f861(x34831,a846)),f189(f861(x34831,a846))),x34832),f189(f861(x34831,a846)))
% 155.90/155.60 [3484]E(f312(f312(f124(f861(x34841,a846)),f235(f861(x34841,a846))),x34842),f235(f861(x34841,a846)))
% 155.90/155.60 [3485]E(f312(f312(f115(f861(x34851,a846)),f189(f861(x34851,a846))),x34852),f189(f861(x34851,a846)))
% 155.90/155.60 [3490]E(f312(f312(f239(a1,a1),x34901),f312(f88(a1),x34902)),f312(a59,f312(f312(f239(a1,a1),x34901),x34902)))
% 155.90/155.60 [3491]E(f312(f282(a1,f312(f312(f89(a1),x34911),f87(a1))),x34912),f285(a1,x34911,x34912))
% 155.90/155.60 [3505]E(f312(f168(a1),f174(f312(f312(f89(a1),x35051),f87(a1)),x35052)),f284(a1,x35051,x35052))
% 155.90/155.60 [3509]P22(f312(f312(f227(f861(x35091,a846)),x35092),x35092))
% 155.90/155.60 [3512]E(f312(f312(f124(f861(x35121,a846)),x35122),f312(f88(f861(x35121,a846)),x35122)),f235(f861(x35121,a846)))
% 155.90/155.60 [3513]E(f312(f312(f115(f861(x35131,a846)),x35132),f312(f88(f861(x35131,a846)),x35132)),f189(f861(x35131,a846)))
% 155.90/155.60 [3520]E(f312(f312(f21(a853),f312(f312(f21(a853),x35201),f87(a853))),x35202),f312(f312(f21(a853),x35201),f312(a126,x35202)))
% 155.90/155.60 [3524]E(f312(f312(f21(f861(x35241,a846)),f235(f861(x35241,a846))),x35242),f312(f88(f861(x35241,a846)),x35242))
% 155.90/155.60 [3525]E(f312(f312(f21(a1),f312(f117(a1),x35251)),f312(f117(a1),x35252)),f312(f117(a1),f312(f312(f89(a1),x35251),f312(f88(a1),x35252))))
% 155.90/155.60 [3536]E(f312(f168(a853),f135(a853,f312(f282(a853,x35361),f312(a126,x35362)))),f283(a853,x35361,x35362))
% 155.90/155.60 [3542]E(f312(f312(f90(a853),f312(f47(a853,x35421),x35422)),x35422),f312(f312(f21(a853),x35421),f54(a853,x35421,x35422)))
% 155.90/155.60 [3544]P22(f312(f312(f312(f312(a198,a23),x35441),x35442),x35441))
% 155.90/155.60 [3550]E(f312(f190(f854(f854(x35501))),f62(x35501,x35502)),f312(f312(f240(a853),f312(a126,f312(a126,f2(a853)))),f312(f190(f854(x35501)),x35502)))
% 155.90/155.60 [3570]E(f312(f312(f184(f860(x35701,x35701),a846),f2(a853)),x35702),f287(x35701,f189(f861(f860(x35701,x35701),a846))))
% 155.90/155.60 [3574]P22(f312(f133(a853),f135(a853,f312(f282(a853,x35741),x35742))))
% 155.90/155.60 [3581]P22(f312(f312(f227(a853),f312(f47(a853,x35811),x35812)),x35811))
% 155.90/155.60 [3589]E(f312(f290(a1,a853,a118),f283(a1,f312(f114(a1),x35891),f312(f114(a1),x35892))),f283(a853,x35891,x35892))
% 155.90/155.60 [3599]E(f186(a853,f2(a853),f5(a853),f312(f312(f21(a853),x35991),x35992)),f312(f312(f21(a853),x35991),f312(a126,x35992)))
% 155.90/155.60 [3600]E(f312(a118,f312(f312(f21(a1),x36001),f312(f312(f89(a1),x36002),f87(a1)))),f312(f53(a1),f285(a1,x36002,x36001)))
% 155.90/155.60 [3633]E(f312(f312(f150(a853,a853),a126),f135(a853,f312(f282(a853,x36331),x36332))),f135(a853,f312(f282(a853,f312(a126,x36331)),f312(a126,x36332))))
% 155.90/155.60 [3641]E(f312(f168(a1),f174(f312(f312(f89(a1),x36411),f87(a1)),f312(f312(f21(a1),x36412),f87(a1)))),f285(a1,x36411,x36412))
% 155.90/155.60 [3652]P22(f312(f312(f227(f861(x36521,a846)),f189(f861(x36521,a846))),x36522))
% 155.90/155.60 [3657]E(f94(x36571,f312(f312(f7(x36571,x36571,a846),a309),x36572)),x36572)
% 155.90/155.60 [3658]E(f99(x36581,f312(f312(f7(x36581,x36581,a846),a309),x36582)),x36582)
% 155.90/155.60 [3662]E(f312(f168(a853),f135(a853,f312(f282(a853,f312(a126,x36621)),f312(a126,x36622)))),f284(a853,x36621,x36622))
% 155.90/155.60 [3686]E(f312(f312(f247(x36861,x36862),f235(f861(x36861,a846))),f312(f16(f861(x36862,a846),x36861),f235(f861(x36862,a846)))),f235(f861(f860(x36861,x36862),a846)))
% 155.90/155.60 [3720]E(f312(f233(x37201),f312(f312(f8(a846,a846,x37201),a307),x37202)),f312(f88(f861(x37201,a846)),f312(f233(x37201),x37202)))
% 155.90/155.60 [3723]E(f312(f233(x37231),f312(f312(f7(x37231,x37231,a846),a309),x37232)),f312(f312(f289(x37231),x37232),f189(f861(x37231,a846))))
% 155.90/155.60 [3730]E(f312(f312(f89(a1),f312(f312(f89(a1),x37301),x37301)),f312(f312(f89(a1),x37302),x37302)),f312(f312(f89(a1),f312(f312(f89(a1),x37301),x37302)),f312(f312(f89(a1),x37301),x37302)))
% 155.90/155.60 [3731]E(f312(f312(f21(a1),f312(f312(f89(a1),x37311),x37311)),f312(f312(f89(a1),x37312),x37312)),f312(f312(f89(a1),f312(f312(f21(a1),x37311),x37312)),f312(f312(f21(a1),x37311),x37312)))
% 155.90/155.60 [3747]P22(f312(f312(f227(a853),f312(f53(x37471),f312(f168(x37471),x37472))),f312(f190(f854(x37471)),x37472)))
% 155.90/155.60 [3748]P22(f312(f312(f227(a853),f312(f190(f854(x37481)),f148(x37481,x37482))),f312(f190(f854(x37481)),x37482)))
% 155.90/155.60 [3757]E(f312(f233(x37571),f312(f312(f7(x37571,f861(x37571,a846),a846),f314(x37571)),x37572)),x37572)
% 155.90/155.60 [3778]E(f312(f312(f169(x37781),f312(f312(f21(a853),f312(f190(f854(x37781)),x37782)),f87(a853))),x37782),f128(x37781,x37782))
% 155.90/155.60 [3794]E(f312(f312(f239(a1,a1),f312(f47(a1,f312(f84(a1),x37941)),f312(f84(a1),x37942))),f54(a1,f312(f84(a1),x37941),f312(f84(a1),x37942))),f61(x37941,x37942))
% 155.90/155.60 [3801]E(f186(a853,f2(a853),f312(f312(f8(a853,a853,a853),a126),f312(f225(a853),x38011)),x38012),f312(f312(f225(a853),f312(a126,x38011)),x38012))
% 155.90/155.60 [3805]E(f48(f861(x38051,a846),f312(f290(f861(f860(x38051,x38051),a846),f861(x38051,a846),f263(x38051)),x38052)),f312(f263(x38051),f48(f861(f860(x38051,x38051),a846),x38052)))
% 155.90/155.60 [3806]E(f186(a853,f312(a126,x38061),f312(f312(f8(a853,a853,a853),a126),f312(f226(a853),x38061)),x38062),f312(f312(f226(a853),f312(a126,x38061)),x38062))
% 155.90/155.60 [3828]P22(f312(f312(f227(f861(f861(x38281,a846),a846)),x38282),f312(f288(x38281),f48(f861(x38281,a846),x38282))))
% 155.90/155.60 [3862]E(f312(f312(f50(x38621,f861(x38621,a846)),x38622),f312(f312(f7(x38621,f861(x38621,a846),f861(x38621,a846)),f289(x38621)),f189(f861(x38621,a846)))),x38622)
% 155.90/155.60 [3863]E(f312(f312(f267(x38631,x38631,x38631),f312(f265(x38631,x38631),x38632)),f287(x38631,f312(f265(x38631,x38631),x38632))),f312(f265(x38631,x38631),f312(f312(f267(x38631,x38631,x38631),x38632),f287(x38631,x38632))))
% 155.90/155.60 [3931]E(f312(f168(x39311),f312(f138(f854(x39311),f854(x39311),f129(x39311),f127(x39311)),x39312)),f312(f312(f50(f854(x39311),f861(x39311,a846)),f312(f168(f854(x39311)),x39312)),f168(x39311)))
% 155.90/155.60 [3961]E(f312(f312(f124(f861(f860(x39611,x39611),a846)),f287(x39611,f189(f861(f860(x39611,x39611),a846)))),f312(f312(f267(x39611,x39611,x39611),f287(x39611,x39612)),x39612)),f287(x39611,x39612))
% 155.90/155.60 [3997]E(f312(f312(f177(x39971,x39971),x39972),x39972),f312(f312(f150(x39971,f860(x39971,x39971)),f312(f312(f18(x39971,x39971,f860(x39971,x39971)),f239(x39971,x39971)),f5(x39971))),x39972))
% 155.90/155.60 [4113]E(f312(f138(a853,f854(x41131),f312(f7(f854(x41131),a853,a853),f312(f312(f8(a853,f861(a853,a853),f854(x41131)),f226(a853)),f190(f854(x41131)))),f2(a853)),f312(f165(f854(x41131)),x41132)),f312(f190(f854(f854(x41131))),f175(x41131,x41132)))
% 155.90/155.60 [4191]E(f312(f312(f266(f860(a853,f854(x41911)),f854(x41911)),f304(a853,f854(x41911),a232,f141(x41911,x41912))),f312(f312(f18(f854(x41911),f854(x41911),f860(a853,f854(x41911))),f312(f312(f8(a853,f861(f854(x41911),f860(a853,f854(x41911))),f854(x41911)),f239(a853,f854(x41911))),f190(f854(x41911)))),f5(f854(x41911)))),f142(x41911,x41912))
% 155.90/155.60 [4316]E(f312(f233(x43161),f312(f312(f8(f861(f861(x43161,a846),a846),a846,x43161),f97(f861(x43161,a846))),f312(f312(f8(f861(f861(x43161,a846),a846),f861(f861(x43161,a846),a846),x43161),f312(f18(f861(x43161,a846),a846,a846),f312(f312(f8(a846,f861(a846,a846),f861(x43161,a846)),a315),f312(f312(f7(f861(x43161,a846),f861(f861(x43161,a846),a846),a846),f314(f861(x43161,a846))),x43162)))),f314(x43161)))),f49(f861(x43161,a846),x43162))
% 155.90/155.60 [4497]~P22(f312(f312(f228(a1),f312(f114(a1),x44971)),f312(f88(a1),f312(f114(a1),x44972))))
% 155.90/155.60 [3403]E(f312(f312(f21(a853),f312(f312(f89(a853),x34031),x34032)),x34032),x34031)
% 155.90/155.60 [3404]E(f312(f312(f21(a853),f312(f312(f89(a853),x34041),x34042)),x34041),x34042)
% 155.90/155.60 [3474]E(f312(f312(f89(a853),f312(f312(f21(a853),x34741),x34742)),x34742),f312(f312(f226(a853),x34741),x34742))
% 155.90/155.60 [3604]E(f312(f168(a853),f135(a853,f312(f282(a853,f312(a126,x36041)),x36042))),f285(a853,x36041,x36042))
% 155.90/155.60 [3610]E(f312(f114(a1),f199(f312(a118,f312(f84(a1),x36101)),f312(a118,f312(f84(a1),x36102)))),f312(f312(a200,x36101),x36102))
% 155.90/155.60 [3612]E(f312(f312(f124(f861(x36121,a846)),f312(f88(f861(x36121,a846)),x36122)),x36122),f235(f861(x36121,a846)))
% 155.90/155.60 [3613]E(f312(f312(f115(f861(x36131,a846)),f312(f88(f861(x36131,a846)),x36132)),x36132),f189(f861(x36131,a846)))
% 155.90/155.60 [3630]P22(f312(f312(f227(a853),f312(f312(f21(a853),x36301),x36302)),x36301))
% 155.90/155.60 [3638]E(f312(f312(f21(a853),x36381),f312(f312(f90(a853),f312(f47(a853,x36381),x36382)),x36382)),f54(a853,x36381,x36382))
% 155.90/155.60 [3639]E(f312(f312(f21(a1),x36391),f312(f312(f90(a1),f312(f47(a1,x36391),x36392)),x36392)),f54(a1,x36391,x36392))
% 155.90/155.60 [3654]P22(f312(f312(f228(a853),x36541),f312(a126,f312(f312(f89(a853),x36542),x36541))))
% 155.90/155.60 [3655]P22(f312(f312(f228(a853),x36551),f312(a126,f312(f312(f89(a853),x36551),x36552))))
% 155.90/155.60 [3672]E(f312(f312(f90(a853),f312(a118,f312(f84(a1),x36721))),f312(a118,f312(f84(a1),x36722))),f312(a118,f312(f84(a1),f312(f312(f90(a1),x36721),x36722))))
% 155.90/155.60 [3682]P22(f312(f312(f227(a1),f2(a1)),f312(f312(f240(a1),f312(f84(a1),x36821)),x36822)))
% 155.90/155.60 [3752]E(f312(f264(f854(x37521),f854(x37521),f154(x37521,x37522)),f312(f312(f289(f854(x37521)),f127(x37521)),f189(f861(f854(x37521),a846)))),f312(f312(f289(f854(x37521)),f127(x37521)),f189(f861(f854(x37521),a846))))
% 155.90/155.60 [3774]E(f312(f312(f124(f861(f860(x37741,x37741),a846)),f287(x37741,x37742)),f287(x37741,f189(f861(f860(x37741,x37741),a846)))),f287(x37741,x37742))
% 155.90/155.60 [3789]E(f312(f47(a1,f312(f117(a1),f312(f312(f89(a1),x37891),x37891))),f312(f117(a1),f312(f312(f89(a1),x37892),x37892))),f312(f47(a1,f312(f117(a1),x37891)),f312(f117(a1),x37892)))
% 155.90/155.60 [3852]E(f312(f312(f240(a1),x38521),f312(f117(a853),f312(f312(f89(a1),x38522),x38522))),f312(f312(f95(a1,a1),f312(f312(f240(a1),x38521),f312(f117(a853),x38522))),f312(f312(f18(a1,a1,a1),f90(a1)),f5(a1))))
% 155.90/155.60 [3858]E(f312(f233(f861(x38581,a846)),f312(f312(f7(f861(x38581,a846),f861(x38581,a846),a846),f227(f861(x38581,a846))),x38582)),f312(f288(x38581),x38582))
% 155.90/155.60 [3874]E(f312(f312(f150(a1,a853),a118),f312(f312(f129(a1),f312(f312(f150(a853,a1),f114(a1)),x38741)),f312(f312(f150(a853,a1),f114(a1)),x38742))),f312(f312(f129(a853),x38741),x38742))
% 155.90/155.60 [3908]E(f312(f290(a1,a1,f312(f312(f7(a1,a1,a1),f89(a1)),x39081)),f312(f282(a1,f2(a1)),f312(f312(f21(a1),x39082),x39081))),f312(f282(a1,x39081),x39082))
% 155.90/155.60 [3911]P51(x39111,f312(f312(f21(f861(f860(x39111,x39111),a846)),x39112),f287(x39111,f189(f861(f860(x39111,x39111),a846)))))
% 155.90/155.60 [3928]E(f312(f190(f854(x39281)),f312(f138(f854(x39281),f854(x39281),f129(x39281),f127(x39281)),x39282)),f312(f162(a853),f312(f312(f150(f854(x39281),a853),f190(f854(x39281))),x39282)))
% 155.90/155.60 [3934]P50(x39341,f235(f861(x39341,a846)),f312(f312(f124(f861(f860(x39341,x39341),a846)),x39342),f287(x39341,f189(f861(f860(x39341,x39341),a846)))))
% 155.90/155.60 [3977]E(f186(a853,f2(a853),f312(f312(f8(a853,a853,a853),a126),f312(f312(f7(a853,a853,a853),f225(a853)),x39771)),x39772),f312(f312(f225(a853),x39772),f312(a126,x39771)))
% 155.90/155.60 [3980]E(f186(a853,f312(a126,x39801),f312(f312(f8(a853,a853,a853),a126),f312(f312(f7(a853,a853,a853),f226(a853)),x39801)),x39802),f312(f312(f226(a853),x39802),f312(a126,x39801)))
% 155.90/155.60 [3983]E(f312(f290(x39831,f854(x39831),f312(f312(f7(x39831,f854(x39831),f854(x39831)),f147(x39831)),f127(x39831))),x39832),f171(x39831,x39832,f312(f312(f289(f854(x39831)),f127(x39831)),f189(f861(f854(x39831),a846)))))
% 155.90/155.60 [3984]E(f312(f312(f124(f861(f860(x39841,x39841),a846)),f312(f312(f267(x39841,x39841,x39841),x39842),f287(x39841,x39842))),f287(x39841,f189(f861(f860(x39841,x39841),a846)))),f287(x39841,x39842))
% 155.90/155.60 [3992]P22(f312(f312(f227(f861(f860(x39921,x39921),a846)),f237(x39921,x39922)),f312(f312(f247(x39921,x39921),x39922),f312(f16(f861(x39921,a846),x39921),x39922))))
% 155.90/155.60 [3995]E(f312(f290(a1,a853,a118),f312(f312(f124(f861(a1,a846)),f312(f290(a853,a1,f114(a1)),x39951)),f312(f290(a853,a1,f114(a1)),x39952))),f312(f312(f124(f861(a853,a846)),x39951),x39952))
% 155.90/155.60 [3996]E(f312(f290(a1,a853,a118),f312(f312(f115(f861(a1,a846)),f312(f290(a853,a1,f114(a1)),x39961)),f312(f290(a853,a1,f114(a1)),x39962))),f312(f312(f115(f861(a853,a846)),x39961),x39962))
% 155.90/155.60 [4000]E(f312(f233(x40001),f312(f312(f8(a846,a846,x40001),a307),f312(f312(f7(x40001,f861(x40001,a846),a846),f314(x40001)),x40002))),f312(f88(f861(x40001,a846)),x40002))
% 155.90/155.60 [4027]E(f312(f138(f854(x40271),f854(x40271),f129(x40271),f127(x40271)),f312(f312(f150(f854(x40271),f854(x40271)),f165(x40271)),f312(f165(f854(x40271)),x40272))),f312(f165(x40271),f312(f138(f854(x40271),f854(x40271),f129(x40271),f127(x40271)),x40272)))
% 155.90/155.60 [4056]E(f312(f312(f50(a853,f861(f860(x40561,x40561),a846)),f235(f861(a853,a846))),f312(f312(f7(a853,f861(f860(x40561,x40561),a846),f861(f860(x40561,x40561),a846)),f184(f860(x40561,x40561),a846)),x40562)),f287(x40561,x40562))
% 155.90/155.60 [4078]E(f94(x40781,f312(f312(f8(f861(x40781,a846),a846,x40781),f312(a309,x40782)),f312(f312(f7(x40781,f861(x40781,a846),f861(x40781,a846)),f289(x40781)),f189(f861(x40781,a846))))),f292(x40781,x40782))
% 155.90/155.60 [4085]E(f312(f190(f854(x40851)),f148(x40851,f312(f138(f854(x40851),f854(x40851),f129(x40851),f127(x40851)),x40852))),f312(f53(x40851),f312(f312(f50(f854(x40851),f861(x40851,a846)),f312(f168(f854(x40851)),x40852)),f168(x40851))))
% 155.90/155.60 [4101]E(f312(f312(f124(f861(f860(x41011,x41011),a846)),x41012),f312(f312(f267(x41011,x41011,x41011),f312(f312(f267(x41011,x41011,x41011),x41012),f287(x41011,x41012))),x41012)),f312(f312(f267(x41011,x41011,x41011),x41012),f287(x41011,x41012)))
% 155.90/155.60 [4122]P22(f312(f312(f227(f861(f860(x41221,x41221),a846)),f312(f312(f267(x41221,x41221,x41221),x41222),f287(x41221,x41222))),f312(f312(f247(x41221,x41221),f312(f263(x41221),x41222)),f312(f16(f861(x41221,a846),x41221),f312(f263(x41221),x41222)))))
% 155.90/155.60 [4164]E(f312(f233(f854(x41641)),f312(f312(f7(f854(x41641),f861(x41641,a846),a846),f312(f312(f8(f861(x41641,a846),f861(f861(x41641,a846),a846),f854(x41641)),f227(f861(x41641,a846))),f168(x41641))),x41642)),f157(x41641,x41642))
% 155.90/155.60 [4177]E(f312(f152(f854(x41771),x41771,f127(x41771),f312(f312(f8(f854(x41771),f861(f854(x41771),f854(x41771)),x41771),f312(f7(f854(x41771),f854(x41771),f854(x41771)),f129(x41771))),f312(f312(f7(x41771,f854(x41771),f854(x41771)),f147(x41771)),f127(x41771)))),x41772),f312(f164(x41771),x41772))
% 155.90/155.60 [4220]P19(f861(x42201,x42202),f861(f860(x42201,x42202),a846),f312(f312(f8(f861(f860(x42201,x42202),a846),f861(f860(x42201,x42202),a846),f861(x42201,x42202)),f233(f860(x42201,x42202))),f312(f312(f8(f861(x42201,f861(x42202,a846)),f861(f860(x42201,x42202),a846),f861(x42201,x42202)),f249(x42201,x42202,a846)),f312(f8(x42202,f861(x42202,a846),x42201),f312(f7(x42202,x42202,a846),a309)))),f235(f861(f861(x42201,x42202),a846)))
% 155.90/155.60 [4225]E(f54(a1,f312(f117(a1),f312(f312(f89(a1),x42251),x42251)),f312(f117(a1),f312(f312(f89(a1),x42252),x42252))),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),x42251),f312(f117(a1),x42252))))
% 155.90/155.60 [4267]E(f312(f312(f50(x42671,f861(f860(x42671,x42671),a846)),x42672),f312(f312(f7(x42671,f861(f860(x42671,x42671),a846),f861(f860(x42671,x42671),a846)),f312(f312(f8(f860(x42671,x42671),f861(f861(f860(x42671,x42671),a846),f861(f860(x42671,x42671),a846)),x42671),f289(f860(x42671,x42671))),f312(f312(f18(x42671,x42671,f860(x42671,x42671)),f239(x42671,x42671)),f5(x42671)))),f189(f861(f860(x42671,x42671),a846)))),f237(x42671,x42672))
% 155.90/155.60 [4351]E(f312(f233(f861(x43511,a846)),f312(f312(f8(f861(f861(x43511,a846),a846),a846,f861(x43511,a846)),f96(f861(x43511,a846))),f312(f312(f7(f861(x43511,a846),f861(f861(x43511,a846),a846),f861(f861(x43511,a846),a846)),f312(f312(f8(f861(f861(x43511,a846),f861(a846,a846)),f861(f861(f861(x43511,a846),a846),f861(f861(x43511,a846),a846)),f861(x43511,a846)),f18(f861(x43511,a846),a846,a846)),f312(f312(f8(f861(f861(x43511,a846),a846),f861(f861(x43511,a846),f861(a846,a846)),f861(x43511,a846)),f312(f8(a846,f861(a846,a846),f861(x43511,a846)),a310)),f312(f312(f7(f861(x43511,a846),f861(f861(x43511,a846),f861(x43511,a846)),f861(f861(x43511,a846),a846)),f312(f312(f8(f861(f861(x43511,a846),a846),f861(f861(f861(x43511,a846),f861(x43511,a846)),f861(f861(x43511,a846),a846)),f861(x43511,a846)),f8(f861(x43511,a846),a846,f861(x43511,a846))),a309)),f88(f861(x43511,a846)))))),f312(f312(f8(f861(f861(x43511,a846),a846),a846,f861(x43511,a846)),f312(f314(f861(x43511,a846)),x43512)),f288(x43511))))),f312(f288(x43511),f312(f88(f861(x43511,a846)),x43512)))
% 155.90/155.60 [4494]~E(f312(f312(f89(a1),x44941),x44941),f312(f312(f21(a1),f312(f312(f89(a1),x44942),x44942)),a111))
% 155.90/155.60 [4499]~P22(f312(f312(f228(a853),f312(f312(f89(a853),x44991),x44992)),x44992))
% 155.90/155.60 [4500]~P22(f312(f312(f228(a853),f312(f312(f89(a853),x45001),x45002)),x45001))
% 155.90/155.60 [3721]E(f312(f312(f150(a853,x37211),f312(f161(x37211),x37212)),f135(a853,f312(f282(a853,f2(a853)),f312(f190(f854(x37211)),x37212)))),x37212)
% 155.90/155.60 [3786]E(f312(f264(x37861,x37861,f287(x37861,f189(f861(f860(x37861,x37861),a846)))),x37862),x37862)
% 155.90/155.60 [3912]E(f287(x39121,f312(f312(f21(f861(f860(x39121,x39121),a846)),x39122),f287(x39121,f189(f861(f860(x39121,x39121),a846))))),f287(x39121,x39122))
% 155.90/155.60 [3913]E(f287(x39131,f312(f312(f124(f861(f860(x39131,x39131),a846)),x39132),f287(x39131,f189(f861(f860(x39131,x39131),a846))))),f287(x39131,x39132))
% 155.90/155.60 [3964]E(f312(f312(f21(a1),f312(f312(f21(a1),f312(f312(f89(a1),x39641),x39641)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x39642),x39642)),a111)),f312(f312(f89(a1),f312(f312(f21(a1),x39641),x39642)),f312(f312(f21(a1),x39641),x39642)))
% 155.90/155.60 [4005]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f89(a1),x40051),x40052)),f312(f312(f89(a1),x40051),x40052))),a111),f312(f312(f89(a1),f312(f312(f89(a1),x40051),x40051)),f312(f312(f21(a1),f312(f312(f89(a1),x40052),x40052)),a111)))
% 155.90/155.60 [4031]E(f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),x40311),x40311)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x40312),x40312)),a111)),f312(f312(f89(a1),f312(f312(f89(a1),x40311),f312(f312(f21(a1),x40312),a111))),f312(f312(f89(a1),x40311),f312(f312(f21(a1),x40312),a111))))
% 155.90/155.60 [4042]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f89(a1),x40421),x40422)),f312(f312(f89(a1),x40421),x40422))),a111),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),x40421),x40421)),a111)),f312(f312(f89(a1),x40422),x40422)))
% 155.90/155.60 [4043]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),x40431),x40432)),f312(f312(f21(a1),x40431),x40432))),a111),f312(f312(f21(a1),f312(f312(f21(a1),f312(f312(f89(a1),x40431),x40431)),a111)),f312(f312(f89(a1),x40432),x40432)))
% 155.90/155.60 [4096]E(f312(f114(a1),f312(f47(a853,f312(f312(f90(a853),f312(a118,f312(f84(a1),x40961))),f312(a118,f312(f84(a1),x40962)))),f199(f312(a118,f312(f84(a1),x40961)),f312(a118,f312(f84(a1),x40962))))),f208(x40961,x40962))
% 155.90/155.60 [4141]E(f312(f312(f251(f860(a113,a113),a113,f860(a113,a113),f860(x41411,f860(a113,a113))),f255(f312(a3,f312(f190(f854(x41411)),x41412)))),f312(f312(f8(x41411,f861(f860(a113,a113),f860(x41411,f860(a113,a113))),a113),f239(x41411,f860(a113,a113))),f312(f312(f8(a853,x41411,a113),f312(f161(x41411),x41412)),a19))),f261(x41411,x41412))
% 155.90/155.60 [4226]E(f312(f138(a853,f854(x42261),f312(f7(f854(x42261),a853,a853),f312(f312(f8(a853,f861(a853,a853),f854(x42261)),f226(a853)),f190(f854(x42261)))),f2(a853)),f312(f165(f854(x42261)),f175(x42261,x42262))),f312(f190(f854(f854(x42261))),f312(f132(f854(x42261),f312(f312(f8(a846,a846,f854(x42261)),a307),f312(f312(f7(f854(x42261),f854(x42261),a846),a309),f127(x42261)))),x42262)))
% 155.90/155.60 [4232]E(f312(f312(f50(a853,f861(x42321,a846)),f235(f861(a853,a846))),f312(f312(f7(a853,f861(a853,f861(x42321,a846)),f861(x42321,a846)),f312(f312(f8(f861(a853,a846),f861(f861(a853,f861(x42321,a846)),f861(x42321,a846)),a853),f50(a853,f861(x42321,a846))),f282(a853,f2(a853)))),x42322)),f312(f312(f50(a853,f861(x42321,a846)),f235(f861(a853,a846))),x42322))
% 155.90/155.60 [4251]P22(f312(f70(a853),f312(f233(a853),f312(f312(f18(a853,a846,a846),f312(f312(f8(a846,f861(a846,a846),a853),a310),x42511)),f312(f312(f7(a853,a853,a846),f228(a853)),x42512)))))
% 155.90/155.60 [4360]E(f312(f233(f860(f854(x43601),f854(x43601))),f312(f249(f854(x43601),f854(x43601),a846),f312(f312(f18(f854(x43601),f861(f854(x43601),a846),f861(f854(x43601),a846)),f312(f312(f8(f861(f854(x43601),f861(a846,a846)),f861(f861(f854(x43601),a846),f861(f854(x43601),a846)),f854(x43601)),f18(f854(x43601),a846,a846)),f312(f312(f8(f861(f854(x43601),a846),f861(f854(x43601),f861(a846,a846)),f854(x43601)),f312(f8(a846,f861(a846,a846),f854(x43601)),a311)),f312(f312(f7(f854(x43601),f861(f854(x43601),a853),f861(f854(x43601),a846)),f312(f312(f8(f861(a853,a846),f861(f861(f854(x43601),a853),f861(f854(x43601),a846)),f854(x43601)),f8(a853,a846,f854(x43601))),f312(f312(f8(a853,f861(a853,a846),f854(x43601)),f228(a853)),f190(f854(x43601))))),f190(f854(x43601)))))),f312(f312(f18(f854(x43601),f861(f854(x43601),a846),f861(f854(x43601),a846)),f312(f312(f8(f861(f854(x43601),f861(a846,a846)),f861(f861(f854(x43601),a846),f861(f854(x43601),a846)),f854(x43601)),f18(f854(x43601),a846,a846)),f312(f312(f8(f861(f854(x43601),a846),f861(f854(x43601),f861(a846,a846)),f854(x43601)),f312(f8(a846,f861(a846,a846),f854(x43601)),a310)),f312(f312(f7(f854(x43601),f861(f854(x43601),a853),f861(f854(x43601),a846)),f312(f312(f8(f861(a853,a846),f861(f861(f854(x43601),a853),f861(f854(x43601),a846)),f854(x43601)),f8(a853,a846,f854(x43601))),f312(f312(f8(a853,f861(a853,a846),f854(x43601)),a309),f190(f854(x43601))))),f190(f854(x43601)))))),f312(f312(f7(f854(x43601),f861(f860(f854(x43601),f854(x43601)),a846),f861(f854(x43601),a846)),f312(f312(f8(f861(f854(x43601),f861(f861(f860(f854(x43601),f854(x43601)),a846),a846)),f861(f861(f860(f854(x43601),f854(x43601)),a846),f861(f854(x43601),a846)),f854(x43601)),f7(f854(x43601),f861(f860(f854(x43601),f854(x43601)),a846),a846)),f312(f312(f8(f861(f854(x43601),f860(f854(x43601),f854(x43601))),f861(f854(x43601),f861(f861(f860(f854(x43601),f854(x43601)),a846),a846)),f854(x43601)),f312(f8(f860(f854(x43601),f854(x43601)),f861(f861(f860(f854(x43601),f854(x43601)),a846),a846),f854(x43601)),f314(f860(f854(x43601),f854(x43601))))),f239(f854(x43601),f854(x43601))))),f141(x43601,x43602)))))),f142(x43601,x43602))
% 155.90/155.60 [4034]E(f312(f312(f89(a1),f312(f312(f89(a1),f312(f312(f90(a1),x40341),x40342)),f312(f312(f90(a1),x40341),x40342))),x40342),f312(f312(f90(a1),f312(f312(f21(a1),f312(f312(f89(a1),x40341),x40341)),a111)),x40342))
% 155.90/155.60 [4139]E(f312(a118,f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x41391),x41392)),f189(f861(f860(a853,a853),a846)))))),f312(f312(f21(a853),x41391),x41392))
% 155.90/155.60 [4144]E(f312(f312(f267(x41441,x41441,x41441),f312(f312(f124(f861(f860(x41441,x41441),a846)),x41442),f287(x41441,f189(f861(f860(x41441,x41441),a846))))),f287(x41441,f312(f312(f124(f861(f860(x41441,x41441),a846)),x41442),f287(x41441,f189(f861(f860(x41441,x41441),a846)))))),f287(x41441,x41442))
% 155.90/155.60 [4184]E(f254(x41841,f312(f132(f860(a113,x41841),f312(f249(a113,x41841,a846),f312(f312(f8(a846,f861(x41841,a846),a113),f16(a846,x41841)),f312(f228(a113),f2(a113))))),x41842)),f254(x41841,x41842))
% 155.90/155.60 [4185]E(f256(x41851,f312(f132(f860(a113,x41851),f312(f249(a113,x41851,a846),f312(f312(f8(a846,f861(x41851,a846),a113),f16(a846,x41851)),f312(f228(a113),f2(a113))))),x41852)),f256(x41851,x41852))
% 155.90/155.60 [4187]E(f312(f88(a1),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x41871),x41872)),f189(f861(f860(a853,a853),a846)))))),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x41872),x41871)),f189(f861(f860(a853,a853),a846))))))
% 155.90/155.60 [4243]E(f312(f312(f266(f854(a853),x42431),f141(a853,a232)),f312(f312(f7(x42431,f854(f861(x42431,a853)),f854(a853)),f312(f312(f8(f861(f861(x42431,a853),a853),f861(f854(f861(x42431,a853)),f854(a853)),x42431),f150(f861(x42431,a853),a853)),f312(f7(f861(x42431,a853),x42431,a853),f5(f861(x42431,a853))))),x42432)),f149(x42431,x42432))
% 155.90/155.60 [4264]E(f312(f312(f95(a1,a853),f312(f117(a1),f312(f312(f89(a1),x42641),a111))),f312(f312(f18(a1,a853,a853),f312(f312(f7(a1,a853,f861(a853,a853)),f312(f312(f8(a846,f861(a853,f861(a853,a853)),a1),f108(a853)),a194)),f2(a853))),f312(f312(f8(a853,a853,a1),a126),f312(f312(f8(a853,a853,a1),f312(f225(a853),x42642)),a118)))),f312(f312(f225(a853),f312(a126,x42642)),f312(f117(a853),x42641)))
% 155.90/155.60 [4265]E(f312(f312(f95(a1,a853),f312(f117(a1),f312(f312(f89(a1),x42651),a111))),f312(f312(f18(a1,a853,a853),f312(f312(f7(a1,a853,f861(a853,a853)),f312(f312(f8(a846,f861(a853,f861(a853,a853)),a1),f108(a853)),a194)),f312(a126,x42652))),f312(f312(f8(a853,a853,a1),a126),f312(f312(f8(a853,a853,a1),f312(f226(a853),x42652)),a118)))),f312(f312(f226(a853),f312(a126,x42652)),f312(f117(a853),x42651)))
% 155.90/155.60 [4284]E(f312(f138(f854(x42841),f854(x42841),f129(x42841),f127(x42841)),f312(f312(f150(f854(x42841),f854(x42841)),f152(f854(x42841),x42841,f127(x42841),f312(f312(f8(f854(x42841),f861(f854(x42841),f854(x42841)),x42841),f16(f854(x42841),f854(x42841))),f312(f312(f7(x42841,f854(x42841),f854(x42841)),f147(x42841)),f127(x42841))))),x42842)),f312(f312(f150(f854(x42841),x42841),f137(x42841)),f312(f132(f854(x42841),f312(f312(f8(a846,a846,f854(x42841)),a307),f312(f312(f7(f854(x42841),f854(x42841),a846),a309),f127(x42841)))),x42842)))
% 155.90/155.60 [4341]E(f312(f249(a1,a1,a846),f312(f312(f7(a1,f861(a1,a846),f861(a1,a846)),f312(f312(f8(f861(a1,f861(a846,a846)),f861(f861(a1,a846),f861(a1,a846)),a1),f18(a1,a846,a846)),f312(f312(f8(f861(a1,a846),f861(a1,f861(a846,a846)),a1),f312(f8(a846,f861(a846,a846),a1),a310)),f312(f312(f8(f861(a1,a1),f861(a1,a846),a1),f312(f8(a1,a846,a1),f312(a309,x43411))),f312(f312(f8(a1,f861(a1,a1),a1),f89(a1)),f312(f90(a1),x43412)))))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f312(f8(a846,a846,a1),f312(a315,f312(f312(f228(a1),f2(a1)),x43412))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f227(a1),f2(a1)))),f312(f312(f7(a1,a1,a846),f228(a1)),x43412))))),f312(f312(f8(a846,a846,a1),f312(a315,f312(a307,f312(f312(f228(a1),f2(a1)),x43412)))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f228(a1),x43412))),f312(f312(f7(a1,a1,a846),f227(a1)),f2(a1))))))),f57(x43411,x43412))
% 155.90/155.60 [4343]E(f312(f233(x43431),f312(f312(f8(f861(a853,a846),a846,x43431),f96(a853)),f312(f312(f7(x43431,f861(a853,a846),f861(a853,a846)),f312(f312(f8(f861(a853,f861(a846,a846)),f861(f861(a853,a846),f861(a853,a846)),x43431),f18(a853,a846,a846)),f312(f312(f8(f861(a853,a846),f861(a853,f861(a846,a846)),x43431),f312(f8(a846,f861(a846,a846),a853),a310)),f312(f312(f7(x43431,f861(a853,x43431),f861(a853,a846)),f312(f312(f8(f861(x43431,a846),f861(f861(a853,x43431),f861(a853,a846)),x43431),f8(x43431,a846,a853)),a309)),f312(f161(x43431),x43432))))),f312(f312(f7(a853,a853,a846),f228(a853)),f312(f190(f854(x43431)),x43432))))),f312(f168(x43431),x43432))
% 155.90/155.60 [4154]E(f312(f312(f21(a1),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),x41541),a111)),x41542)),f312(f312(f21(a1),f312(f312(f89(a1),x41541),a111)),x41542))),a111),f312(f312(f21(a1),f312(f312(f89(a1),x41541),x41541)),f312(f312(f21(a1),f312(f312(f89(a1),x41542),x41542)),a111)))
% 155.90/155.60 [4279]E(f312(f138(f854(f854(x42791)),f854(f854(x42791)),f129(f854(x42791)),f127(f854(x42791))),f312(f312(f150(f854(x42791),f854(f854(x42791))),f152(f854(f854(x42791)),x42791,f127(f854(x42791)),f312(f16(f861(f854(x42791),f854(f854(x42791))),x42791),f312(f312(f7(f854(x42791),f854(f854(x42791)),f854(f854(x42791))),f147(f854(x42791))),f127(f854(x42791)))))),x42792)),f312(f312(f150(f854(x42791),f854(x42791)),f167(x42791)),f312(f132(f854(x42791),f312(f312(f8(a846,a846,f854(x42791)),a307),f312(f312(f7(f854(x42791),f854(x42791),a846),a309),f127(x42791)))),x42792)))
% 155.90/155.60 [4289]E(f312(f312(f95(a1,a853),f312(f117(a1),f312(f312(f89(a1),x42891),a111))),f312(f312(f18(a1,a853,a853),f312(f312(f7(a1,a853,f861(a853,a853)),f312(f312(f8(a846,f861(a853,f861(a853,a853)),a1),f108(a853)),a194)),f2(a853))),f312(f312(f8(a853,a853,a1),a126),f312(f312(f7(a1,a853,a853),f312(f312(f8(a853,f861(a853,a853),a1),f225(a853)),a118)),x42892)))),f312(f312(f225(a853),f312(f117(a853),x42891)),f312(a126,x42892)))
% 155.90/155.60 [4290]E(f312(f312(f95(a1,a853),f312(f117(a1),f312(f312(f89(a1),x42901),a111))),f312(f312(f18(a1,a853,a853),f312(f312(f7(a1,a853,f861(a853,a853)),f312(f312(f8(a846,f861(a853,f861(a853,a853)),a1),f108(a853)),a194)),f312(a126,x42902))),f312(f312(f8(a853,a853,a1),a126),f312(f312(f7(a1,a853,a853),f312(f312(f8(a853,f861(a853,a853),a1),f226(a853)),a118)),x42902)))),f312(f312(f226(a853),f312(f117(a853),x42901)),f312(a126,x42902)))
% 155.90/155.60 [4278]E(f312(f249(x42781,x42781,a846),f312(f312(f18(x42781,a846,f861(x42781,a846)),f312(f312(f8(f861(x42781,f861(a846,a846)),f861(a846,f861(x42781,a846)),x42781),f7(x42781,a846,a846)),f312(f312(f8(f861(x42781,a846),f861(x42781,f861(a846,a846)),x42781),f312(f8(a846,f861(a846,a846),x42781),a310)),a309))),x42782)),f237(x42781,x42782))
% 155.90/155.60 [4321]E(f312(f47(a853,x43211),f312(f312(f89(a853),f312(f117(a853),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))),x43212)),f312(f47(a853,x43211),f312(a126,f312(a126,f312(a126,x43212)))))
% 155.90/155.60 [4322]E(f54(a853,x43221,f312(f312(f89(a853),f312(f117(a853),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))),x43222)),f54(a853,x43221,f312(a126,f312(a126,f312(a126,x43222)))))
% 155.90/155.60 [4323]E(f54(a853,f312(f312(f89(a853),f312(f117(a853),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))),x43231),x43232),f54(a853,f312(a126,f312(a126,f312(a126,x43231))),x43232))
% 155.90/155.60 [4334]E(f130(f312(x43341,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))),x43342))),f312(f206(x43341),x43342))
% 155.90/155.60 [4335]E(f312(f47(a853,f312(f312(f89(a853),f312(f117(a853),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))),x43351)),x43352),f312(f47(a853,f312(a126,f312(a126,f312(a126,x43351)))),x43352))
% 155.90/155.60 [3431]P36(x34311,x34312,x34313,x34313)
% 155.90/155.60 [4404]~E(f36(x44041,x44042),f312(a27,x44043))
% 155.90/155.60 [4405]~E(f35(x44051,x44052),f312(a27,x44053))
% 155.90/155.60 [4406]~E(f28(x44061,x44062),f312(a27,x44063))
% 155.90/155.60 [4407]~E(f312(a27,x44071),f36(x44072,x44073))
% 155.90/155.60 [4408]~E(f312(a27,x44081),f35(x44082,x44083))
% 155.90/155.60 [4409]~E(f312(a27,x44091),f28(x44092,x44093))
% 155.90/155.60 [4428]~E(f33(x44281,x44282,x44283),a23)
% 155.90/155.60 [4429]~E(f32(x44291,x44292,x44293),a23)
% 155.90/155.60 [4430]~E(f31(x44301,x44302,x44303),a23)
% 155.90/155.60 [3215]E(f312(f312(f193(x32151,x32152),x32153),f192(x32151)),f192(x32152))
% 155.90/155.60 [3216]E(f312(f312(f150(x32161,x32162),x32163),f127(x32161)),f127(x32162))
% 155.90/155.60 [3235]E(f34(f31(x32351,x32352,x32353)),f2(a853))
% 155.90/155.60 [3256]E(f312(f185(x32561,x32562,x32563),f2(a853)),x32562)
% 155.90/155.60 [3257]E(f312(f190(a847),f31(x32571,x32572,x32573)),f2(a853))
% 155.90/155.60 [3259]E(f312(f312(f177(x32591,x32592),x32593),f127(x32592)),f127(f860(x32591,x32592)))
% 155.90/155.60 [3293]E(f94(x32931,f71(x32931,x32932,x32933)),f312(f72(x32931,x32932),x32933))
% 155.90/155.60 [3346]E(f136(x33461,x33462,f148(x33461,x33463)),f148(x33461,f136(x33461,x33462,x33463)))
% 155.90/155.60 [3366]E(f312(f246(f854(x33661),f854(x33661)),f163(x33661,x33662,x33663)),f312(f132(x33661,x33662),x33663))
% 155.90/155.60 [3444]E(f186(x34441,x34442,x34443,f2(a853)),x34442)
% 155.90/155.60 [3445]E(f17(x34451,x34452,x34453,f2(a113)),x34452)
% 155.90/155.60 [3451]E(f159(x34511,x34512,x34513,f127(x34511)),f127(x34512))
% 155.90/155.60 [3452]E(f160(x34521,x34522,x34523,f127(x34521)),f127(x34522))
% 155.90/155.60 [3458]E(f312(f312(f161(x34581),f312(f312(f147(x34581),x34582),x34583)),f2(a853)),x34582)
% 155.90/155.60 [3492]E(f68(x34921,x34922,f127(x34921),x34923),f127(f860(x34921,x34922)))
% 155.90/155.60 [3511]P19(x35111,x35112,x35113,f189(f861(x35111,a846)))
% 155.90/155.60 [3556]P36(x35561,x35562,f312(f16(f857(x35562),x35561),f192(x35562)),x35563)
% 155.90/155.60 [3664]E(f312(f82(x36641,x36642,x36641,x36643),f39(x36641)),x36643)
% 155.90/155.60 [3843]P22(f312(f312(f314(f860(x38431,x38431)),f312(f312(f239(x38431,x38431),x38432),x38432)),f287(x38431,x38433)))
% 155.90/155.60 [4504]~P22(f312(f312(f314(f860(f854(x45041),f854(x45041))),f312(f312(f239(f854(x45041),f854(x45041)),x45042),f127(x45041))),f141(x45041,x45043)))
% 155.90/155.60 [4505]~P22(f312(f312(f314(f860(f854(x45051),f854(x45051))),f312(f312(f239(f854(x45051),f854(x45051)),x45052),f127(x45051))),f143(x45051,x45053)))
% 155.90/155.60 [4506]~P22(f312(f312(f314(f860(f854(x45061),f854(x45061))),f312(f312(f239(f854(x45061),f854(x45061)),x45062),f127(x45061))),f153(x45061,x45063)))
% 155.90/155.60 [4507]~P22(f312(f312(f314(f860(f854(x45071),f854(x45071))),f312(f312(f239(f854(x45071),f854(x45071)),f127(x45071)),x45072)),f141(x45071,x45073)))
% 155.90/155.60 [4508]~P22(f312(f312(f314(f860(f854(x45081),f854(x45081))),f312(f312(f239(f854(x45081),f854(x45081)),f127(x45081)),x45082)),f153(x45081,x45083)))
% 155.90/155.60 [3228]E(f312(f312(f197(x32281,x32282),f192(x32281)),x32283),f192(x32282))
% 155.90/155.60 [3245]E(f312(f265(x32451,x32452),f312(f265(x32452,x32451),x32453)),x32453)
% 155.90/155.60 [3269]E(f312(f312(f177(x32691,x32692),f127(x32691)),x32693),f127(f860(x32691,x32692)))
% 155.90/155.60 [3272]E(f170(x32721,x32722,f312(f279(a853),x32723)),f312(f312(f169(x32721),x32723),x32722))
% 155.90/155.60 [3289]E(f148(x32891,f312(f132(x32891,x32892),x32893)),f312(f132(x32891,x32892),f148(x32891,x32893)))
% 155.90/155.60 [3291]E(f312(f236(x32911,x32912),f312(f265(x32912,x32911),x32913)),f312(f238(x32912,x32911),x32913))
% 155.90/155.60 [3292]E(f312(f238(x32921,x32922),f312(f265(x32922,x32921),x32923)),f312(f236(x32922,x32921),x32923))
% 155.90/155.60 [3311]E(f312(f132(x33111,x33112),f312(f165(x33111),x33113)),f312(f165(x33111),f312(f132(x33111,x33112),x33113)))
% 155.90/155.60 [3325]E(f312(f312(f134(x33251),x33252),f312(f167(x33251),x33253)),f312(f312(f134(x33251),f312(a126,x33252)),x33253))
% 155.90/155.60 [3341]E(f34(f32(x33411,x33412,x33413)),f312(f312(f89(a853),f34(x33413)),f312(a126,f2(a853))))
% 155.90/155.60 [3342]E(f312(f290(x33421,x33422,x33423),f189(f861(x33421,a846))),f189(f861(x33422,a846)))
% 155.90/155.60 [3343]E(f312(f291(x33431,x33432,x33433),f189(f861(x33432,a846))),f189(f861(x33431,a846)))
% 155.90/155.60 [3344]E(f312(f291(x33441,x33442,x33443),f235(f861(x33442,a846))),f235(f861(x33441,a846)))
% 155.90/155.60 [3345]E(f312(f264(x33451,x33452,x33453),f189(f861(x33451,a846))),f189(f861(x33452,a846)))
% 155.90/155.60 [3365]E(f312(f312(f197(x33651,x33652),x33653),f312(f16(f857(x33652),x33651),f192(x33652))),f192(x33652))
% 155.90/155.60 [3374]E(f312(f312(f289(x33741),x33742),f312(f168(x33741),x33743)),f312(f168(x33741),f136(x33741,x33742,x33743)))
% 155.90/155.60 [3386]E(f220(x33861,x33862,f312(f219(x33861),x33863)),f312(f312(f89(a853),f312(x33862,x33863)),f312(a126,f2(a853))))
% 155.90/155.60 [3462]E(f312(f190(a847),f32(x34621,x34622,x34623)),f312(f312(f89(a853),f312(f190(a847),x34623)),f312(a126,f2(a853))))
% 155.90/155.60 [3463]E(f312(f290(f860(x34631,x34632),x34632,f248(x34631,x34632)),x34633),f312(f236(x34631,x34632),x34633))
% 155.90/155.60 [3464]E(f312(f290(f860(x34641,x34642),x34641,f246(x34641,x34642)),x34643),f312(f238(x34641,x34642),x34643))
% 155.90/155.60 [3535]E(f312(f312(f239(x35351,x35352),f312(f246(x35351,x35352),x35353)),f312(f248(x35351,x35352),x35353)),x35353)
% 155.90/155.60 [3545]E(f312(f312(f249(x35451,x35452,x35451),f16(x35451,x35452)),x35453),f312(f246(x35451,x35452),x35453))
% 155.90/155.60 [3565]E(f180(x35651,x35652,x35653,f312(f16(f857(x35652),x35651),f192(x35652))),x35653)
% 155.90/155.60 [3566]E(f180(x35661,x35662,f312(f16(f857(x35662),x35661),f192(x35662)),x35663),x35663)
% 155.90/155.60 [3619]E(f34(f33(x36191,x36192,x36193)),f312(f312(f89(a853),f312(f312(f89(a853),f34(x36192)),f34(x36193))),f312(a126,f2(a853))))
% 155.90/155.60 [3667]E(f312(f82(x36671,x36671,x36672,f39(x36671)),x36673),x36673)
% 155.90/155.60 [3777]P22(f312(f312(f195(f28(x37771,x37772)),x37773),f312(f312(f312(a201,x37773),x37771),f312(x37772,x37773))))
% 155.90/155.60 [3779]E(f312(f190(a847),f33(x37791,x37792,x37793)),f312(f312(f89(a853),f312(f312(f89(a853),f312(f190(a847),x37792)),f312(f190(a847),x37793))),f312(a126,f2(a853))))
% 155.90/155.60 [3853]P22(f312(f312(f227(f861(x38531,a846)),f312(f168(x38531),f312(f132(x38531,x38532),x38533))),f312(f168(x38531),x38533)))
% 155.90/155.60 [3899]P22(f312(f312(f227(f861(x38991,a846)),f312(f168(x38991),f312(f312(f169(x38991),x38992),x38993))),f312(f168(x38991),x38993)))
% 155.90/155.60 [3900]P22(f312(f312(f227(f861(x39001,a846)),f312(f168(x39001),f312(f312(f134(x39001),x39002),x39003))),f312(f168(x39001),x39003)))
% 155.90/155.60 [3904]P22(f312(f312(f227(f861(x39041,a846)),f312(f168(x39041),f166(x39041,x39042,x39043))),f312(f168(x39041),x39043)))
% 155.90/155.60 [3905]P22(f312(f312(f227(f861(x39051,a846)),f312(f168(x39051),f170(x39051,x39052,x39053))),f312(f168(x39051),x39052)))
% 155.90/155.60 [3926]P19(f860(x39261,x39262),f860(x39262,x39261),f312(f249(x39261,x39262,f860(x39262,x39261)),f312(f7(x39262,x39261,f860(x39262,x39261)),f239(x39262,x39261))),x39263)
% 155.90/155.60 [3939]E(f312(f312(f312(f184(f854(x39391),f854(x39391)),f54(a853,x39392,f312(f190(f854(x39391)),x39393))),f164(x39391)),x39393),f312(f312(f312(f184(f854(x39391),f854(x39391)),x39392),f164(x39391)),x39393))
% 155.90/155.60 [3981]P22(f312(f312(f314(f860(f854(x39811),f854(x39811))),f312(f312(f239(f854(x39811),f854(x39811)),x39812),x39812)),f154(x39811,f287(x39811,x39813))))
% 155.90/155.60 [4124]E(f94(f860(x41241,x41242),f312(f312(f18(f860(x41241,x41242),x41242,a846),f312(f312(f8(x41241,f861(x41242,a846),f860(x41241,x41242)),x41243),f246(x41241,x41242))),f248(x41241,x41242))),f94(f860(x41241,x41242),f312(f249(x41241,x41242,a846),x41243)))
% 155.90/155.60 [4125]E(f99(f860(x41251,x41252),f312(f312(f18(f860(x41251,x41252),x41252,a846),f312(f312(f8(x41251,f861(x41252,a846),f860(x41251,x41252)),x41253),f246(x41251,x41252))),f248(x41251,x41252))),f99(f860(x41251,x41252),f312(f249(x41251,x41252,a846),x41253)))
% 155.90/155.60 [4161]E(f312(f312(f266(f860(a853,x41611),x41611),f304(a853,x41611,a232,x41612)),f312(f312(f18(x41611,x41611,f860(a853,x41611)),f312(f312(f8(a853,f861(x41611,f860(a853,x41611)),x41611),f239(a853,x41611)),x41613)),f5(x41611))),f306(x41611,x41613,x41612))
% 155.90/155.60 [4228]E(f312(f250(x42281,x42281,x42282,x42282,f5(x42281),f5(x42282)),x42283),x42283)
% 155.90/155.60 [4300]E(f312(f138(f854(f854(x43001)),f854(f854(x43001)),f129(f854(x43001)),f127(f854(x43001))),f312(f312(f150(f854(x43001),f854(f854(x43001))),f312(f312(f7(f854(x43001),f854(x43001),f854(f854(x43001))),f312(f312(f8(f861(x43001,f854(x43001)),f861(f854(x43001),f854(f854(x43001))),f854(x43001)),f150(x43001,f854(x43001))),f312(f7(x43001,f854(x43001),f854(x43001)),f147(x43001)))),x43002)),f63(x43001,x43003,x43002))),f63(x43001,f312(a126,x43003),x43002))
% 155.90/155.60 [4423]~E(f312(f312(f147(x44231),x44232),x44233),x44233)
% 155.90/155.60 [4432]~E(f312(f312(f147(x44321),x44322),x44323),f127(x44321))
% 155.90/155.60 [4459]~E(f312(f312(f289(x44591),x44592),x44593),f189(f861(x44591,a846)))
% 155.90/155.60 [4485]~E(f312(f290(x44851,f861(x44851,a846),x44852),x44853),f312(f288(x44851),x44853))
% 155.90/155.60 [3250]E(f312(f312(f155(x32501,f127(x32501)),x32502),x32503),f127(x32501))
% 155.90/155.60 [3251]E(f312(f137(x32511),f312(f312(f147(x32511),x32512),x32513)),x32512)
% 155.90/155.60 [3252]E(f312(f167(x32521),f312(f312(f147(x32521),x32522),x32523)),x32523)
% 155.90/155.60 [3296]E(f312(f312(f134(x32961),f87(a853)),f312(f312(f147(x32961),x32962),x32963)),x32963)
% 155.90/155.60 [3331]E(f128(x33311,f312(f312(f134(x33311),x33312),x33313)),f312(f312(f134(x33311),x33312),f128(x33311,x33313)))
% 155.90/155.60 [3333]E(f312(f312(f155(x33331,x33332),x33333),f312(f312(f161(x33331),x33332),x33333)),x33332)
% 155.90/155.60 [3356]E(f312(f312(f289(x33561),x33562),f312(f312(f289(x33561),x33562),x33563)),f312(f312(f289(x33561),x33562),x33563))
% 155.90/155.60 [3368]E(f312(f312(f173(x33681,x33682),f127(f860(x33681,x33682))),x33683),f192(x33682))
% 155.90/155.60 [3371]E(f312(f312(f289(x33711),x33712),f312(f168(x33711),x33713)),f312(f168(x33711),f312(f312(f147(x33711),x33712),x33713)))
% 155.90/155.60 [3373]E(f312(f312(f134(x33731),x33732),f312(f167(x33731),x33733)),f312(f167(x33731),f312(f312(f134(x33731),x33732),x33733)))
% 155.90/155.60 [3383]E(f312(f312(f169(x33831),f87(a853)),f312(f312(f147(x33831),x33832),x33833)),f312(f312(f147(x33831),x33832),f127(x33831)))
% 155.90/155.60 [3430]E(f312(f72(x34301,x34302),f312(f312(f289(x34301),x34303),f189(f861(x34301,a846)))),x34303)
% 155.90/155.60 [3476]E(f312(f312(f89(a853),x34761),f312(f312(f89(a853),x34762),x34763)),f312(f312(f89(a853),x34762),f312(f312(f89(a853),x34761),x34763)))
% 155.90/155.60 [3477]E(f312(f312(f89(a1),x34771),f312(f312(f89(a1),x34772),x34773)),f312(f312(f89(a1),x34772),f312(f312(f89(a1),x34771),x34773)))
% 155.90/155.60 [3482]E(f312(f312(f247(x34821,x34822),f189(f861(x34821,a846))),x34823),f189(f861(f860(x34821,x34822),a846)))
% 155.90/155.60 [3502]E(f312(f312(f124(f861(x35021,a846)),x35022),x35023),f312(f312(f124(f861(x35021,a846)),x35023),x35022))
% 155.90/155.60 [3503]E(f312(f312(f115(f861(x35031,a846)),x35032),x35033),f312(f312(f115(f861(x35031,a846)),x35033),x35032))
% 155.90/155.60 [3506]E(f312(f312(f129(x35061),x35062),f312(f312(f147(x35061),x35063),f127(x35061))),f312(f164(x35061),f312(f312(f147(x35061),x35063),x35062)))
% 155.90/155.60 [3507]E(f312(f312(f129(x35071),f312(f165(x35071),x35072)),f312(f165(x35071),x35073)),f312(f165(x35071),f312(f312(f129(x35071),x35073),x35072)))
% 155.90/155.60 [3515]E(f312(f167(x35151),f312(f312(f169(x35151),f312(a126,x35152)),x35153)),f312(f312(f169(x35151),x35152),f312(f167(x35151),x35153)))
% 155.90/155.60 [3519]E(f312(f47(a853,x35191),f312(f312(f90(a853),x35192),x35193)),f312(f47(a853,f312(f47(a853,x35191),x35192)),x35193))
% 155.90/155.60 [3522]P22(f312(f312(f314(x35221),x35222),f312(f312(f289(x35221),x35222),x35223)))
% 155.90/155.60 [3526]E(f312(f312(f51(x35261,f861(x35262,a846)),f189(f861(x35261,a846))),x35263),f235(f861(x35262,a846)))
% 155.90/155.60 [3528]E(f312(f264(x35281,x35281,f237(x35281,x35282)),x35283),f312(f312(f115(f861(x35281,a846)),x35282),x35283))
% 155.90/155.60 [3541]E(f312(f190(f854(x35411)),f312(f312(f147(x35411),x35412),x35413)),f312(f312(f89(a853),f312(f190(f854(x35411)),x35413)),f312(a126,f2(a853))))
% 155.90/155.60 [3547]E(f128(x35471,f312(f312(f129(x35471),x35472),f312(f312(f147(x35471),x35473),f127(x35471)))),x35472)
% 155.90/155.60 [3548]E(f140(x35481,f312(f312(f129(x35481),x35482),f312(f312(f147(x35481),x35483),f127(x35481)))),x35483)
% 155.90/155.60 [3554]E(f312(f312(f129(x35541),f312(f312(f169(x35541),x35542),x35543)),f312(f312(f134(x35541),x35542),x35543)),x35543)
% 155.90/155.60 [3563]E(f312(f312(f21(a853),f312(f312(f89(a853),x35631),x35632)),f312(f312(f89(a853),x35633),x35632)),f312(f312(f21(a853),x35631),x35633))
% 155.90/155.60 [3564]E(f312(f312(f21(a853),f312(f312(f89(a853),x35641),x35642)),f312(f312(f89(a853),x35641),x35643)),f312(f312(f21(a853),x35642),x35643))
% 155.90/155.60 [3571]E(f312(f312(f129(x35711),f312(f165(x35711),x35712)),f312(f312(f147(x35711),x35713),f127(x35711))),f312(f165(x35711),f312(f312(f147(x35711),x35713),x35712)))
% 155.90/155.60 [3573]E(f312(f312(f89(a853),f312(f190(f854(x35731)),x35732)),f312(f190(f854(x35731)),x35733)),f312(f190(f854(x35731)),f312(f312(f129(x35731),x35732),x35733)))
% 155.90/155.60 [3580]E(f312(f312(f124(f861(x35801,a846)),f312(f168(x35801),x35802)),f312(f168(x35801),x35803)),f312(f168(x35801),f312(f312(f129(x35801),x35802),x35803)))
% 155.90/155.60 [3582]E(f54(a853,f312(f312(f90(a853),x35821),x35822),f312(f312(f90(a853),x35821),x35823)),f312(f312(f90(a853),x35821),f54(a853,x35822,x35823)))
% 155.90/155.60 [3596]E(f312(f312(f169(x35961),f312(f312(f21(a853),x35962),f87(a853))),f312(f167(x35961),x35963)),f312(f167(x35961),f312(f312(f169(x35961),x35962),x35963)))
% 155.90/155.60 [3601]E(f312(f312(f115(f861(x36011,a846)),x36012),f312(f88(f861(x36011,a846)),x36013)),f312(f312(f21(f861(x36011,a846)),x36012),x36013))
% 155.90/155.60 [3602]E(f312(f312(f21(f861(x36021,a846)),x36022),f312(f88(f861(x36021,a846)),x36023)),f312(f312(f115(f861(x36021,a846)),x36022),x36023))
% 155.90/155.60 [3623]E(f312(f312(f247(x36231,x36232),x36233),f312(f16(f861(x36232,a846),x36231),f189(f861(x36232,a846)))),f189(f861(f860(x36231,x36232),a846)))
% 155.90/155.60 [3625]E(f312(f312(f89(a853),f312(f312(f90(a853),x36251),x36252)),f312(f312(f90(a853),x36251),x36253)),f312(f312(f90(a853),x36251),f312(f312(f89(a853),x36252),x36253)))
% 155.90/155.60 [3626]E(f312(f312(f21(a853),f312(f312(f90(a853),x36261),x36262)),f312(f312(f90(a853),x36261),x36263)),f312(f312(f90(a853),x36261),f312(f312(f21(a853),x36262),x36263)))
% 155.90/155.60 [3627]E(f312(f312(f89(a1),f312(f312(f90(a1),x36271),x36272)),f312(f312(f90(a1),x36271),x36273)),f312(f312(f90(a1),x36271),f312(f312(f89(a1),x36272),x36273)))
% 155.90/155.60 [3628]E(f312(f312(f21(a1),f312(f312(f90(a1),x36281),x36282)),f312(f312(f90(a1),x36281),x36283)),f312(f312(f90(a1),x36281),f312(f312(f21(a1),x36282),x36283)))
% 155.90/155.60 [3629]E(f312(f312(f90(a1),f312(f312(f240(a1),x36291),x36292)),f312(f312(f240(a1),x36291),x36293)),f312(f312(f240(a1),x36291),f312(f312(f89(a853),x36292),x36293)))
% 155.90/155.60 [3642]E(f312(f312(f50(x36421,f861(x36422,a846)),x36423),f312(f16(f861(x36422,a846),x36421),f189(f861(x36422,a846)))),f189(f861(x36422,a846)))
% 155.90/155.60 [3644]E(f54(a853,f312(f312(f90(a853),x36441),x36442),f312(f312(f90(a853),x36443),x36442)),f312(f312(f90(a853),f54(a853,x36441,x36443)),x36442))
% 155.90/155.60 [3648]E(f54(a1,f312(f312(f21(a1),x36481),f54(a1,x36482,x36483)),x36483),f54(a1,f312(f312(f21(a1),x36481),x36482),x36483))
% 155.90/155.60 [3649]E(f54(a1,f312(f312(f90(a1),x36491),f54(a1,x36492,x36493)),x36493),f54(a1,f312(f312(f90(a1),x36491),x36492),x36493))
% 155.90/155.60 [3650]P22(f312(f312(f227(f861(x36501,a846)),x36502),f312(f312(f289(x36501),x36503),x36502)))
% 155.90/155.60 [3653]E(f312(f290(f860(x36531,x36532),x36531,f246(x36531,x36532)),f312(f168(f860(x36531,x36532)),x36533)),f179(x36531,x36532,f312(f173(x36531,x36532),x36533)))
% 155.90/155.60 [3700]P22(f312(f70(x37001),f179(x37001,x37002,f312(f173(x37001,x37002),x37003))))
% 155.90/155.60 [3726]E(f312(f312(f51(f861(x37261,a846),f861(x37261,a846)),x37262),f312(f124(f861(x37261,a846)),x37263)),f312(f312(f124(f861(x37261,a846)),x37263),f49(f861(x37261,a846),x37262)))
% 155.90/155.60 [3727]E(f312(f312(f50(f861(x37271,a846),f861(x37271,a846)),x37272),f312(f115(f861(x37271,a846)),x37273)),f312(f312(f115(f861(x37271,a846)),x37273),f48(f861(x37271,a846),x37272)))
% 155.90/155.60 [3737]E(f312(f168(x37371),f312(f312(f312(f184(f854(x37371),f854(x37371)),x37372),f164(x37371)),x37373)),f312(f168(x37371),x37373))
% 155.90/155.60 [3741]E(f312(f312(f169(x37411),f312(f190(f854(x37411)),f172(x37411,x37412,x37413))),x37413),f172(x37411,x37412,x37413))
% 155.90/155.60 [3742]E(f179(x37421,x37422,f312(f312(f8(x37422,f857(x37422),x37421),f219(x37422)),x37423)),f235(f861(x37421,a846)))
% 155.90/155.60 [3746]E(f312(f190(f854(x37461)),f312(f312(f312(f184(f854(x37461),f854(x37461)),x37462),f164(x37461)),x37463)),f312(f190(f854(x37461)),x37463))
% 155.90/155.60 [3749]E(f312(f312(f249(x37491,x37492,x37492),f312(f16(f861(x37492,x37492),x37491),f5(x37492))),x37493),f312(f248(x37491,x37492),x37493))
% 155.90/155.60 [3754]E(f54(a1,f312(f312(f21(a1),f54(a1,x37541,x37542)),x37543),x37542),f54(a1,f312(f312(f21(a1),x37541),x37543),x37542))
% 155.90/155.60 [3755]E(f54(a1,f312(f312(f240(a1),f54(a1,x37551,x37552)),x37553),x37552),f54(a1,f312(f312(f240(a1),x37551),x37553),x37552))
% 155.90/155.60 [3759]E(f312(f312(f50(f861(f860(x37591,x37592),a846),f861(x37592,a846)),x37593),f236(x37591,x37592)),f312(f236(x37591,x37592),f48(f861(f860(x37591,x37592),a846),x37593)))
% 155.90/155.60 [3760]E(f312(f312(f50(f861(f860(x37601,x37602),a846),f861(x37601,a846)),x37603),f238(x37601,x37602)),f312(f238(x37601,x37602),f48(f861(f860(x37601,x37602),a846),x37603)))
% 155.90/155.60 [3791]E(f312(f82(x37911,x37911,x37911,x37912),f312(f312(f184(x37911,x37911),x37913),x37912)),f312(f312(f184(x37911,x37911),f312(a126,x37913)),x37912))
% 155.90/155.60 [3802]E(f221(f857(x38021),x38022,f192(x38021),f312(f312(f8(x38021,f857(x38021),x38022),f219(x38021)),x38023)),f312(f193(x38022,x38021),x38023))
% 155.90/155.60 [3808]E(f312(f312(f134(x38081),f312(f312(f21(a853),f312(f190(f854(x38081)),x38082)),x38083)),f312(f165(x38081),x38082)),f312(f165(x38081),f312(f312(f169(x38081),x38083),x38082)))
% 155.90/155.60 [3809]E(f312(f312(f169(x38091),f312(f312(f21(a853),f312(f190(f854(x38091)),x38092)),x38093)),f312(f165(x38091),x38092)),f312(f165(x38091),f312(f312(f134(x38091),x38093),x38092)))
% 155.90/155.60 [3812]E(f312(f312(f89(a853),f312(f162(a853),f312(f312(f150(x38121,a853),x38122),x38123))),f312(f190(f854(x38121)),x38123)),f151(x38121,x38122,x38123))
% 155.90/155.60 [3829]E(f312(f164(x38291),f312(f312(f312(f184(f854(x38291),f854(x38291)),x38292),f164(x38291)),x38293)),f312(f312(f312(f184(f854(x38291),f854(x38291)),f312(a126,x38292)),f164(x38291)),x38293))
% 155.90/155.60 [3844]P22(f312(f312(f227(a853),f312(f190(f854(x38441)),f312(f132(x38441,x38442),x38443))),f312(f190(f854(x38441)),x38443)))
% 155.90/155.60 [3861]E(f312(f312(f124(f861(f861(x38611,a846),a846)),f312(f288(x38611),x38612)),f312(f290(f861(x38611,a846),f861(x38611,a846),f312(f289(x38611),x38613)),f312(f288(x38611),x38612))),f312(f288(x38611),f312(f312(f289(x38611),x38613),x38612)))
% 155.90/155.60 [3881]P18(x38811,x38812,f312(f312(f289(f852(x38811)),f312(f312(f312(f100(x38811),x38813),a23),x38813)),f189(f861(f852(x38811),a846))))
% 155.90/155.60 [3896]P22(f312(f312(f227(a853),f312(f190(f854(x38961)),f172(x38961,x38962,x38963))),f312(f190(f854(x38961)),x38963)))
% 155.90/155.60 [3903]E(f312(f238(x39031,x39032),f312(f233(f860(x39031,x39032)),f312(f249(x39031,x39032,a846),x39033))),f312(f233(x39031),f312(f312(f8(f861(x39032,a846),a846,x39031),f96(x39032)),x39033)))
% 155.90/155.60 [3914]E(f312(f290(a853,a853,f312(f312(f7(a853,a853,a853),f89(a853)),x39141)),f283(a853,x39142,x39143)),f283(a853,f312(f312(f89(a853),x39142),x39141),f312(f312(f89(a853),x39143),x39141)))
% 155.90/155.60 [3916]P22(f312(f70(f857(x39161)),f312(f290(x39162,f857(x39161),f312(f173(x39162,x39161),x39163)),f235(f861(x39162,a846)))))
% 155.90/155.60 [3929]E(f312(f290(a853,a853,f312(f312(f7(a853,a853,a853),f89(a853)),x39291)),f312(f282(a853,x39292),x39293)),f312(f282(a853,f312(f312(f89(a853),x39292),x39291)),f312(f312(f89(a853),x39293),x39291)))
% 155.90/155.60 [3930]E(f312(f312(f89(a853),f312(f312(f90(a853),x39301),f54(a853,f312(f47(a853,x39302),x39301),x39303))),f54(a853,x39302,x39301)),f54(a853,x39302,f312(f312(f90(a853),x39301),x39303)))
% 155.90/155.60 [3947]E(f312(f312(f177(x39471,x39472),f312(f312(f150(f860(x39471,x39472),x39471),f246(x39471,x39472)),x39473)),f312(f312(f150(f860(x39471,x39472),x39472),f248(x39471,x39472)),x39473)),x39473)
% 155.90/155.60 [3965]E(f312(f312(f129(x39651),x39652),f312(f138(f854(x39651),f854(x39651),f129(x39651),f127(x39651)),x39653)),f312(f138(f854(x39651),f854(x39651),f129(x39651),x39652),x39653))
% 155.90/155.60 [3985]P22(f312(f312(f314(f860(x39851,x39851)),f312(f312(f239(x39851,x39851),x39852),x39852)),f312(f312(f184(f860(x39851,x39851),a846),f2(a853)),x39853)))
% 155.90/155.60 [3991]E(f312(f233(x39911),f312(f312(f8(f861(x39912,a846),a846,x39911),f96(x39912)),f312(f7(x39912,x39911,a846),x39913))),f312(f236(x39912,x39911),f312(f233(f860(x39912,x39911)),f312(f249(x39912,x39911,a846),x39913))))
% 155.90/155.60 [4011]E(f312(f312(f124(f861(x40111,a846)),f312(f312(f50(a853,f861(x40111,a846)),f283(a853,f87(a853),x40112)),x40113)),f312(x40113,f2(a853))),f312(f312(f50(a853,f861(x40111,a846)),f312(f281(a853),x40112)),x40113))
% 155.90/155.60 [4026]E(f312(f138(f854(x40261),f854(x40261),f129(x40261),f127(x40261)),f312(f312(f150(f854(x40261),f854(x40261)),f132(x40261,x40262)),x40263)),f312(f132(x40261,x40262),f312(f138(f854(x40261),f854(x40261),f129(x40261),f127(x40261)),x40263)))
% 155.90/155.60 [4029]E(f312(f248(f854(x40291),f854(x40291)),f163(x40291,x40292,x40293)),f312(f132(x40291,f312(f82(a846,a846,x40291,a307),x40292)),x40293))
% 155.90/155.60 [4047]E(f312(f312(f51(x40471,f861(x40472,a846)),f235(f861(x40471,a846))),f312(f312(f8(f861(x40472,a846),f861(x40472,a846),x40471),f233(x40472)),f312(f7(x40472,x40471,a846),x40473))),f312(f233(x40472),f312(f312(f8(f861(x40471,a846),a846,x40472),f97(x40471)),x40473)))
% 155.90/155.60 [4061]E(f312(f312(f89(a1),f312(f312(f89(a1),f312(f312(f90(a1),x40611),f312(f47(a1,x40612),x40611))),f54(a1,x40612,x40611))),x40613),f312(f312(f89(a1),x40612),x40613))
% 155.90/155.60 [4108]E(f312(f312(f89(a1),f312(f312(f89(a1),f312(f312(f90(a1),f312(f47(a1,x41081),x41082)),x41082)),f54(a1,x41081,x41082))),x41083),f312(f312(f89(a1),x41081),x41083))
% 155.90/155.60 [4142]E(f94(f860(x41421,x41422),f312(f249(x41421,x41422,a846),f312(f312(f8(f861(x41422,f860(x41421,x41422)),f861(x41422,a846),x41421),f312(f8(f860(x41421,x41422),a846,x41422),x41423)),f239(x41421,x41422)))),f94(f860(x41421,x41422),x41423))
% 155.90/155.60 [4143]E(f99(f860(x41431,x41432),f312(f249(x41431,x41432,a846),f312(f312(f8(f861(x41432,f860(x41431,x41432)),f861(x41432,a846),x41431),f312(f8(f860(x41431,x41432),a846,x41432),x41433)),f239(x41431,x41432)))),f99(f860(x41431,x41432),x41433))
% 155.90/155.60 [4172]P22(f312(f312(f227(f861(x41721,a846)),f48(f861(x41721,a846),f312(f312(f115(f861(f861(x41721,a846),a846)),x41722),x41723))),f312(f312(f115(f861(x41721,a846)),f48(f861(x41721,a846),x41722)),f48(f861(x41721,a846),x41723))))
% 155.90/155.60 [4173]E(f312(f165(x41731),f312(f312(f312(f184(f854(x41731),f854(x41731)),f312(f312(f21(a853),f312(f190(f854(x41731)),x41732)),f54(a853,x41733,f312(f190(f854(x41731)),x41732)))),f164(x41731)),x41732)),f312(f312(f312(f184(f854(x41731),f854(x41731)),x41733),f164(x41731)),f312(f165(x41731),x41732)))
% 155.90/155.60 [4188]E(f312(f233(x41881),f312(f312(f8(a846,a846,x41881),a307),f312(f312(f7(x41881,f857(x41882),a846),f312(f312(f8(f857(x41882),f861(f857(x41882),a846),x41881),a309),x41883)),f192(x41882)))),f179(x41881,x41882,x41883))
% 155.90/155.60 [4213]P22(f312(f312(f227(a853),f312(f190(f854(x42131)),f312(f312(f134(x42131),f312(f190(f854(x42131)),f172(x42131,x42132,x42133))),x42133))),f312(f190(f854(x42131)),x42133)))
% 155.90/155.60 [4253]E(f312(f233(x42531),f312(f312(f8(f861(x42532,a846),a846,x42531),f96(x42532)),f312(f312(f8(f857(x42531),f861(x42532,a846),x42531),f312(f7(x42532,f857(x42531),a846),f312(f312(f8(f857(x42531),f861(f857(x42531),a846),x42532),a309),x42533))),f219(x42531)))),f181(x42532,x42531,x42533))
% 155.90/155.60 [4498]~P22(f312(f71(x44981,x44982,f189(f861(x44981,a846))),x44983))
% 155.90/155.60 [4503]~P22(f312(f312(f314(f860(x45031,x45031)),f312(f312(f239(x45031,x45031),x45032),x45033)),f149(x45031,f127(f861(x45031,a853)))))
% 155.90/155.60 [3516]E(f312(f190(f854(x35161)),f312(f312(f169(x35161),x35162),x35163)),f312(f312(f225(a853),f312(f190(f854(x35161)),x35163)),x35162))
% 155.90/155.60 [3517]E(f312(f190(f854(x35171)),f312(f312(f134(x35171),x35172),x35173)),f312(f312(f21(a853),f312(f190(f854(x35171)),x35173)),x35172))
% 155.90/155.60 [3540]E(f312(f190(f854(f854(x35401))),f63(x35401,x35402,x35403)),f312(f312(f240(a853),f312(f190(f854(x35401)),x35403)),x35402))
% 155.90/155.60 [3557]E(f312(f312(f89(a853),f312(f312(f89(a853),x35571),x35572)),x35573),f312(f312(f89(a853),x35571),f312(f312(f89(a853),x35572),x35573)))
% 155.90/155.60 [3558]E(f312(f312(f89(a1),f312(f312(f89(a1),x35581),x35582)),x35583),f312(f312(f89(a1),x35581),f312(f312(f89(a1),x35582),x35583)))
% 155.90/155.60 [3559]E(f312(f312(f21(a853),f312(f312(f21(a853),x35591),x35592)),x35593),f312(f312(f21(a853),x35591),f312(f312(f89(a853),x35592),x35593)))
% 155.90/155.60 [3560]E(f312(f312(f90(a853),f312(f312(f90(a853),x35601),x35602)),x35603),f312(f312(f90(a853),x35601),f312(f312(f90(a853),x35602),x35603)))
% 155.90/155.60 [3561]E(f312(f312(f90(a1),f312(f312(f90(a1),x35611),x35612)),x35613),f312(f312(f90(a1),x35611),f312(f312(f90(a1),x35612),x35613)))
% 155.90/155.60 [3562]E(f312(f312(f240(a1),f312(f312(f240(a1),x35621),x35622)),x35623),f312(f312(f240(a1),x35621),f312(f312(f90(a853),x35622),x35623)))
% 155.90/155.60 [3578]E(f158(x35781,f312(f312(f147(f861(x35781,a846)),x35782),x35783)),f171(x35781,x35782,f158(x35781,x35783)))
% 155.90/155.60 [3624]E(f312(f312(f21(a853),f312(f312(f21(a853),x36241),x36242)),x36243),f312(f312(f21(a853),f312(f312(f21(a853),x36241),x36243)),x36242))
% 155.90/155.60 [3631]E(f312(f312(f115(f861(x36311,a846)),x36312),f312(f312(f21(f861(x36311,a846)),x36313),x36312)),f189(f861(x36311,a846)))
% 155.90/155.60 [3673]E(f48(f861(x36731,a846),f312(f312(f289(f861(x36731,a846)),x36732),x36733)),f312(f312(f124(f861(x36731,a846)),x36732),f48(f861(x36731,a846),x36733)))
% 155.90/155.60 [3674]E(f49(f861(x36741,a846),f312(f312(f289(f861(x36741,a846)),x36742),x36743)),f312(f312(f115(f861(x36741,a846)),x36742),f49(f861(x36741,a846),x36743)))
% 155.90/155.60 [3676]E(f312(f312(f89(a853),f312(f312(f90(a853),x36761),x36762)),f312(f312(f90(a853),x36763),x36762)),f312(f312(f90(a853),f312(f312(f89(a853),x36761),x36763)),x36762))
% 155.90/155.60 [3677]E(f312(f312(f21(a853),f312(f312(f90(a853),x36771),x36772)),f312(f312(f90(a853),x36773),x36772)),f312(f312(f90(a853),f312(f312(f21(a853),x36771),x36773)),x36772))
% 155.90/155.60 [3678]E(f312(f312(f89(a1),f312(f312(f90(a1),x36781),x36782)),f312(f312(f90(a1),x36783),x36782)),f312(f312(f90(a1),f312(f312(f89(a1),x36781),x36783)),x36782))
% 155.90/155.60 [3680]E(f312(f312(f21(a1),f312(f312(f90(a1),x36801),x36802)),f312(f312(f90(a1),x36803),x36802)),f312(f312(f90(a1),f312(f312(f21(a1),x36801),x36803)),x36802))
% 155.90/155.60 [3681]E(f312(f312(f225(a853),f312(f312(f21(a853),x36811),x36812)),f312(f312(f21(a853),x36813),x36812)),f312(f312(f21(a853),f312(f312(f225(a853),x36811),x36813)),x36812))
% 155.90/155.60 [3703]E(f312(f312(f115(f861(f854(x37031),a846)),f156(x37031,x37032)),f156(x37031,x37033)),f156(x37031,f312(f312(f115(f861(x37031,a846)),x37032),x37033)))
% 155.90/155.60 [3705]E(f312(f312(f124(f861(x37051,a846)),x37052),f312(f312(f21(f861(x37051,a846)),x37053),x37052)),f312(f312(f124(f861(x37051,a846)),x37052),x37053))
% 155.90/155.60 [3706]E(f312(f312(f124(f861(x37061,a846)),x37062),f312(f312(f124(f861(x37061,a846)),x37062),x37063)),f312(f312(f124(f861(x37061,a846)),x37062),x37063))
% 155.90/155.60 [3707]E(f312(f312(f115(f861(x37071,a846)),x37072),f312(f312(f115(f861(x37071,a846)),x37072),x37073)),f312(f312(f115(f861(x37071,a846)),x37072),x37073))
% 155.90/155.60 [3719]E(f312(f312(f267(x37191,x37192,x37192),x37193),f287(x37192,f189(f861(f860(x37192,x37192),a846)))),x37193)
% 155.90/155.60 [3722]E(f312(f312(f124(f861(x37221,a846)),f312(f312(f289(x37221),x37222),f189(f861(x37221,a846)))),x37223),f312(f312(f289(x37221),x37222),x37223))
% 155.90/155.60 [3740]E(f312(f312(f21(a853),f312(f312(f21(a853),f312(a126,x37401)),x37402)),f312(a126,x37403)),f312(f312(f21(a853),f312(f312(f21(a853),x37401),x37402)),x37403))
% 155.90/155.60 [3771]E(f312(f312(f115(f861(f861(x37711,a846),a846)),f312(f288(x37711),x37712)),f312(f288(x37711),x37713)),f312(f288(x37711),f312(f312(f115(f861(x37711,a846)),x37712),x37713)))
% 155.90/155.60 [3775]E(f312(f312(f124(f861(x37751,a846)),f312(f88(f861(x37751,a846)),x37752)),x37753),f312(f88(f861(x37751,a846)),f312(f312(f21(f861(x37751,a846)),x37752),x37753)))
% 155.90/155.60 [3788]E(f312(f312(f289(x37881),x37882),f312(f312(f21(f861(x37881,a846)),x37883),f312(f312(f289(x37881),x37882),f189(f861(x37881,a846))))),f312(f312(f289(x37881),x37882),x37883))
% 155.90/155.60 [3799]P22(f312(f312(f227(f861(x37991,a846)),x37992),f312(f312(f124(f861(x37991,a846)),x37993),x37992)))
% 155.90/155.60 [3800]P22(f312(f312(f227(f861(x38001,a846)),x38002),f312(f312(f124(f861(x38001,a846)),x38002),x38003)))
% 155.90/155.60 [3803]E(f312(f312(f115(f861(x38031,a846)),f312(f88(f861(x38031,a846)),x38032)),f312(f88(f861(x38031,a846)),x38033)),f312(f88(f861(x38031,a846)),f312(f312(f124(f861(x38031,a846)),x38032),x38033)))
% 155.90/155.60 [3804]E(f312(f312(f124(f861(x38041,a846)),f312(f88(f861(x38041,a846)),x38042)),f312(f88(f861(x38041,a846)),x38043)),f312(f88(f861(x38041,a846)),f312(f312(f115(f861(x38041,a846)),x38042),x38043)))
% 155.90/155.60 [3816]P22(f312(f312(f227(f861(x38161,a846)),f312(f168(x38161),x38162)),f312(f168(x38161),f312(f312(f147(x38161),x38163),x38162))))
% 155.90/155.60 [3826]E(f312(f312(f124(f861(x38261,a846)),f312(f312(f21(f861(x38261,a846)),x38262),x38263)),f312(f312(f115(f861(x38261,a846)),x38262),x38263)),x38262)
% 155.90/155.60 [3883]E(f312(f312(f9(x38831,a1),f312(f312(f8(a853,a1,x38831),f114(a1)),x38832)),x38833),f312(f114(a1),f312(f312(f9(x38831,a853),x38832),x38833)))
% 155.90/155.60 [3884]E(f312(f312(f6(x38841,a1),f312(f312(f8(a853,a1,x38841),f114(a1)),x38842)),x38843),f312(f114(a1),f312(f312(f6(x38841,a853),x38842),x38843)))
% 155.90/155.60 [3932]E(f312(f312(f129(x39321),f172(x39321,x39322,x39323)),f312(f312(f134(x39321),f312(f190(f854(x39321)),f172(x39321,x39322,x39323))),x39323)),x39323)
% 155.90/155.60 [3937]E(f312(f88(f861(f860(x39371,x39372),a846)),f312(f312(f247(x39371,x39372),x39373),f312(f16(f861(x39372,a846),x39371),f235(f861(x39372,a846))))),f312(f312(f247(x39371,x39372),f312(f88(f861(x39371,a846)),x39373)),f312(f16(f861(x39372,a846),x39371),f235(f861(x39372,a846)))))
% 155.90/155.60 [3938]E(f312(f88(f861(f860(x39381,x39382),a846)),f312(f312(f247(x39381,x39382),f235(f861(x39381,a846))),f312(f16(f861(x39382,a846),x39381),x39383))),f312(f312(f247(x39381,x39382),f235(f861(x39381,a846))),f312(f16(f861(x39382,a846),x39381),f312(f88(f861(x39382,a846)),x39383))))
% 155.90/155.60 [3986]E(f312(f312(f50(f861(x39861,a846),f861(x39861,a846)),x39862),f312(f312(f7(f861(x39861,a846),f861(x39861,a846),f861(x39861,a846)),f115(f861(x39861,a846))),x39863)),f312(f312(f115(f861(x39861,a846)),f48(f861(x39861,a846),x39862)),x39863))
% 155.90/155.60 [3993]E(f312(f138(f854(x39931),f854(x39931),f129(x39931),f127(x39931)),f312(f312(f147(f854(x39931)),x39932),x39933)),f312(f312(f129(x39931),x39932),f312(f138(f854(x39931),f854(x39931),f129(x39931),f127(x39931)),x39933)))
% 155.90/155.60 [4006]E(f312(f312(f89(a853),f312(f312(f90(a853),x40061),f312(f47(a853,x40062),x40063))),f312(f47(a853,f312(f312(f90(a853),x40061),f54(a853,x40062,x40063))),x40063)),f312(f47(a853,f312(f312(f90(a853),x40061),x40062)),x40063))
% 155.90/155.60 [4007]E(f312(f312(f89(a1),f312(f312(f90(a1),x40071),f312(f47(a1,x40072),x40073))),f312(f47(a1,f312(f312(f90(a1),x40071),f54(a1,x40072,x40073))),x40073)),f312(f47(a1,f312(f312(f90(a1),x40071),x40072)),x40073))
% 155.90/155.60 [4017]E(f312(f312(f289(f861(x40171,a846)),f312(f264(x40171,x40171,x40172),f312(f312(f289(x40171),x40173),f189(f861(x40171,a846))))),f189(f861(f861(x40171,a846),a846))),f312(f312(f69(x40171),f312(f312(f289(x40171),x40173),f189(f861(x40171,a846)))),x40172))
% 155.90/155.60 [4064]E(f312(f312(f21(f861(x40641,a846)),f312(f168(x40641),x40642)),f312(f312(f289(x40641),x40643),f189(f861(x40641,a846)))),f312(f168(x40641),f312(f132(x40641,f312(f312(f8(a846,a846,x40641),a307),f312(a309,x40643))),x40642)))
% 155.90/155.60 [4112]E(f312(f312(f129(x41121),f312(f138(f854(x41121),f854(x41121),f129(x41121),f127(x41121)),x41122)),f312(f138(f854(x41121),f854(x41121),f129(x41121),f127(x41121)),x41123)),f312(f138(f854(x41121),f854(x41121),f129(x41121),f127(x41121)),f312(f312(f129(f854(x41121)),x41122),x41123)))
% 155.90/155.60 [4115]E(f312(f312(f89(a853),f312(f312(f89(a853),f312(f47(a853,x41151),x41152)),f312(f47(a853,x41153),x41152))),f312(f47(a853,f312(f312(f89(a853),f54(a853,x41151,x41152)),f54(a853,x41153,x41152))),x41152)),f312(f47(a853,f312(f312(f89(a853),x41151),x41153)),x41152))
% 155.90/155.60 [4116]E(f312(f312(f89(a1),f312(f312(f89(a1),f312(f47(a1,x41161),x41162)),f312(f47(a1,x41163),x41162))),f312(f47(a1,f312(f312(f89(a1),f54(a1,x41161,x41162)),f54(a1,x41163,x41162))),x41162)),f312(f47(a1,f312(f312(f89(a1),x41161),x41163)),x41162))
% 155.90/155.60 [4118]E(f312(f312(f239(f854(x41181),f854(x41181)),f312(f132(x41181,x41182),x41183)),f312(f132(x41181,f312(f82(a846,a846,x41181,a307),x41182)),x41183)),f163(x41181,x41182,x41183))
% 155.90/155.60 [4176]E(f312(f312(f115(f861(f854(x41761),a846)),f312(f312(f7(f854(x41761),f861(f854(x41761),a846),a846),f314(f854(x41761))),f157(x41761,x41762))),f312(f312(f7(f854(x41761),f861(f854(x41761),a846),a846),f314(f854(x41761))),f157(x41761,x41763))),f156(x41761,f312(f312(f115(f861(x41761,a846)),f312(f312(f7(x41761,f861(x41761,a846),a846),f314(x41761)),x41762)),f312(f312(f7(x41761,f861(x41761,a846),a846),f314(x41761)),x41763))))
% 155.90/155.60 [4190]E(f312(f233(x41901),f312(f312(f18(x41901,a846,a846),f312(f312(f8(a846,f861(a846,a846),x41901),a311),f312(f312(f7(x41901,x41901,a846),a309),x41902))),f312(f312(f7(x41901,f861(x41901,a846),a846),f314(x41901)),x41903))),f312(f312(f289(x41901),x41902),x41903))
% 155.90/155.60 [4210]E(f312(f312(f95(f854(f854(x42101)),f854(f854(x42101))),f62(x42101,x42102)),f312(f312(f18(f854(f854(x42101)),f854(f854(x42101)),f854(f854(x42101))),f312(f312(f8(f854(f854(x42101)),f861(f854(f854(x42101)),f854(f854(x42101))),f854(f854(x42101))),f129(f854(x42101))),f312(f150(f854(x42101),f854(x42101)),f312(f147(x42101),x42103)))),f5(f854(f854(x42101))))),f62(x42101,f312(f312(f147(x42101),x42103),x42102)))
% 155.90/155.60 [4214]E(f312(f233(x42141),f312(f312(f18(x42141,a846,a846),f312(f312(f8(a846,f861(a846,a846),x42141),a311),f312(f312(f7(x42141,f861(x42141,a846),a846),f314(x42141)),x42142))),f312(f312(f7(x42141,f861(x42141,a846),a846),f314(x42141)),x42143))),f312(f312(f124(f861(x42141,a846)),x42142),x42143))
% 155.90/155.60 [4215]E(f312(f233(x42151),f312(f312(f18(x42151,a846,a846),f312(f312(f8(a846,f861(a846,a846),x42151),a310),f312(f312(f7(x42151,f861(x42151,a846),a846),f314(x42151)),x42152))),f312(f312(f7(x42151,f861(x42151,a846),a846),f314(x42151)),x42153))),f312(f312(f115(f861(x42151,a846)),x42152),x42153))
% 155.90/155.60 [4303]E(f312(f312(f50(x43031,f861(f861(x43031,a846),a846)),x43032),f312(f312(f7(x43031,f861(f861(x43031,a846),a846),f861(f861(x43031,a846),a846)),f312(f312(f8(f861(x43031,a846),f861(f861(f861(x43031,a846),a846),f861(f861(x43031,a846),a846)),x43031),f289(f861(x43031,a846))),f312(f312(f8(f861(x43031,a846),f861(x43031,a846),x43031),f264(x43031,x43031,x43033)),f312(f312(f7(x43031,f861(x43031,a846),f861(x43031,a846)),f289(x43031)),f189(f861(x43031,a846)))))),f189(f861(f861(x43031,a846),a846)))),f312(f312(f69(x43031),x43032),x43033))
% 155.90/155.60 [4307]E(f312(f233(f854(x43071)),f312(f312(f18(f854(x43071),a846,a846),f312(f312(f8(a846,f861(a846,a846),f854(x43071)),a310),f312(f312(f7(f854(x43071),a853,a846),f312(f312(f8(a853,f861(a853,a846),f854(x43071)),a309),f190(f854(x43071)))),x43072))),f312(f312(f7(f854(x43071),f861(x43071,a846),a846),f312(f312(f8(f861(x43071,a846),f861(f861(x43071,a846),a846),f854(x43071)),f227(f861(x43071,a846))),f168(x43071))),f312(f168(x43071),x43073)))),f312(f168(f854(x43071)),f63(x43071,x43072,x43073)))
% 155.90/155.60 [3692]E(f54(a853,f312(f312(f89(a853),f312(f312(f90(a853),x36921),x36922)),x36923),x36922),f54(a853,x36923,x36922))
% 155.90/155.60 [3739]E(f135(a853,f312(f282(a853,f312(f312(f89(a853),x37391),x37392)),x37393)),f312(f312(f134(a853),x37392),f135(a853,f312(f282(a853,x37391),x37393))))
% 155.90/155.60 [3787]E(f312(f312(f89(a1),f312(f114(a1),x37871)),f312(f312(f89(a1),f312(f114(a1),x37872)),x37873)),f312(f312(f89(a1),f312(f114(a1),f312(f312(f89(a853),x37871),x37872))),x37873))
% 155.90/155.60 [3795]E(f312(f312(f21(f861(x37951,a846)),f312(f312(f21(f861(x37951,a846)),x37952),x37953)),x37953),f312(f312(f21(f861(x37951,a846)),x37952),x37953))
% 155.90/155.60 [3796]E(f312(f312(f124(f861(x37961,a846)),f312(f312(f21(f861(x37961,a846)),x37962),x37963)),x37963),f312(f312(f124(f861(x37961,a846)),x37962),x37963))
% 155.90/155.60 [3817]E(f312(f312(f267(x38171,x38171,x38172),f287(x38171,f189(f861(f860(x38171,x38171),a846)))),x38173),x38173)
% 155.90/155.60 [3823]E(f312(f312(f124(f861(x38231,a846)),f312(f263(x38231),x38232)),f312(f263(x38231),x38233)),f312(f263(x38231),f312(f312(f124(f861(f860(x38231,x38231),a846)),x38232),x38233)))
% 155.90/155.60 [3834]E(f254(x38341,f312(f312(f147(f860(a113,x38341)),f312(f312(f239(a113,x38341),f2(a113)),x38342)),x38343)),f254(x38341,x38343))
% 155.90/155.60 [3837]E(f312(f312(f124(f861(x38371,a846)),f48(f861(x38371,a846),x38372)),f48(f861(x38371,a846),x38373)),f48(f861(x38371,a846),f312(f312(f124(f861(f861(x38371,a846),a846)),x38372),x38373)))
% 155.90/155.60 [3838]E(f312(f312(f115(f861(x38381,a846)),f49(f861(x38381,a846),x38382)),f49(f861(x38381,a846),x38383)),f49(f861(x38381,a846),f312(f312(f124(f861(f861(x38381,a846),a846)),x38382),x38383)))
% 155.90/155.60 [3875]E(f312(f312(f267(x38751,x38751,x38751),f312(f312(f184(f860(x38751,x38751),a846),x38752),x38753)),x38753),f312(f312(f184(f860(x38751,x38751),a846),f312(a126,x38752)),x38753))
% 155.90/155.60 [3922]P22(f312(f312(f227(f861(x39221,a846)),f312(f312(f21(f861(x39221,a846)),x39222),x39223)),x39222))
% 155.90/155.60 [3923]P22(f312(f312(f227(f861(x39231,a846)),f312(f312(f115(f861(x39231,a846)),x39232),x39233)),x39233))
% 155.90/155.60 [3924]P22(f312(f312(f227(f861(x39241,a846)),f312(f312(f115(f861(x39241,a846)),x39242),x39243)),x39242))
% 155.90/155.60 [3949]E(f287(x39491,f312(f312(f124(f861(f860(x39491,x39491),a846)),f287(x39491,x39492)),f287(x39491,x39493))),f287(x39491,f312(f312(f124(f861(f860(x39491,x39491),a846)),x39492),x39493)))
% 155.90/155.60 [3952]E(f48(f861(x39521,a846),f312(f312(f289(f861(x39521,a846)),x39522),f312(f312(f289(f861(x39521,a846)),x39523),f189(f861(f861(x39521,a846),a846))))),f312(f312(f124(f861(x39521,a846)),x39522),x39523))
% 155.90/155.60 [3953]E(f49(f861(x39531,a846),f312(f312(f289(f861(x39531,a846)),x39532),f312(f312(f289(f861(x39531,a846)),x39533),f189(f861(f861(x39531,a846),a846))))),f312(f312(f115(f861(x39531,a846)),x39532),x39533))
% 155.90/155.60 [3959]E(f312(f312(f267(x39591,x39591,x39591),f312(f312(f184(f860(x39591,x39591),a846),x39592),x39593)),x39593),f312(f312(f267(x39591,x39591,x39591),x39593),f312(f312(f184(f860(x39591,x39591),a846),x39592),x39593)))
% 155.90/155.60 [4030]E(f312(f312(f124(f861(x40301,a846)),f312(f233(x40301),f312(f312(f7(x40301,x40301,a846),a309),x40302))),x40303),f312(f312(f289(x40301),x40302),x40303))
% 155.90/155.60 [4032]E(f312(a118,f312(f312(f9(x40321,a1),f312(f312(f8(a853,a1,x40321),f114(a1)),x40322)),x40323)),f312(f312(f9(x40321,a853),x40322),x40323))
% 155.90/155.60 [4033]E(f312(a118,f312(f312(f6(x40331,a1),f312(f312(f8(a853,a1,x40331),f114(a1)),x40332)),x40333)),f312(f312(f6(x40331,a853),x40332),x40333))
% 155.90/155.60 [4109]E(f312(f152(f854(x41091),x41091,f312(f167(x41091),x41092),f312(f16(f861(f854(x41091),f854(x41091)),x41091),f312(f312(f7(f854(x41091),f854(x41091),f854(x41091)),f129(x41091)),x41092))),x41093),f312(f167(x41091),f312(f312(f129(x41091),x41093),x41092)))
% 155.90/155.60 [4138]P22(f312(f312(f227(f861(f861(x41381,a846),a846)),f312(f312(f124(f861(f861(x41381,a846),a846)),f312(f288(x41381),x41382)),f312(f288(x41381),x41383))),f312(f288(x41381),f312(f312(f124(f861(x41381,a846)),x41382),x41383))))
% 155.90/155.60 [4233]E(f312(f233(x42331),f312(f312(f18(x42331,a846,a846),f312(f312(f8(a846,f861(a846,a846),x42331),a310),f312(f312(f7(x42331,f861(x42331,a846),a846),f314(x42331)),x42332))),f312(f312(f8(a846,a846,x42331),a307),f312(f312(f7(x42331,f861(x42331,a846),a846),f314(x42331)),x42333)))),f312(f312(f21(f861(x42331,a846)),x42332),x42333))
% 155.90/155.60 [4254]E(f312(f53(a853),f312(f233(a853),f312(f312(f18(a853,a846,a846),f312(f312(f8(a846,f861(a846,a846),a853),a310),f312(f312(f7(a853,a853,a846),f228(a853)),f312(f190(f854(x42541)),x42542)))),f312(f312(f8(x42541,a846,a853),x42543),f312(f161(x42541),x42542))))),f312(f190(f854(x42541)),f312(f132(x42541,x42543),x42542)))
% 155.90/155.60 [4256]E(f312(f190(f854(x42561)),f170(x42561,x42562,x42563)),f312(f53(a853),f312(f233(a853),f312(f312(f18(a853,a846,a846),f312(f312(f8(a846,f861(a846,a846),a853),a310),f312(f312(f7(a853,a853,a846),f228(a853)),f312(f190(f854(x42561)),x42562)))),f312(f312(f7(a853,f861(a853,a846),a846),f314(a853)),x42563)))))
% 155.90/155.60 [4346]E(f312(f312(f115(f861(f860(f854(x43461),f854(x43461)),a846)),f312(f290(f860(f860(x43461,f854(x43461)),f860(x43461,f854(x43461))),f860(f854(x43461),f854(x43461)),f250(f860(x43461,f854(x43461)),f854(x43461),f860(x43461,f854(x43461)),f854(x43461),f312(f249(x43461,f854(x43461),f854(x43461)),f147(x43461)),f312(f249(x43461,f854(x43461),f854(x43461)),f147(x43461)))),f304(x43461,f854(x43461),x43462,f312(f139(x43461,x43462),x43463)))),f312(f233(f860(f854(x43461),f854(x43461))),f312(f249(f854(x43461),f854(x43461),a846),f312(f312(f7(f854(x43461),f861(f854(x43461),a846),f861(f854(x43461),a846)),f312(f312(f8(f861(a846,a846),f861(f861(f854(x43461),a846),f861(f854(x43461),a846)),f854(x43461)),f8(a846,a846,f854(x43461))),f312(f312(f8(a846,f861(a846,a846),f854(x43461)),a310),f312(f312(f7(f854(x43461),a853,a846),f312(f312(f8(a853,f861(a853,a846),f854(x43461)),a309),f190(f854(x43461)))),f312(a126,x43463))))),f312(f312(f7(f854(x43461),a853,a846),f312(f312(f8(a853,f861(a853,a846),f854(x43461)),a309),f190(f854(x43461)))),f312(a126,x43463)))))),f312(f139(x43461,x43462),f312(a126,x43463)))
% 155.90/155.60 [3839]E(f54(a853,f312(a126,f312(f312(f89(a853),f312(f312(f90(a853),x38391),x38392)),x38393)),x38392),f54(a853,f312(a126,x38393),x38392))
% 155.90/155.60 [4099]E(f312(f233(x40991),f312(f312(f18(x40991,a846,a846),f312(f312(f8(a846,f861(a846,a846),x40991),a310),x40992)),x40993)),f312(f312(f115(f861(x40991,a846)),f312(f233(x40991),x40992)),f312(f233(x40991),x40993)))
% 155.90/155.60 [4100]E(f312(f233(x41001),f312(f312(f18(x41001,a846,a846),f312(f312(f8(a846,f861(a846,a846),x41001),a311),x41002)),x41003)),f312(f312(f124(f861(x41001,a846)),f312(f233(x41001),x41002)),f312(f233(x41001),x41003)))
% 155.90/155.60 [4102]E(f312(f312(f129(x41021),f312(f312(f134(x41021),f54(a853,x41022,f312(f190(f854(x41021)),x41023))),x41023)),f312(f312(f169(x41021),f54(a853,x41022,f312(f190(f854(x41021)),x41023))),x41023)),f312(f312(f312(f184(f854(x41021),f854(x41021)),x41022),f164(x41021)),x41023))
% 155.90/155.60 [4107]E(f312(f233(x41071),f312(f312(f18(x41071,a846,a846),f312(f312(f8(a846,f861(a846,a846),x41071),a315),x41072)),x41073)),f312(f312(f124(f861(x41071,a846)),f312(f88(f861(x41071,a846)),f312(f233(x41071),x41072))),f312(f233(x41071),x41073)))
% 155.90/155.60 [4121]E(f312(f312(f89(a853),f312(f190(f854(x41211)),f312(f132(x41211,x41212),x41213))),f312(f190(f854(x41211)),f312(f132(x41211,f312(f312(f8(a846,a846,x41211),a307),x41212)),x41213))),f312(f190(f854(x41211)),x41213))
% 155.90/155.60 [4145]P22(f312(f312(f227(f861(x41451,a846)),f312(f312(f124(f861(x41451,a846)),f49(f861(x41451,a846),x41452)),f49(f861(x41451,a846),x41453))),f49(f861(x41451,a846),f312(f312(f115(f861(f861(x41451,a846),a846)),x41452),x41453))))
% 155.90/155.60 [4159]E(f312(f168(x41591),f312(f132(x41591,f312(f312(f8(a846,a846,x41591),a307),f312(f312(f7(x41591,x41591,a846),a309),x41592))),x41593)),f312(f312(f21(f861(x41591,a846)),f312(f168(x41591),x41593)),f312(f312(f289(x41591),x41592),f189(f861(x41591,a846)))))
% 155.90/155.60 [4168]P22(f312(f312(f227(f861(f860(x41681,x41681),a846)),f312(f312(f124(f861(f860(x41681,x41681),a846)),f287(x41681,x41682)),f287(x41681,x41683))),f287(x41681,f312(f312(f124(f861(f860(x41681,x41681),a846)),x41682),x41683))))
% 155.90/155.60 [4195]E(f312(f312(f90(a853),f312(a126,f312(a126,f2(a853)))),f312(f312(f6(a853,a853),f312(f312(f8(a853,a853,a853),f312(f89(a853),x41951)),f312(f312(f7(a853,a853,a853),f90(a853)),x41952))),f312(f279(a853),x41953))),f312(f312(f90(a853),x41953),f312(f312(f89(a853),x41951),f312(f312(f89(a853),x41951),f312(f312(f90(a853),f312(f312(f21(a853),x41953),f87(a853))),x41952)))))
% 155.90/155.60 [4205]E(f312(f233(x42051),f312(f312(f18(x42051,a846,a846),f312(f312(f8(a846,f861(a846,a846),x42051),a310),f312(f312(f7(x42051,f861(x42051,a846),a846),f314(x42051)),f312(f168(x42051),x42052)))),x42053)),f312(f168(x42051),f312(f132(x42051,x42053),x42052)))
% 155.90/155.60 [4345]E(f312(f233(x43451),f312(f312(f8(f861(a853,a846),a846,x43451),f96(a853)),f312(f312(f7(x43451,f861(a853,a846),f861(a853,a846)),f312(f312(f8(f861(a853,f861(a846,a846)),f861(f861(a853,a846),f861(a853,a846)),x43451),f18(a853,a846,a846)),f312(f312(f8(f861(a853,a846),f861(a853,f861(a846,a846)),x43451),f312(f8(a846,f861(a846,a846),a853),a310)),f312(f312(f7(x43451,f861(a853,x43451),f861(a853,a846)),f312(f312(f8(f861(x43451,a846),f861(f861(a853,x43451),f861(a853,a846)),x43451),f8(x43451,a846,a853)),a309)),f312(f161(x43451),x43452))))),f312(f312(f18(a853,a846,a846),f312(f312(f8(a846,f861(a846,a846),a853),a310),f312(f312(f7(a853,a853,a846),f228(a853)),f312(f190(f854(x43451)),x43452)))),f312(f312(f7(a853,f861(a853,a846),a846),f314(a853)),x43453))))),f312(f168(x43451),f170(x43451,x43452,x43453)))
% 155.90/155.60 [4244]E(f312(f233(x42441),f312(f312(f18(x42441,a846,a846),f312(f312(f8(a846,f861(a846,a846),x42441),a315),f312(f312(f8(a846,a846,x42441),a307),f312(f312(f7(x42441,x42441,a846),a309),x42442)))),x42443)),f312(f312(f289(x42441),x42442),f312(f233(x42441),x42443)))
% 155.90/155.60 [4275]E(f312(f312(f150(f860(x42751,a853),x42751),f246(x42751,a853)),f312(f132(f860(x42751,a853),f312(f312(f7(f860(x42751,a853),f861(a853,a846),a846),f312(f312(f8(a853,f861(f861(a853,a846),a846),f860(x42751,a853)),f314(a853)),f248(x42751,a853))),x42752)),f312(f312(f177(x42751,a853),x42753),f135(a853,f312(f282(a853,f2(a853)),f312(f190(f854(x42751)),x42753)))))),f170(x42751,x42753,x42752))
% 155.90/155.60 [4304]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(a853,a1),f312(f312(f8(a1,a1,a853),f312(f89(a1),x43041)),f312(f312(f7(a853,a1,a1),f312(f312(f8(a1,f861(a1,a1),a853),f90(a1)),f114(a1))),x43042))),f312(f279(a853),x43043))),f312(f312(f90(a1),f312(f114(a1),x43043)),f312(f312(f89(a1),x43041),f312(f312(f89(a1),x43041),f312(f312(f90(a1),f312(f114(a1),f312(f312(f21(a853),x43043),f87(a853)))),x43042)))))
% 155.90/155.60 [4339]E(f312(f233(f860(x43391,x43392)),f312(f249(x43391,x43392,a846),f312(f312(f7(x43391,f861(f860(x43392,x43391),a846),f861(x43392,a846)),f312(f312(f8(f861(x43392,f861(f861(f860(x43392,x43391),a846),a846)),f861(f861(f860(x43392,x43391),a846),f861(x43392,a846)),x43391),f7(x43392,f861(f860(x43392,x43391),a846),a846)),f312(f312(f8(f861(x43392,f860(x43392,x43391)),f861(x43392,f861(f861(f860(x43392,x43391),a846),a846)),x43391),f312(f8(f860(x43392,x43391),f861(f861(f860(x43392,x43391),a846),a846),x43392),f314(f860(x43392,x43391)))),f312(f7(x43392,x43391,f860(x43392,x43391)),f239(x43392,x43391))))),x43393))),f312(f265(x43392,x43391),x43393))
% 155.90/155.60 [4373]E(f312(f233(f854(x43731)),f312(f312(f8(f861(x43731,a846),a846,f854(x43731)),f96(x43731)),f312(f312(f8(f861(x43731,f861(f854(x43731),a846)),f861(x43731,a846),f854(x43731)),f312(f8(f861(f854(x43731),a846),a846,x43731),f96(f854(x43731)))),f312(f312(f7(f854(x43731),f861(x43731,f861(f854(x43731),a846)),f861(x43731,f861(f854(x43731),a846))),f312(f312(f8(f861(x43731,f861(f861(f854(x43731),a846),f861(f854(x43731),a846))),f861(f861(x43731,f861(f854(x43731),a846)),f861(x43731,f861(f854(x43731),a846))),f854(x43731)),f18(x43731,f861(f854(x43731),a846),f861(f854(x43731),a846))),f312(f312(f8(f861(x43731,f861(f854(x43731),f861(a846,a846))),f861(x43731,f861(f861(f854(x43731),a846),f861(f854(x43731),a846))),f854(x43731)),f312(f8(f861(f854(x43731),f861(a846,a846)),f861(f861(f854(x43731),a846),f861(f854(x43731),a846)),x43731),f18(f854(x43731),a846,a846))),f312(f312(f8(f861(x43731,f861(f854(x43731),a846)),f861(x43731,f861(f854(x43731),f861(a846,a846))),f854(x43731)),f312(f8(f861(f854(x43731),a846),f861(f854(x43731),f861(a846,a846)),x43731),f312(f8(a846,f861(a846,a846),f854(x43731)),a310))),f312(f312(f7(f854(x43731),f861(x43731,f861(f854(x43731),f854(x43731))),f861(x43731,f861(f854(x43731),a846))),f312(f312(f8(f861(f861(f854(x43731),f854(x43731)),f861(f854(x43731),a846)),f861(f861(x43731,f861(f854(x43731),f854(x43731))),f861(x43731,f861(f854(x43731),a846))),f854(x43731)),f8(f861(f854(x43731),f854(x43731)),f861(f854(x43731),a846),x43731)),f312(f312(f8(f861(f854(x43731),a846),f861(f861(f854(x43731),f854(x43731)),f861(f854(x43731),a846)),f854(x43731)),f8(f854(x43731),a846,f854(x43731))),a309))),f147(x43731)))))),f312(f312(f7(x43731,f861(f854(x43731),a846),f861(f854(x43731),a846)),f312(f312(f8(f861(a846,a846),f861(f861(f854(x43731),a846),f861(f854(x43731),a846)),x43731),f8(a846,a846,f854(x43731))),f312(f312(f8(a846,f861(a846,a846),x43731),a310),f312(f312(f7(x43731,f861(x43731,a846),a846),f314(x43731)),x43732)))),f312(f312(f7(f854(x43731),f861(f854(x43731),a846),a846),f314(f854(x43731))),x43733)))))),f171(x43731,x43732,x43733))
% 155.90/155.60 [4359]E(f312(f312(f95(a1,f860(a1,a1)),f312(f312(f21(a1),x43591),x43592)),f312(f312(f7(a1,f860(a1,a1),f860(a1,a1)),f312(f312(f18(a1,f860(a1,a1),f861(f860(a1,a1),f860(a1,a1))),f312(f312(f8(a846,f861(f860(a1,a1),f861(f860(a1,a1),f860(a1,a1))),a1),f108(f860(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)))),x43593)),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)))),x43593)),x43591))),f312(f52(x43592),f312(f312(f239(a1,a1),x43593),x43591)))
% 155.90/155.60 [3769]P36(x37691,x37692,x37693,f180(x37691,x37692,x37694,x37693))
% 155.90/155.60 [4411]~E(f35(x44111,x44112),f36(x44113,x44114))
% 155.90/155.60 [4414]~E(f28(x44141,x44142),f36(x44143,x44144))
% 155.90/155.60 [4415]~E(f28(x44151,x44152),f35(x44153,x44154))
% 155.90/155.60 [4434]~E(f312(a27,x44341),f33(x44342,x44343,x44344))
% 155.90/155.60 [4435]~E(f312(a27,x44351),f32(x44352,x44353,x44354))
% 155.90/155.60 [4436]~E(f312(a27,x44361),f31(x44362,x44363,x44364))
% 155.90/155.60 [4437]~E(f33(x44371,x44372,x44373),f312(a27,x44374))
% 155.90/155.60 [4438]~E(f32(x44381,x44382,x44383),f312(a27,x44384))
% 155.90/155.60 [4439]~E(f31(x44391,x44392,x44393),f312(a27,x44394))
% 155.90/155.60 [3395]E(f312(f312(f312(f81(x33951,x33952),x33953),x33954),f312(x33953,x33954)),x33953)
% 155.90/155.60 [3453]E(f312(f312(f241(x34531,x34532,x34533),x34534),f2(a853)),x34532)
% 155.90/155.60 [3467]E(f43(x34671,x34672,x34673,f40(x34674)),f312(x34673,x34674))
% 155.90/155.60 [3468]E(f43(x34681,x34682,x34683,f41(x34684)),f312(x34682,x34684))
% 155.90/155.60 [3469]E(f44(x34691,x34692,x34693,f40(x34694)),f312(x34693,x34694))
% 155.90/155.60 [3470]E(f44(x34701,x34702,x34703,f41(x34704)),f312(x34702,x34704))
% 155.90/155.60 [3497]E(f186(x34971,x34972,x34973,f312(a126,x34974)),f312(x34973,x34974))
% 155.90/155.60 [3533]E(f166(x35331,x35332,f166(x35331,x35333,x35334)),f166(x35331,x35333,f166(x35331,x35332,x35334)))
% 155.90/155.60 [3663]E(f312(f221(x36631,x36632,x36633,x36634),f192(x36632)),x36633)
% 155.90/155.60 [3665]E(f312(f152(x36651,x36652,x36653,x36654),f127(x36652)),x36653)
% 155.90/155.60 [3666]E(f312(f138(x36661,x36662,x36663,x36664),f127(x36662)),x36664)
% 155.90/155.60 [3699]E(f312(f190(f858(x36991,x36992)),f209(x36991,x36992,x36993,x36994)),f2(a853))
% 155.90/155.60 [3770]P36(x37701,x37702,f312(f312(f312(f81(x37701,f857(x37702)),x37703),x37704),f192(x37702)),x37703)
% 155.90/155.60 [3784]E(f312(f221(f857(x37841),x37842,f192(x37841),f312(f16(f857(x37841),x37842),f192(x37841))),f312(x37843,x37844)),f192(x37841))
% 155.90/155.60 [3827]E(f312(f312(f124(f861(x38271,a846)),f179(x38271,x38272,x38273)),f179(x38271,x38272,x38274)),f179(x38271,x38272,f180(x38271,x38272,x38274,x38273)))
% 155.90/155.60 [3859]E(f312(f312(f251(x38591,x38592,x38593,f860(x38592,x38593)),x38594),f239(x38592,x38593)),x38594)
% 155.90/155.60 [3868]E(f222(x38681,x38682,x38683,x38684,f192(x38682)),x38683)
% 155.90/155.60 [3869]E(f182(x38691,x38692,x38693,x38694,f127(x38692)),x38693)
% 155.90/155.60 [3870]E(f182(x38701,x38702,x38703,f127(x38701),x38704),x38703)
% 155.90/155.60 [4152]P45(x41521,x41522,x41523,x41524,f189(f861(x41521,a846)),x41524)
% 155.90/155.60 [3194]E(f312(f312(f16(x31941,x31942),x31943),x31944),x31943)
% 155.90/155.60 [3312]E(f312(f312(f193(x33121,x33122),x33123),f312(f219(x33121),x33124)),f312(f219(x33122),f312(x33123,x33124)))
% 155.90/155.60 [3488]E(f166(x34881,x34882,f312(f132(x34881,x34883),x34884)),f312(f132(x34881,x34883),f166(x34881,x34882,x34884)))
% 155.90/155.60 [3518]E(f312(f312(f73(x35181,x35182,x35183),x35184),f189(f861(x35181,a846))),x35184)
% 155.90/155.60 [3539]E(f312(f312(f161(x35391),f312(f312(f147(x35391),x35392),x35393)),f312(a126,x35394)),f312(f312(f161(x35391),x35393),x35394))
% 155.90/155.60 [3579]P34(x35791,f2(a853),f312(f312(f312(f100(x35791),x35792),f312(a27,x35793)),x35794))
% 155.90/155.60 [3606]E(f312(f312(x36061,x36062),f312(f185(x36063,x36064,x36061),x36062)),f312(f185(x36063,x36064,x36061),f312(a126,x36062)))
% 155.90/155.60 [3697]E(f312(f312(f155(x36971,f312(f312(f147(x36971),x36972),x36973)),f2(a853)),x36974),f312(f312(f147(x36971),x36974),x36973))
% 155.90/155.60 [3709]E(f312(f312(f50(f861(x37091,a846),f861(x37092,a846)),x37093),f290(x37091,x37092,x37094)),f312(f290(x37091,x37092,x37094),f48(f861(x37091,a846),x37093)))
% 155.90/155.60 [3710]E(f312(f312(f50(f861(x37101,a846),f861(x37102,a846)),x37103),f291(x37102,x37101,x37104)),f312(f291(x37102,x37101,x37104),f48(f861(x37101,a846),x37103)))
% 155.90/155.60 [3811]E(f179(x38111,x38112,f183(x38111,x38112,x38113,x38114)),f312(f312(f115(f861(x38111,a846)),f179(x38111,x38112,x38113)),x38114))
% 155.90/155.60 [3833]E(f312(f138(x38331,x38332,f312(f7(x38332,x38331,x38331),x38333),x38334),f312(f165(x38332),f127(x38332))),x38334)
% 155.90/155.60 [3873]P22(f312(f312(f312(f312(a198,f28(x38731,x38732)),x38733),x38734),f312(f312(f312(a201,x38733),x38731),f312(x38732,x38733))))
% 155.90/155.60 [3882]E(f85(x38821,x38822,x38823,x38824,f189(f861(x38821,a846))),x38823)
% 155.90/155.60 [3925]E(f312(f312(f312(f312(f81(x39251,f857(x39252)),f312(f16(f857(x39252),x39251),f192(x39252))),x39253),f192(x39252)),x39254),f192(x39252))
% 155.90/155.60 [4082]E(f312(f249(x40821,x40822,x40823),f312(f312(f8(f861(x40822,f860(x40821,x40822)),f861(x40822,x40823),x40821),f312(f8(f860(x40821,x40822),x40823,x40822),x40824)),f239(x40821,x40822))),x40824)
% 155.90/155.60 [3320]E(f312(f312(f197(x33201,x33202),f312(f219(x33201),x33203)),x33204),f312(x33204,x33203))
% 155.90/155.60 [3393]E(f312(f248(x33931,x33932),f312(f312(f239(x33931,x33932),x33933),x33934)),x33934)
% 155.90/155.60 [3394]E(f312(f246(x33941,x33942),f312(f312(f239(x33941,x33942),x33943),x33944)),x33943)
% 155.90/155.60 [3427]E(f312(f190(f854(x34271)),f312(f312(f150(x34272,x34271),x34273),x34274)),f312(f190(f854(x34272)),x34274))
% 155.90/155.60 [3428]E(f312(f190(f854(x34281)),f312(f312(f155(x34281,x34282),x34283),x34284)),f312(f190(f854(x34281)),x34282))
% 155.90/155.60 [3448]E(f312(f312(f134(x34481),f312(a126,x34482)),f312(f312(f147(x34481),x34483),x34484)),f312(f312(f134(x34481),x34482),x34484))
% 155.90/155.60 [3521]E(f312(f312(f289(x35211),x35212),f312(f312(f289(x35211),x35213),x35214)),f312(f312(f289(x35211),x35213),f312(f312(f289(x35211),x35212),x35214)))
% 155.90/155.60 [3523]E(f312(f312(f150(x35231,x35232),x35233),f128(x35231,x35234)),f128(x35232,f312(f312(f150(x35231,x35232),x35233),x35234)))
% 155.90/155.60 [3537]E(f312(f165(x35371),f312(f312(f150(x35372,x35371),x35373),x35374)),f312(f312(f150(x35372,x35371),x35373),f312(f165(x35372),x35374)))
% 155.90/155.60 [3538]E(f312(f312(f150(x35381,x35382),x35383),f312(f167(x35381),x35384)),f312(f167(x35382),f312(f312(f150(x35381,x35382),x35383),x35384)))
% 155.90/155.60 [3551]E(f312(f312(f169(x35511),f312(a126,x35512)),f312(f312(f147(x35511),x35513),x35514)),f312(f312(f147(x35511),x35513),f312(f312(f169(x35511),x35512),x35514)))
% 155.90/155.60 [3555]E(f312(f168(x35551),f312(f312(f150(x35552,x35551),x35553),x35554)),f312(f290(x35552,x35551,x35553),f312(f168(x35552),x35554)))
% 155.90/155.60 [3605]E(f17(x36051,x36052,x36053,f312(a3,f312(a126,f312(a19,x36054)))),f312(x36053,x36054))
% 155.90/155.60 [3607]E(f312(f312(f129(x36071),f312(f132(x36071,x36072),x36073)),f312(f132(x36071,x36072),x36074)),f312(f132(x36071,x36072),f312(f312(f129(x36071),x36073),x36074)))
% 155.90/155.60 [3620]E(f148(x36201,f312(f312(f150(x36202,x36201),x36203),f148(x36202,x36204))),f148(x36201,f312(f312(f150(x36202,x36201),x36203),x36204)))
% 155.90/155.60 [3634]E(f312(f265(x36341,x36341),f312(f312(f266(x36342,x36341),x36343),x36344)),f312(f312(f266(x36342,x36341),f312(f265(x36342,x36342),x36343)),x36344))
% 155.90/155.60 [3645]E(f312(f312(f267(x36451,x36452,x36453),x36454),f189(f861(f860(x36452,x36453),a846))),f189(f861(f860(x36451,x36453),a846)))
% 155.90/155.60 [3646]E(f312(f312(f169(x36461),f312(f312(f21(a853),x36462),x36463)),f312(f312(f134(x36461),x36463),x36464)),f312(f312(f134(x36461),x36463),f312(f312(f169(x36461),x36462),x36464)))
% 155.90/155.60 [3689]E(f48(f861(x36891,a846),f312(f290(x36892,f861(x36891,a846),x36893),x36894)),f312(f312(f50(x36892,f861(x36891,a846)),x36894),x36893))
% 155.90/155.60 [3690]E(f49(f861(x36901,a846),f312(f290(x36902,f861(x36901,a846),x36903),x36904)),f312(f312(f51(x36902,f861(x36901,a846)),x36904),x36903))
% 155.90/155.60 [3691]E(f312(f190(f854(f860(x36911,x36912))),f312(f312(f177(x36911,x36912),x36913),x36914)),f312(f312(f225(a853),f312(f190(f854(x36911)),x36913)),f312(f190(f854(x36912)),x36914)))
% 155.90/155.60 [3693]E(f312(f291(x36931,x36932,x36933),f312(f88(f861(x36932,a846)),x36934)),f312(f88(f861(x36931,a846)),f312(f291(x36931,x36932,x36933),x36934)))
% 155.90/155.60 [3724]E(f312(f183(x37241,x37242,x37243,f189(f861(x37241,a846))),x37244),f192(x37242))
% 155.90/155.60 [3745]E(f312(f291(x37451,x37452,x37453),f312(f233(x37452),x37454)),f312(f233(x37451),f312(f312(f8(x37452,a846,x37451),x37454),x37453)))
% 155.90/155.60 [3762]E(f312(f312(f161(x37621),f312(f312(f129(x37621),x37622),f312(f312(f147(x37621),x37623),x37624))),f312(f190(f854(x37621)),x37622)),x37623)
% 155.90/155.60 [3768]E(f312(f183(x37681,x37682,f312(f16(f857(x37682),x37681),f192(x37682)),x37683),x37684),f192(x37682))
% 155.90/155.60 [3792]E(f312(f290(x37921,x37922,x37923),f312(f291(x37921,x37922,x37923),x37924)),f312(f312(f115(f861(x37922,a846)),x37924),f312(f290(x37921,x37922,x37923),f235(f861(x37921,a846)))))
% 155.90/155.60 [3810]P22(f312(f312(f314(x38101),f312(x38102,x38103)),f312(f290(x38104,x38101,x38102),f235(f861(x38104,a846)))))
% 155.90/155.60 [3822]E(f312(f312(f247(x38221,x38222),f312(f168(x38221),x38223)),f312(f16(f861(x38222,a846),x38221),f312(f168(x38222),x38224))),f312(f168(f860(x38221,x38222)),f68(x38221,x38222,x38223,x38224)))
% 155.90/155.60 [3836]E(f151(x38361,x38362,f312(f312(f147(x38361),x38363),x38364)),f312(f312(f89(a853),f312(f312(f89(a853),f312(x38362,x38363)),f151(x38361,x38362,x38364))),f312(a126,f2(a853))))
% 155.90/155.60 [3850]E(f186(f854(x38501),f312(f312(f147(x38501),x38502),x38503),f312(f312(f7(a853,f854(x38501),f854(x38501)),f134(x38501)),x38503),x38504),f312(f312(f134(x38501),x38504),f312(f312(f147(x38501),x38502),x38503)))
% 155.90/155.60 [3851]P19(x38511,f860(x38512,x38511),f316(x38513,x38514,x38512,x38511),f312(f312(f50(x38512,f861(x38511,a846)),x38514),x38513))
% 155.90/155.60 [3860]E(f312(f312(f21(f861(x38601,a846)),f312(f312(f21(f861(x38601,a846)),x38602),x38603)),f312(f312(f289(x38601),x38604),f189(f861(x38601,a846)))),f312(f312(f21(f861(x38601,a846)),x38602),f312(f312(f289(x38601),x38604),x38603)))
% 155.90/155.60 [3871]E(f312(f312(f184(f861(x38711,x38712),f861(x38711,x38712)),x38713),f82(x38712,x38712,x38711,x38714)),f82(x38712,x38712,x38711,f312(f312(f184(x38712,x38712),x38713),x38714)))
% 155.90/155.60 [3948]E(f312(f312(f312(f184(f854(x39481),f854(x39481)),x39482),f164(x39481)),f312(f312(f312(f184(f854(x39481),f854(x39481)),x39483),f164(x39481)),x39484)),f312(f312(f312(f184(f854(x39481),f854(x39481)),f312(f312(f89(a853),x39482),x39483)),f164(x39481)),x39484))
% 155.90/155.60 [4035]P22(f312(f312(f227(f861(x40351,a846)),f312(f168(x40351),f312(f312(f155(x40351,x40352),x40353),x40354))),f312(f312(f289(x40351),x40354),f312(f168(x40351),x40352))))
% 155.90/155.60 [4072]E(f312(f312(f50(f861(x40721,a846),f861(f860(x40721,x40722),a846)),x40723),f312(f312(f7(f861(x40721,a846),f861(x40721,f861(x40722,a846)),f861(f860(x40721,x40722),a846)),f247(x40721,x40722)),x40724)),f312(f312(f247(x40721,x40722),f48(f861(x40721,a846),x40723)),x40724))
% 155.90/155.60 [4128]P22(f312(f75(x41281,x41282,x41283,x41284,f189(f861(x41281,a846))),x41284))
% 155.90/155.60 [4171]E(f312(f312(f50(x41711,f861(x41712,a846)),x41713),f312(f312(f7(x41711,f861(x41712,a846),f861(x41712,a846)),f312(f312(f8(x41712,f861(f861(x41712,a846),f861(x41712,a846)),x41711),f289(x41712)),x41714)),f189(f861(x41712,a846)))),f312(f290(x41711,x41712,x41714),x41713))
% 155.90/155.60 [4179]P22(f312(f312(f227(f861(x41791,a846)),f312(f236(x41792,x41791),f312(f312(f115(f861(f860(x41792,x41791),a846)),x41793),x41794))),f312(f312(f115(f861(x41791,a846)),f312(f236(x41792,x41791),x41793)),f312(f236(x41792,x41791),x41794))))
% 155.90/155.60 [4180]P22(f312(f312(f227(f861(x41801,a846)),f312(f238(x41801,x41802),f312(f312(f115(f861(f860(x41801,x41802),a846)),x41803),x41804))),f312(f312(f115(f861(x41801,a846)),f312(f238(x41801,x41802),x41803)),f312(f238(x41801,x41802),x41804))))
% 155.90/155.60 [4242]P22(f312(f312(f227(f861(f860(x42421,x42422),a846)),f312(f290(x42422,f860(x42421,x42422),f316(x42423,x42424,x42421,x42422)),f312(f312(f50(x42421,f861(x42422,a846)),x42424),x42423))),f312(f312(f247(x42421,x42422),x42424),x42423)))
% 155.90/155.60 [4281]E(f94(f860(x42811,x42812),f312(f249(x42811,x42812,a846),f312(f312(f7(x42811,f861(x42812,a846),f861(x42812,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x42812,a846),f861(x42812,a846)),x42811),f8(a846,a846,x42812)),f312(f312(f8(a846,f861(a846,a846),x42811),a310),f312(a309,x42813)))),f312(a309,x42814)))),f312(f312(f239(x42811,x42812),x42813),x42814))
% 155.90/155.60 [4282]E(f99(f860(x42821,x42822),f312(f249(x42821,x42822,a846),f312(f312(f7(x42821,f861(x42822,a846),f861(x42822,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x42822,a846),f861(x42822,a846)),x42821),f8(a846,a846,x42822)),f312(f312(f8(a846,f861(a846,a846),x42821),a310),f312(a309,x42823)))),f312(a309,x42824)))),f312(f312(f239(x42821,x42822),x42823),x42824))
% 155.90/155.60 [4349]E(f312(f312(f249(f854(x43491),f854(x43491),f860(f854(x43491),f854(x43491))),f312(f312(f18(f854(x43491),f861(f854(x43491),f860(f854(x43491),f854(x43491))),f861(f854(x43491),f860(f854(x43491),f854(x43491)))),f312(f312(f8(f861(f854(x43491),f861(f860(f854(x43491),f854(x43491)),f860(f854(x43491),f854(x43491)))),f861(f861(f854(x43491),f860(f854(x43491),f854(x43491))),f861(f854(x43491),f860(f854(x43491),f854(x43491)))),f854(x43491)),f18(f854(x43491),f860(f854(x43491),f854(x43491)),f860(f854(x43491),f854(x43491)))),f312(f312(f8(f861(f854(x43491),f860(f854(x43491),f854(x43491))),f861(f854(x43491),f861(f860(f854(x43491),f854(x43491)),f860(f854(x43491),f854(x43491)))),f854(x43491)),f312(f8(f860(f854(x43491),f854(x43491)),f861(f860(f854(x43491),f854(x43491)),f860(f854(x43491),f854(x43491))),f854(x43491)),f312(f108(f860(f854(x43491),f854(x43491))),f312(x43492,x43493)))),f312(f312(f8(f854(x43491),f861(f854(x43491),f860(f854(x43491),f854(x43491))),f854(x43491)),f239(f854(x43491),f854(x43491))),f312(f147(x43491),x43493))))),f312(f312(f7(f854(x43491),f861(f854(x43491),f854(x43491)),f861(f854(x43491),f860(f854(x43491),f854(x43491)))),f312(f312(f8(f861(f854(x43491),f860(f854(x43491),f854(x43491))),f861(f861(f854(x43491),f854(x43491)),f861(f854(x43491),f860(f854(x43491),f854(x43491)))),f854(x43491)),f8(f854(x43491),f860(f854(x43491),f854(x43491)),f854(x43491))),f239(f854(x43491),f854(x43491)))),f312(f147(x43491),x43493)))),f163(x43491,x43492,x43494)),f163(x43491,x43492,f312(f312(f147(x43491),x43493),x43494)))
% 155.90/155.60 [4355]E(f312(f138(f861(x43551,f857(x43552)),f860(x43551,x43552),f312(f7(f860(x43551,x43552),f861(x43551,f857(x43552)),f861(x43551,f857(x43552))),f312(f249(x43551,x43552,f861(f861(x43551,f857(x43552)),f861(x43551,f857(x43552)))),f312(f312(f7(x43551,f861(x43552,f857(x43552)),f861(x43552,f861(f861(x43551,f857(x43552)),f861(x43551,f857(x43552))))),f312(f312(f8(f861(f857(x43552),f861(f861(x43551,f857(x43552)),f861(x43551,f857(x43552)))),f861(f861(x43552,f857(x43552)),f861(x43552,f861(f861(x43551,f857(x43552)),f861(x43551,f857(x43552))))),x43551),f8(f857(x43552),f861(f861(x43551,f857(x43552)),f861(x43551,f857(x43552))),x43552)),f312(f312(f8(f861(f861(x43551,f857(x43552)),f861(f857(x43552),f861(x43551,f857(x43552)))),f861(f857(x43552),f861(f861(x43551,f857(x43552)),f861(x43551,f857(x43552)))),x43551),f7(f861(x43551,f857(x43552)),f857(x43552),f861(x43551,f857(x43552)))),f312(f7(f861(x43551,f857(x43552)),x43551,f861(f857(x43552),f861(x43551,f857(x43552)))),f81(x43551,f857(x43552)))))),f219(x43552)))),x43553),f312(f165(f860(x43551,x43552)),x43554)),f180(x43551,x43552,x43553,f312(f173(x43551,x43552),x43554)))
% 155.90/155.60 [3465]E(f312(f190(f852(x34651)),f312(f312(f312(f100(x34651),x34652),x34653),x34654)),f2(a853))
% 155.90/155.60 [3583]E(f312(f312(f169(x35831),x35832),f312(f312(f169(x35831),x35833),x35834)),f312(f312(f169(x35831),f312(f312(f225(a853),x35832),x35833)),x35834))
% 155.90/155.60 [3584]E(f312(f312(f134(x35841),x35842),f312(f312(f134(x35841),x35843),x35844)),f312(f312(f134(x35841),f312(f312(f89(a853),x35842),x35843)),x35844))
% 155.90/155.60 [3597]E(f312(f312(f129(x35971),f312(f312(f147(x35971),x35972),x35973)),x35974),f312(f312(f147(x35971),x35972),f312(f312(f129(x35971),x35973),x35974)))
% 155.90/155.60 [3598]E(f312(f312(f129(x35981),f312(f312(f129(x35981),x35982),x35983)),x35984),f312(f312(f129(x35981),x35982),f312(f312(f129(x35981),x35983),x35984)))
% 155.90/155.60 [3675]E(f312(f312(f161(x36751),f312(f312(f147(x36751),x36752),x36753)),x36754),f186(x36751,x36752,f312(f161(x36751),x36753),x36754))
% 155.90/155.60 [3684]E(f312(f312(f184(x36841,x36841),x36842),f312(f312(f184(x36841,x36841),x36843),x36844)),f312(f312(f184(x36841,x36841),f312(f312(f90(a853),x36843),x36842)),x36844))
% 155.90/155.60 [3712]E(f312(f312(f124(f861(x37121,a846)),x37122),f312(f312(f289(x37121),x37123),x37124)),f312(f312(f289(x37121),x37123),f312(f312(f124(f861(x37121,a846)),x37122),x37124)))
% 155.90/155.60 [3728]E(f312(f312(f312(f184(x37281,x37281),x37282),x37283),f312(x37283,x37284)),f312(x37283,f312(f312(f312(f184(x37281,x37281),x37282),x37283),x37284)))
% 155.90/155.60 [3735]E(f312(f312(f267(x37351,x37352,x37353),f189(f861(f860(x37351,x37352),a846))),x37354),f189(f861(f860(x37351,x37353),a846)))
% 155.90/155.60 [3751]E(f312(f312(f124(f861(x37511,a846)),f312(f312(f289(x37511),x37512),x37513)),x37514),f312(f312(f289(x37511),x37512),f312(f312(f124(f861(x37511,a846)),x37513),x37514)))
% 155.90/155.60 [3772]E(f180(x37721,x37722,f312(f173(x37721,x37722),x37723),f312(f173(x37721,x37722),x37724)),f312(f173(x37721,x37722),f312(f312(f129(f860(x37721,x37722)),x37724),x37723)))
% 155.90/155.60 [3773]E(f312(f53(f860(x37731,x37732)),f312(f312(f247(x37731,x37732),x37733),f312(f16(f861(x37732,a846),x37731),x37734))),f312(f312(f90(a853),f312(f53(x37731),x37733)),f312(f53(x37732),x37734)))
% 155.90/155.60 [3781]E(f312(f312(f115(f861(x37811,a846)),f312(f312(f289(x37811),x37812),x37813)),f312(f312(f289(x37811),x37812),x37814)),f312(f312(f289(x37811),x37812),f312(f312(f115(f861(x37811,a846)),x37813),x37814)))
% 155.90/155.60 [3797]E(f312(f312(f124(f861(x37971,a846)),x37972),f312(f312(f124(f861(x37971,a846)),x37973),x37974)),f312(f312(f124(f861(x37971,a846)),x37973),f312(f312(f124(f861(x37971,a846)),x37972),x37974)))
% 155.90/155.60 [3798]E(f312(f312(f115(f861(x37981,a846)),x37982),f312(f312(f115(f861(x37981,a846)),x37983),x37984)),f312(f312(f115(f861(x37981,a846)),x37983),f312(f312(f115(f861(x37981,a846)),x37982),x37984)))
% 155.90/155.60 [3807]E(f73(x38071,x38072,f312(f312(f8(x38072,f861(x38072,x38072),x38071),x38073),x38074)),f312(f74(x38072,x38071,x38073),x38074))
% 155.90/155.60 [3815]E(f175(x38151,f312(f312(f150(f854(x38152),f854(x38151)),f312(f150(x38152,x38151),x38153)),x38154)),f312(f312(f150(f854(x38152),f854(x38151)),f312(f150(x38152,x38151),x38153)),f175(x38152,x38154)))
% 155.90/155.60 [3832]E(f312(f138(f854(x38321),f854(x38321),f129(x38321),f127(x38321)),f312(f312(f150(x38322,f854(x38321)),x38323),x38324)),f160(x38322,x38321,x38323,x38324))
% 155.90/155.60 [3835]E(f183(x38351,x38352,x38353,f312(f88(f861(x38351,a846)),f312(f312(f289(x38351),x38354),f189(f861(x38351,a846))))),f312(f312(f312(f81(x38351,f857(x38352)),x38353),x38354),f192(x38352)))
% 155.90/155.60 [3878]E(f312(f312(f312(f81(x38781,f857(x38782)),f312(f173(x38781,x38782),x38783)),f312(f246(x38781,x38782),x38784)),f312(f219(x38782),f312(f248(x38781,x38782),x38784))),f312(f173(x38781,x38782),f312(f312(f147(f860(x38781,x38782)),x38784),x38783)))
% 155.90/155.60 [3895]E(f312(f82(x38951,x38951,x38951,f312(f312(f184(x38951,x38951),x38952),x38953)),f312(f312(f184(x38951,x38951),x38954),x38953)),f312(f312(f184(x38951,x38951),f312(f312(f89(a853),x38952),x38954)),x38953))
% 155.90/155.60 [3917]E(f312(f312(f115(f861(x39171,a846)),f312(f312(f21(f861(x39171,a846)),x39172),x39173)),f312(f312(f21(f861(x39171,a846)),x39172),x39174)),f312(f312(f21(f861(x39171,a846)),x39172),f312(f312(f124(f861(x39171,a846)),x39173),x39174)))
% 155.90/155.60 [3918]E(f312(f312(f124(f861(x39181,a846)),f312(f312(f21(f861(x39181,a846)),x39182),x39183)),f312(f312(f21(f861(x39181,a846)),x39182),x39184)),f312(f312(f21(f861(x39181,a846)),x39182),f312(f312(f115(f861(x39181,a846)),x39183),x39184)))
% 155.90/155.60 [3919]E(f312(f312(f115(f861(x39191,a846)),f312(f312(f124(f861(x39191,a846)),x39192),x39193)),f312(f312(f124(f861(x39191,a846)),x39192),x39194)),f312(f312(f124(f861(x39191,a846)),x39192),f312(f312(f115(f861(x39191,a846)),x39193),x39194)))
% 155.90/155.60 [3920]E(f312(f312(f21(f861(x39201,a846)),f312(f312(f115(f861(x39201,a846)),x39202),x39203)),f312(f312(f115(f861(x39201,a846)),x39202),x39204)),f312(f312(f115(f861(x39201,a846)),x39202),f312(f312(f21(f861(x39201,a846)),x39203),x39204)))
% 155.90/155.60 [3921]E(f312(f312(f124(f861(x39211,a846)),f312(f312(f115(f861(x39211,a846)),x39212),x39213)),f312(f312(f115(f861(x39211,a846)),x39212),x39214)),f312(f312(f115(f861(x39211,a846)),x39212),f312(f312(f124(f861(x39211,a846)),x39213),x39214)))
% 155.90/155.60 [3927]E(f312(f53(f860(x39271,x39272)),f312(f312(f247(x39271,x39272),f312(f312(f289(x39271),x39273),f189(f861(x39271,a846)))),f312(f16(f861(x39272,a846),x39271),x39274))),f312(f53(x39272),x39274))
% 155.90/155.60 [3962]E(f312(f312(f51(x39621,f861(x39622,a846)),x39623),f312(f312(f8(f861(x39622,a846),f861(x39622,a846),x39621),f88(f861(x39622,a846))),x39624)),f312(f88(f861(x39622,a846)),f312(f312(f50(x39621,f861(x39622,a846)),x39623),x39624)))
% 155.90/155.60 [3963]E(f312(f312(f50(x39631,f861(x39632,a846)),x39633),f312(f312(f8(f861(x39632,a846),f861(x39632,a846),x39631),f88(f861(x39632,a846))),x39634)),f312(f88(f861(x39632,a846)),f312(f312(f51(x39631,f861(x39632,a846)),x39633),x39634)))
% 155.90/155.60 [3979]E(f312(f312(f267(x39791,x39791,x39791),f312(f312(f184(f860(x39791,x39791),a846),x39792),x39793)),f312(f312(f184(f860(x39791,x39791),a846),x39794),x39793)),f312(f312(f184(f860(x39791,x39791),a846),f312(f312(f89(a853),x39792),x39794)),x39793))
% 155.90/155.60 [4012]E(f312(f312(f51(x40121,f861(f861(x40122,a846),a846)),x40123),f312(f312(f8(f861(x40122,a846),f861(f861(x40122,a846),a846),x40121),f288(x40122)),x40124)),f312(f288(x40122),f312(f312(f51(x40121,f861(x40122,a846)),x40123),x40124)))
% 155.90/155.60 [4040]E(f312(f312(f50(f861(x40401,a846),f861(x40402,a846)),x40403),f312(f312(f7(f861(x40401,a846),f861(x40401,f861(x40402,a846)),f861(x40402,a846)),f50(x40401,f861(x40402,a846))),x40404)),f312(f312(f50(x40401,f861(x40402,a846)),f48(f861(x40401,a846),x40403)),x40404))
% 155.90/155.60 [4041]E(f312(f312(f51(f861(x40411,a846),f861(x40412,a846)),x40413),f312(f312(f7(f861(x40411,a846),f861(x40411,f861(x40412,a846)),f861(x40412,a846)),f51(x40411,f861(x40412,a846))),x40414)),f312(f312(f51(x40411,f861(x40412,a846)),f48(f861(x40411,a846),x40413)),x40414))
% 155.90/155.60 [4046]E(f312(f312(f150(x40461,x40462),x40463),f312(f138(f854(x40461),f854(x40461),f129(x40461),f127(x40461)),x40464)),f312(f138(f854(x40462),f854(x40462),f129(x40462),f127(x40462)),f312(f312(f150(f854(x40461),f854(x40462)),f312(f150(x40461,x40462),x40463)),x40464)))
% 155.90/155.60 [4049]E(f186(f854(x40491),f127(x40491),f312(f312(f8(f854(x40491),f854(x40491),a853),f312(f147(x40491),x40492)),f312(f312(f7(a853,f854(x40491),f854(x40491)),f169(x40491)),x40493)),x40494),f312(f312(f169(x40491),x40494),f312(f312(f147(x40491),x40492),x40493)))
% 155.90/155.60 [4092]P22(f312(f312(f227(f861(x40921,a846)),f312(f290(x40922,x40921,x40923),f312(f291(x40922,x40921,x40923),x40924))),x40924))
% 155.90/155.60 [4095]E(f312(f290(f860(x40951,x40952),f860(x40952,x40951),f312(f249(x40951,x40952,f860(x40952,x40951)),f312(f7(x40952,x40951,f860(x40952,x40951)),f239(x40952,x40951)))),f312(f312(f247(x40951,x40952),x40953),f312(f16(f861(x40952,a846),x40951),x40954))),f312(f312(f247(x40952,x40951),x40954),f312(f16(f861(x40951,a846),x40952),x40953)))
% 155.90/155.60 [4104]E(f312(f312(f50(x41041,f861(x41042,a846)),x41043),f312(f312(f8(f861(x41041,a846),f861(x41042,a846),x41041),f291(x41042,x41041,x41044)),f312(f312(f7(x41041,f861(x41041,a846),f861(x41041,a846)),f289(x41041)),f189(f861(x41041,a846))))),f312(f291(x41042,x41041,x41044),x41043))
% 155.90/155.60 [4105]E(f312(f312(f50(x41051,f861(x41052,a846)),x41053),f312(f312(f8(f861(x41051,a846),f861(x41052,a846),x41051),f264(x41051,x41052,x41054)),f312(f312(f7(x41051,f861(x41051,a846),f861(x41051,a846)),f289(x41051)),f189(f861(x41051,a846))))),f312(f264(x41051,x41052,x41054),x41053))
% 155.90/155.60 [4194]E(f312(f312(f124(f861(x41941,a846)),f312(f312(f124(f861(x41941,a846)),f312(f312(f115(f861(x41941,a846)),x41942),x41943)),f312(f312(f115(f861(x41941,a846)),x41943),x41944))),f312(f312(f115(f861(x41941,a846)),x41944),x41942)),f312(f312(f115(f861(x41941,a846)),f312(f312(f115(f861(x41941,a846)),f312(f312(f124(f861(x41941,a846)),x41942),x41943)),f312(f312(f124(f861(x41941,a846)),x41943),x41944))),f312(f312(f124(f861(x41941,a846)),x41944),x41942)))
% 155.90/155.60 [4255]E(f312(f138(f854(x42551),f854(x42551),f129(x42551),f127(x42551)),f312(f312(f150(x42552,f854(x42551)),f312(f312(f7(x42552,f854(x42551),f854(x42551)),f312(f312(f8(x42551,f861(f854(x42551),f854(x42551)),x42552),f147(x42551)),x42553)),f127(x42551))),x42554)),f312(f312(f150(x42552,x42551),x42553),x42554))
% 155.90/155.60 [4266]E(f312(f312(f95(a1,x42661),f312(f117(a1),f312(f312(f89(a1),x42662),a111))),f312(f312(f18(a1,x42661,x42661),f312(f312(f7(a1,x42661,f861(x42661,x42661)),f312(f312(f8(a846,f861(x42661,f861(x42661,x42661)),a1),f108(x42661)),a194)),x42663)),f312(f312(f8(a853,x42661,a1),x42664),a118))),f186(x42661,x42663,x42664,f312(f117(a853),x42662)))
% 155.90/155.60 [4502]~P22(f312(f312(f189(f861(x45021,f861(x45022,a846))),x45023),x45024))
% 155.90/155.60 [3738]E(f312(f312(f161(x37381),f312(f312(f129(x37381),x37382),x37383)),f312(f312(f89(a853),f312(f190(f854(x37381)),x37382)),x37384)),f312(f312(f161(x37381),x37383),x37384))
% 155.90/155.60 [3744]E(f312(f312(f134(x37441),x37442),f312(f312(f169(x37441),f312(f312(f89(a853),x37443),x37442)),x37444)),f312(f312(f169(x37441),x37443),f312(f312(f134(x37441),x37442),x37444)))
% 155.90/155.60 [3848]E(f312(f312(f124(f861(x38481,a846)),f312(f236(x38482,x38481),x38483)),f312(f236(x38482,x38481),x38484)),f312(f236(x38482,x38481),f312(f312(f124(f861(f860(x38482,x38481),a846)),x38483),x38484)))
% 155.90/155.60 [3849]E(f312(f312(f124(f861(x38491,a846)),f312(f238(x38491,x38492),x38493)),f312(f238(x38491,x38492),x38494)),f312(f238(x38491,x38492),f312(f312(f124(f861(f860(x38491,x38492),a846)),x38493),x38494)))
% 155.90/155.60 [3854]E(f312(f312(f21(f861(x38541,a846)),f312(f312(f115(f861(x38541,a846)),x38542),x38543)),x38544),f312(f312(f115(f861(x38541,a846)),x38542),f312(f312(f21(f861(x38541,a846)),x38543),x38544)))
% 155.90/155.60 [3855]E(f312(f312(f124(f861(x38551,a846)),f312(f312(f124(f861(x38551,a846)),x38552),x38553)),x38554),f312(f312(f124(f861(x38551,a846)),x38552),f312(f312(f124(f861(x38551,a846)),x38553),x38554)))
% 155.90/155.60 [3856]E(f312(f312(f115(f861(x38561,a846)),f312(f312(f115(f861(x38561,a846)),x38562),x38563)),x38564),f312(f312(f115(f861(x38561,a846)),x38562),f312(f312(f115(f861(x38561,a846)),x38563),x38564)))
% 155.90/155.60 [3897]E(f312(f312(f124(f861(f860(x38971,x38972),a846)),f312(f265(x38972,x38971),x38973)),f312(f265(x38972,x38971),x38974)),f312(f265(x38972,x38971),f312(f312(f124(f861(f860(x38972,x38971),a846)),x38973),x38974)))
% 155.90/155.60 [3898]E(f312(f312(f115(f861(f860(x38981,x38982),a846)),f312(f265(x38982,x38981),x38983)),f312(f265(x38982,x38981),x38984)),f312(f265(x38982,x38981),f312(f312(f115(f861(f860(x38982,x38981),a846)),x38983),x38984)))
% 155.90/155.60 [3966]E(f312(f312(f124(f861(x39661,a846)),f312(f312(f21(f861(x39661,a846)),x39662),x39663)),f312(f312(f21(f861(x39661,a846)),x39664),x39663)),f312(f312(f21(f861(x39661,a846)),f312(f312(f124(f861(x39661,a846)),x39662),x39664)),x39663))
% 155.90/155.60 [3967]E(f312(f312(f115(f861(x39671,a846)),f312(f312(f124(f861(x39671,a846)),x39672),x39673)),f312(f312(f124(f861(x39671,a846)),x39674),x39673)),f312(f312(f124(f861(x39671,a846)),f312(f312(f115(f861(x39671,a846)),x39672),x39674)),x39673))
% 155.90/155.60 [3968]E(f312(f312(f21(f861(x39681,a846)),f312(f312(f115(f861(x39681,a846)),x39682),x39683)),f312(f312(f115(f861(x39681,a846)),x39684),x39683)),f312(f312(f115(f861(x39681,a846)),f312(f312(f21(f861(x39681,a846)),x39682),x39684)),x39683))
% 155.90/155.60 [3969]E(f312(f312(f124(f861(x39691,a846)),f312(f312(f115(f861(x39691,a846)),x39692),x39693)),f312(f312(f115(f861(x39691,a846)),x39694),x39693)),f312(f312(f115(f861(x39691,a846)),f312(f312(f124(f861(x39691,a846)),x39692),x39694)),x39693))
% 155.90/155.60 [3970]E(f312(f312(f21(f861(x39701,a846)),f312(f312(f115(f861(x39701,a846)),x39702),x39703)),f312(f312(f115(f861(x39701,a846)),x39704),x39703)),f312(f312(f21(f861(x39701,a846)),f312(f312(f115(f861(x39701,a846)),x39702),x39703)),x39704))
% 155.90/155.60 [3982]E(f312(f312(f21(f861(x39821,a846)),f312(f312(f21(f861(x39821,a846)),x39822),f312(f312(f289(x39821),x39823),f189(f861(x39821,a846))))),x39824),f312(f312(f21(f861(x39821,a846)),x39822),f312(f312(f289(x39821),x39823),x39824)))
% 155.90/155.60 [4037]E(f312(f312(f124(f861(x40371,a846)),f312(f312(f289(x40371),x40372),f312(f312(f289(x40371),x40373),f189(f861(x40371,a846))))),f312(f263(x40371),x40374)),f312(f263(x40371),f312(f312(f289(f860(x40371,x40371)),f312(f312(f239(x40371,x40371),x40372),x40373)),x40374)))
% 155.90/155.60 [4067]E(f312(f312(f50(a853,f861(x40671,a846)),f312(f281(a853),x40672)),f312(f312(f8(a853,f861(x40671,a846),a853),x40673),f312(f312(f7(a853,a853,a853),f89(a853)),x40674))),f312(f312(f50(a853,f861(x40671,a846)),f283(a853,x40674,f312(f312(f89(a853),x40672),x40674))),x40673))
% 155.90/155.60 [4068]E(f171(x40681,f312(f264(x40681,x40681,x40682),f312(f312(f289(x40681),x40683),f189(f861(x40681,a846)))),f312(f264(f854(x40681),f854(x40681),f154(x40681,x40682)),f312(f312(f289(f854(x40681)),x40684),f189(f861(f854(x40681),a846))))),f312(f264(f854(x40681),f854(x40681),f154(x40681,x40682)),f312(f312(f289(f854(x40681)),f312(f312(f147(x40681),x40683),x40684)),f189(f861(f854(x40681),a846)))))
% 155.90/155.60 [4126]E(f312(f173(x41261,x41262),f312(f312(f150(x41261,f860(x41261,x41262)),f312(f312(f18(x41261,x41262,f860(x41261,x41262)),f239(x41261,x41262)),x41263)),x41264)),f183(x41261,x41262,f312(f82(x41262,f857(x41262),x41261,f219(x41262)),x41263),f312(f168(x41261),x41264)))
% 155.90/155.60 [4131]E(f312(f233(x41311),f312(f312(f7(x41311,f861(x41312,a846),a846),f312(f312(f8(x41312,f861(f861(x41312,a846),a846),x41311),f314(x41312)),x41313)),x41314)),f312(f291(x41311,x41312,x41313),x41314))
% 155.90/155.60 [4227]E(f312(f233(x42271),f312(f312(f7(x42271,f861(f860(x42272,x42271),a846),a846),f312(f312(f8(f860(x42272,x42271),f861(f861(f860(x42272,x42271),a846),a846),x42271),f314(f860(x42272,x42271))),f312(f239(x42272,x42271),x42273))),x42274)),f312(f264(x42272,x42271,x42274),f312(f312(f289(x42272),x42273),f189(f861(x42272,a846)))))
% 155.90/155.60 [4241]E(f312(f312(f150(f860(x42411,a853),x42411),f246(x42411,a853)),f312(f132(f860(x42411,a853),f312(f312(f8(a853,a846,f860(x42411,a853)),x42412),f312(f312(f8(a853,a853,f860(x42411,a853)),a126),f248(x42411,a853)))),f312(f312(f177(x42411,a853),x42413),x42414))),f312(f312(f150(f860(x42411,a853),x42411),f246(x42411,a853)),f312(f132(f860(x42411,a853),f312(f312(f8(a853,a846,f860(x42411,a853)),x42412),f248(x42411,a853))),f312(f312(f177(x42411,a853),x42413),f312(f312(f150(a853,a853),a126),x42414)))))
% 155.90/155.60 [4248]P22(f312(f312(f227(f861(f861(x42481,a846),a846)),f312(f312(f50(x42482,f861(f861(x42481,a846),a846)),x42483),f312(f312(f8(f861(x42481,a846),f861(f861(x42481,a846),a846),x42482),f288(x42481)),x42484))),f312(f288(x42481),f312(f312(f50(x42482,f861(x42481,a846)),x42483),x42484))))
% 155.90/155.60 [4288]E(f312(f312(f95(a1,x42881),f312(f117(a1),f312(f312(f89(a1),x42882),a111))),f312(f312(f18(a1,x42881,x42881),f312(f312(f7(a1,x42881,f861(x42881,x42881)),f312(f312(f8(a846,f861(x42881,f861(x42881,x42881)),a1),f108(x42881)),a194)),x42883)),f312(f312(f18(a1,x42881,x42881),f312(f312(f8(a853,f861(x42881,x42881),a1),x42884),a118)),f312(f312(f8(a853,x42881,a1),f185(x42881,x42883,x42884)),a118)))),f312(f185(x42881,x42883,x42884),f312(f117(a853),x42882)))
% 155.90/155.60 [4291]E(f312(f312(f150(x42911,x42912),f312(f82(f857(x42912),x42912,x42911,f223(x42912)),x42913)),f312(f132(x42911,f312(f312(f8(a846,a846,x42911),a307),f312(f312(f7(x42911,f857(x42912),a846),f312(f312(f8(f857(x42912),f861(f857(x42912),a846),x42911),a309),x42913)),f192(x42912)))),x42914)),f159(x42911,x42912,x42913,x42914))
% 155.90/155.60 [4313]E(f312(f233(f860(x43131,x43132)),f312(f249(x43131,x43132,a846),f312(f312(f7(x43131,f861(x43132,a846),f861(x43132,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x43132,a846),f861(x43132,a846)),x43131),f8(a846,a846,x43132)),f312(f312(f8(a846,f861(a846,a846),x43131),a310),f312(f312(f7(x43131,f861(x43131,a846),a846),f314(x43131)),x43133)))),f312(f312(f7(x43132,f861(x43132,a846),a846),f314(x43132)),x43134)))),f216(x43131,x43132,x43133,x43134))
% 155.90/155.60 [4342]E(f312(f312(f50(x43421,f861(f860(x43421,x43422),a846)),x43423),f312(f312(f18(x43421,f861(x43422,f861(f860(x43421,x43422),a846)),f861(f860(x43421,x43422),a846)),f312(f312(f8(f861(x43422,a846),f861(f861(x43422,f861(f860(x43421,x43422),a846)),f861(f860(x43421,x43422),a846)),x43421),f50(x43422,f861(f860(x43421,x43422),a846))),x43424)),f312(f312(f7(x43421,f861(f860(x43421,x43422),a846),f861(x43422,f861(f860(x43421,x43422),a846))),f312(f312(f8(f861(x43422,f861(f861(f860(x43421,x43422),a846),f861(f860(x43421,x43422),a846))),f861(f861(f860(x43421,x43422),a846),f861(x43422,f861(f860(x43421,x43422),a846))),x43421),f7(x43422,f861(f860(x43421,x43422),a846),f861(f860(x43421,x43422),a846))),f312(f312(f8(f861(x43422,f860(x43421,x43422)),f861(x43422,f861(f861(f860(x43421,x43422),a846),f861(f860(x43421,x43422),a846))),x43421),f312(f8(f860(x43421,x43422),f861(f861(f860(x43421,x43422),a846),f861(f860(x43421,x43422),a846)),x43422),f289(f860(x43421,x43422)))),f239(x43421,x43422)))),f189(f861(f860(x43421,x43422),a846))))),f312(f312(f247(x43421,x43422),x43423),x43424))
% 155.90/155.60 [3906]E(f312(f312(f129(x39061),f312(f312(f169(x39061),x39062),x39063)),f312(f312(f169(x39061),f312(f312(f21(a853),x39062),f312(f190(f854(x39061)),x39063))),x39064)),f312(f312(f169(x39061),x39062),f312(f312(f129(x39061),x39063),x39064)))
% 155.90/155.60 [3907]E(f312(f312(f129(x39071),f312(f312(f134(x39071),x39072),x39073)),f312(f312(f134(x39071),f312(f312(f21(a853),x39072),f312(f190(f854(x39071)),x39073))),x39074)),f312(f312(f134(x39071),x39072),f312(f312(f129(x39071),x39073),x39074)))
% 155.90/155.60 [3956]E(f312(f312(f89(a853),f312(f312(f90(a853),x39561),x39562)),f312(f312(f89(a853),f312(f312(f90(a853),x39563),x39562)),x39564)),f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f89(a853),x39561),x39563)),x39562)),x39564))
% 155.90/155.60 [4156]P22(f312(f312(f227(f861(x41561,a846)),f312(f312(f21(f861(x41561,a846)),f312(f236(x41562,x41561),x41563)),f312(f236(x41562,x41561),x41564))),f312(f236(x41562,x41561),f312(f312(f21(f861(f860(x41562,x41561),a846)),x41563),x41564))))
% 155.90/155.60 [4157]P22(f312(f312(f227(f861(x41571,a846)),f312(f312(f21(f861(x41571,a846)),f312(f238(x41571,x41572),x41573)),f312(f238(x41571,x41572),x41574))),f312(f238(x41571,x41572),f312(f312(f21(f861(f860(x41571,x41572),a846)),x41573),x41574))))
% 155.90/155.60 [4268]E(f312(f312(f89(a1),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x42681),x42682)),f189(f861(f860(a853,a853),a846)))))),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x42683),x42684)),f189(f861(f860(a853,a853),a846)))))),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),f312(f312(f89(a853),x42681),x42683)),f312(f312(f89(a853),x42682),x42684))),f189(f861(f860(a853,a853),a846))))))
% 155.90/155.60 [4308]E(f312(f312(f90(a1),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x43081),x43082)),f189(f861(f860(a853,a853),a846)))))),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x43083),x43084)),f189(f861(f860(a853,a853),a846)))))),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),f312(f312(f89(a853),f312(f312(f90(a853),x43081),x43083)),f312(f312(f90(a853),x43082),x43084))),f312(f312(f89(a853),f312(f312(f90(a853),x43081),x43084)),f312(f312(f90(a853),x43082),x43083)))),f189(f861(f860(a853,a853),a846))))))
% 155.90/155.60 [4325]E(f312(f233(x43251),f312(f312(f8(f861(x43252,a846),a846,x43251),f97(x43252)),f312(f312(f8(f861(x43252,a846),f861(x43252,a846),x43251),f312(f18(x43252,a846,a846),f312(f312(f8(a846,f861(a846,a846),x43252),a315),f312(f312(f7(x43252,f861(x43252,a846),a846),f314(x43252)),x43253)))),f312(f312(f7(x43251,f861(x43252,f861(x43251,a846)),f861(x43252,a846)),f312(f312(f8(f861(f861(x43251,a846),a846),f861(f861(x43252,f861(x43251,a846)),f861(x43252,a846)),x43251),f8(f861(x43251,a846),a846,x43252)),f314(x43251))),x43254)))),f312(f312(f51(x43252,f861(x43251,a846)),x43253),x43254))
% 155.90/155.60 [4358]E(f312(f312(f267(x43581,x43581,x43581),f312(f312(f289(f860(x43581,x43581)),f312(f312(f239(x43581,x43581),x43582),x43583)),x43584)),f287(x43581,f312(f312(f289(f860(x43581,x43581)),f312(f312(f239(x43581,x43581),x43582),x43583)),x43584))),f312(f312(f124(f861(f860(x43581,x43581),a846)),f312(f312(f267(x43581,x43581,x43581),x43584),f287(x43581,x43584))),f312(f233(f860(x43581,x43581)),f312(f249(x43581,x43581,a846),f312(f312(f7(x43581,f861(x43581,a846),f861(x43581,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x43581,a846),f861(x43581,a846)),x43581),f8(a846,a846,x43581)),f312(f312(f8(a846,f861(a846,a846),x43581),a310),f312(f312(f7(x43581,f861(f860(x43581,x43581),a846),a846),f312(f312(f8(f860(x43581,x43581),f861(f861(f860(x43581,x43581),a846),a846),x43581),f314(f860(x43581,x43581))),f312(f312(f7(x43581,x43581,f860(x43581,x43581)),f239(x43581,x43581)),x43582))),f287(x43581,x43584))))),f312(f312(f7(x43581,f861(f860(x43581,x43581),a846),a846),f312(f312(f8(f860(x43581,x43581),f861(f861(f860(x43581,x43581),a846),a846),x43581),f314(f860(x43581,x43581))),f312(f239(x43581,x43581),x43583))),f287(x43581,x43584)))))))
% 155.90/155.60 [4158]E(f312(f132(x41581,f312(f312(f18(x41581,a846,a846),f312(f312(f8(a846,f861(a846,a846),x41581),a310),x41582)),x41583)),x41584),f312(f132(x41581,x41583),f312(f132(x41581,x41582),x41584)))
% 155.90/155.60 [4262]E(f312(f312(f129(x42621),f312(f312(f312(f108(f854(x42621)),f312(f312(f314(a853),f2(a853)),x42622)),f312(f312(f147(x42621),x42623),f127(x42621))),f127(x42621))),f170(x42621,x42624,f312(f233(a853),f312(f312(f7(a853,f861(a853,a846),a846),f312(f312(f8(a853,f861(f861(a853,a846),a846),a853),f314(a853)),a126)),x42622)))),f170(x42621,f312(f312(f147(x42621),x42623),x42624),x42622))
% 155.90/155.60 [4353]E(f312(f233(f860(x43531,x43532)),f312(f312(f8(f861(a853,a846),a846,f860(x43531,x43532)),f96(a853)),f312(f312(f7(f860(x43531,x43532),f861(a853,a846),f861(a853,a846)),f312(f312(f8(f861(a853,f861(a846,a846)),f861(f861(a853,a846),f861(a853,a846)),f860(x43531,x43532)),f18(a853,a846,a846)),f312(f312(f8(f861(a853,a846),f861(a853,f861(a846,a846)),f860(x43531,x43532)),f312(f8(a846,f861(a846,a846),a853),a310)),f312(f312(f7(f860(x43531,x43532),f861(a853,f860(x43531,x43532)),f861(a853,a846)),f312(f312(f8(f861(f860(x43531,x43532),a846),f861(f861(a853,f860(x43531,x43532)),f861(a853,a846)),f860(x43531,x43532)),f8(f860(x43531,x43532),a846,a853)),a309)),f312(f312(f18(a853,x43532,f860(x43531,x43532)),f312(f312(f8(x43531,f861(x43532,f860(x43531,x43532)),a853),f239(x43531,x43532)),f312(f161(x43531),x43533))),f312(f161(x43532),x43534)))))),f312(f312(f7(a853,a853,a846),f228(a853)),f312(f312(f225(a853),f312(f190(f854(x43531)),x43533)),f312(f190(f854(x43532)),x43534)))))),f312(f168(f860(x43531,x43532)),f312(f312(f177(x43531,x43532),x43533),x43534)))
% 155.90/155.60 [4280]E(f312(f233(f860(x42801,x42802)),f312(f249(x42801,x42802,a846),f312(f312(f7(x42801,f861(x42802,a846),f861(x42802,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x42802,a846),f861(x42802,a846)),x42801),f8(a846,a846,x42802)),f312(f312(f8(a846,f861(a846,a846),x42801),a310),x42803))),x42804))),f312(f312(f247(x42801,x42802),f312(f233(x42801),x42803)),f312(f16(f861(x42802,a846),x42801),f312(f233(x42802),x42804))))
% 155.90/155.60 [4283]E(f312(f233(f860(x42831,x42832)),f312(f249(x42831,x42832,a846),f312(f312(f18(x42831,f861(x42832,a846),f861(x42832,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x42832,a846),f861(x42832,a846)),x42831),f8(a846,a846,x42832)),f312(f312(f8(a846,f861(a846,a846),x42831),a310),x42833))),x42834))),f312(f312(f247(x42831,x42832),f312(f233(x42831),x42833)),f312(f312(f8(f861(x42832,a846),f861(x42832,a846),x42831),f233(x42832)),x42834)))
% 155.90/155.60 [4298]E(f312(f233(x42981),f312(f312(f8(f861(x42982,a846),a846,x42981),f97(x42982)),f312(f312(f8(f861(x42982,a846),f861(x42982,a846),x42981),f312(f18(x42982,a846,a846),f312(f312(f8(a846,f861(a846,a846),x42982),a315),f312(f312(f7(x42982,f861(x42982,a846),a846),f314(x42982)),x42983)))),x42984))),f312(f312(f51(x42982,f861(x42981,a846)),x42983),f312(f312(f8(f861(x42981,a846),f861(x42981,a846),x42982),f233(x42981)),f312(f7(x42981,x42982,a846),x42984))))
% 155.90/155.60 [4337]E(f312(f312(f150(f860(x43371,a853),x43371),f246(x43371,a853)),f312(f132(f860(x43371,a853),f312(f312(f7(f860(x43371,a853),f861(a853,a846),a846),f312(f312(f8(a853,f861(f861(a853,a846),a846),f860(x43371,a853)),f314(a853)),f248(x43371,a853))),x43372)),f312(f312(f177(x43371,a853),x43373),f135(a853,f312(f282(a853,x43374),f312(f312(f89(a853),x43374),f312(f190(f854(x43371)),x43373))))))),f312(f312(f150(f860(x43371,a853),x43371),f246(x43371,a853)),f312(f132(f860(x43371,a853),f312(f312(f7(f860(x43371,a853),f861(a853,a846),a846),f312(f312(f8(a853,f861(f861(a853,a846),a846),f860(x43371,a853)),f314(a853)),f312(f312(f7(f860(x43371,a853),a853,a853),f312(f312(f8(a853,f861(a853,a853),f860(x43371,a853)),f89(a853)),f248(x43371,a853))),x43374))),x43372)),f312(f312(f177(x43371,a853),x43373),f135(a853,f312(f282(a853,f2(a853)),f312(f190(f854(x43371)),x43373)))))))
% 155.90/155.60 [4338]E(f312(a126,f312(f312(f226(a853),f312(f190(f854(x43381)),x43382)),f312(f138(a853,f854(x43383),f312(f7(f854(x43383),a853,a853),f312(f312(f8(a853,f861(a853,a853),f854(x43383)),f226(a853)),f312(f312(f7(f854(x43383),a853,a853),f312(f312(f8(a853,f861(a853,a853),f854(x43383)),f21(a853)),f190(f854(x43383)))),f312(a126,f2(a853))))),f2(a853)),f312(f165(f854(x43383)),f312(f132(f854(x43383),f312(f312(f8(a846,a846,f854(x43383)),a307),f312(f312(f7(f854(x43383),f854(x43383),a846),a309),f127(x43383)))),x43384))))),f312(f312(f226(a853),f312(a126,f312(f190(f854(x43381)),x43382))),f312(f138(a853,f854(x43383),f312(f7(f854(x43383),a853,a853),f312(f312(f8(a853,f861(a853,a853),f854(x43383)),f226(a853)),f190(f854(x43383)))),f2(a853)),f312(f165(f854(x43383)),x43384))))
% 155.90/155.60 [4297]E(f312(f312(f129(x42971),f170(x42971,x42972,x42973)),f170(x42971,x42974,f312(f233(a853),f312(f312(f7(a853,f861(a853,a846),a846),f312(f312(f8(a853,f861(f861(a853,a846),a846),a853),f314(a853)),f312(f312(f7(a853,a853,a853),f89(a853)),f312(f190(f854(x42971)),x42972)))),x42973)))),f170(x42971,f312(f312(f129(x42971),x42972),x42974),x42973))
% 155.90/155.60 [4344]E(f312(f312(f147(f854(x43441)),f312(f312(f147(x43441),x43442),f312(f138(f854(x43441),f854(x43441),f129(x43441),f127(x43441)),f312(f312(f150(f854(x43441),f854(x43441)),f152(f854(x43441),x43441,f127(x43441),f312(f312(f8(f854(x43441),f861(f854(x43441),f854(x43441)),x43441),f16(f854(x43441),f854(x43441))),f312(f312(f7(x43441,f854(x43441),f854(x43441)),f147(x43441)),f127(x43441))))),x43443)))),f175(x43441,f312(f312(f147(f854(x43441)),x43444),f312(f138(f854(f854(x43441)),f854(f854(x43441)),f129(f854(x43441)),f127(f854(x43441))),f312(f312(f150(f854(x43441),f854(f854(x43441))),f152(f854(f854(x43441)),x43441,f127(f854(x43441)),f312(f16(f861(f854(x43441),f854(f854(x43441))),x43441),f312(f312(f7(f854(x43441),f854(f854(x43441)),f854(f854(x43441))),f147(f854(x43441))),f127(f854(x43441)))))),x43443))))),f175(x43441,f312(f312(f147(f854(x43441)),f312(f312(f147(x43441),x43442),x43444)),x43443)))
% 155.90/155.60 [4354]E(f312(f233(f860(x43541,x43541)),f312(f249(x43541,x43541,a846),f312(f312(f7(x43541,f861(f860(x43542,x43542),a846),f861(x43541,a846)),f312(f312(f8(f861(x43541,f861(f861(f860(x43542,x43542),a846),a846)),f861(f861(f860(x43542,x43542),a846),f861(x43541,a846)),x43541),f7(x43541,f861(f860(x43542,x43542),a846),a846)),f312(f312(f8(f861(x43541,f860(x43542,x43542)),f861(x43541,f861(f861(f860(x43542,x43542),a846),a846)),x43541),f312(f8(f860(x43542,x43542),f861(f861(f860(x43542,x43542),a846),a846),x43541),f314(f860(x43542,x43542)))),f312(f312(f7(x43541,f861(x43541,x43542),f861(x43541,f860(x43542,x43542))),f312(f312(f8(f861(x43542,f860(x43542,x43542)),f861(f861(x43541,x43542),f861(x43541,f860(x43542,x43542))),x43541),f8(x43542,f860(x43542,x43542),x43541)),f312(f312(f8(x43542,f861(x43542,f860(x43542,x43542)),x43541),f239(x43542,x43542)),x43543))),x43543)))),x43544))),f312(f312(f266(x43542,x43541),x43544),x43543))
% 155.90/155.60 [4440]~E(f36(x44401,x44402),f33(x44403,x44404,x44405))
% 155.90/155.60 [4441]~E(f36(x44411,x44412),f32(x44413,x44414,x44415))
% 155.90/155.60 [4442]~E(f36(x44421,x44422),f31(x44423,x44424,x44425))
% 155.90/155.60 [4443]~E(f35(x44431,x44432),f33(x44433,x44434,x44435))
% 155.90/155.60 [4444]~E(f35(x44441,x44442),f32(x44443,x44444,x44445))
% 155.90/155.60 [4445]~E(f35(x44451,x44452),f31(x44453,x44454,x44455))
% 155.90/155.60 [4446]~E(f28(x44461,x44462),f33(x44463,x44464,x44465))
% 155.90/155.60 [4447]~E(f28(x44471,x44472),f32(x44473,x44474,x44475))
% 155.90/155.60 [4448]~E(f28(x44481,x44482),f31(x44483,x44484,x44485))
% 155.90/155.60 [4449]~E(f33(x44491,x44492,x44493),f36(x44494,x44495))
% 155.90/155.60 [4450]~E(f33(x44501,x44502,x44503),f35(x44504,x44505))
% 155.90/155.60 [4451]~E(f33(x44511,x44512,x44513),f28(x44514,x44515))
% 155.90/155.60 [4452]~E(f32(x44521,x44522,x44523),f36(x44524,x44525))
% 155.90/155.60 [4453]~E(f32(x44531,x44532,x44533),f35(x44534,x44535))
% 155.90/155.60 [4454]~E(f32(x44541,x44542,x44543),f28(x44544,x44545))
% 155.90/155.60 [4455]~E(f31(x44551,x44552,x44553),f36(x44554,x44555))
% 155.90/155.60 [4456]~E(f31(x44561,x44562,x44563),f35(x44564,x44565))
% 155.90/155.60 [4457]~E(f31(x44571,x44572,x44573),f28(x44574,x44575))
% 155.90/155.60 [3846]E(f312(f180(x38461,x38462,x38463,x38464),x38465),f312(f221(f857(x38462),x38462,f312(x38463,x38465),f219(x38462)),f312(x38464,x38465)))
% 155.90/155.60 [3933]E(f180(x39331,x39332,f180(x39331,x39332,x39333,x39334),x39335),f180(x39331,x39332,x39333,f180(x39331,x39332,x39334,x39335)))
% 155.90/155.60 [4114]E(f312(f312(f124(f861(x41141,a846)),f312(f168(x41141),f312(f312(f169(x41141),f312(f190(f854(x41142)),x41143)),x41144))),f179(x41141,x41142,x41145)),f179(x41141,x41142,f182(x41141,x41142,x41145,x41144,x41143)))
% 155.90/155.60 [3671]E(f312(f312(f249(x36711,x36712,x36713),x36714),x36715),f312(f312(x36714,f312(f246(x36711,x36712),x36715)),f312(f248(x36711,x36712),x36715)))
% 155.90/155.60 [3694]E(f312(f221(x36941,x36942,x36943,x36944),f312(f219(x36942),x36945)),f312(x36944,x36945))
% 155.90/155.60 [3704]E(f312(f312(f312(f74(x37041,x37042,x37043),x37044),x37045),f189(f861(x37042,a846))),x37045)
% 155.90/155.60 [3879]E(f222(x38791,x38792,x38793,x38794,f312(f219(x38792),x38795)),f312(x38794,x38795))
% 155.90/155.60 [3988]E(f312(f82(f857(x39881),f857(x39882),f857(x39883),f312(f193(x39881,x39882),x39884)),f312(f193(x39883,x39881),x39885)),f312(f193(x39883,x39882),f312(f82(x39881,x39882,x39883,x39884),x39885)))
% 155.90/155.60 [3990]E(f312(f82(f854(x39901),f854(x39902),f854(x39903),f312(f150(x39901,x39902),x39904)),f312(f150(x39903,x39901),x39905)),f312(f150(x39903,x39902),f312(f82(x39901,x39902,x39903,x39904),x39905)))
% 155.90/155.60 [4071]E(f94(x40711,f75(x40712,x40711,x40713,x40714,x40715)),f312(f312(f73(x40712,x40711,x40713),x40714),x40715))
% 155.90/155.60 [4106]E(f312(f312(f89(a853),f312(f312(f89(a853),f312(x41061,f312(f246(x41062,x41063),x41064))),f312(x41065,f312(f248(x41062,x41063),x41064)))),f312(a126,f2(a853))),f253(x41062,x41063,x41061,x41065,x41064))
% 155.90/155.60 [4293]E(f159(x42931,x42932,f312(f312(f7(x42931,f857(x42932),f857(x42932)),f312(f312(f18(x42931,f857(x42932),f861(f857(x42932),f857(x42932))),f312(f312(f8(a846,f861(f857(x42932),f861(f857(x42932),f857(x42932))),x42931),f108(f857(x42932))),x42933)),f312(f312(f8(x42932,f857(x42932),x42931),f219(x42932)),x42934))),f192(x42932)),x42935),f312(f312(f150(x42931,x42932),x42934),f312(f132(x42931,x42933),x42935)))
% 155.90/155.60 [4495]~E(f312(f312(f312(f81(x44951,f857(x44952)),x44953),x44954),f312(f219(x44952),x44955)),f312(f16(f857(x44952),x44951),f192(x44952)))
% 155.90/155.60 [3608]E(f312(f312(f169(x36081),x36082),f312(f312(f150(x36083,x36081),x36084),x36085)),f312(f312(f150(x36083,x36081),x36084),f312(f312(f169(x36083),x36082),x36085)))
% 155.90/155.60 [3609]E(f312(f312(f134(x36091),x36092),f312(f312(f150(x36093,x36091),x36094),x36095)),f312(f312(f150(x36093,x36091),x36094),f312(f312(f134(x36093),x36092),x36095)))
% 155.90/155.60 [3640]E(f312(f312(f150(x36401,x36402),x36403),f312(f312(f147(x36401),x36404),x36405)),f312(f312(f147(x36402),f312(x36403,x36404)),f312(f312(f150(x36401,x36402),x36403),x36405)))
% 155.90/155.60 [3698]E(f312(f290(x36981,x36982,x36983),f312(f312(f289(x36981),x36984),x36985)),f312(f312(f289(x36982),f312(x36983,x36984)),f312(f290(x36981,x36982,x36983),x36985)))
% 155.90/155.60 [3764]E(f312(f312(f177(x37641,x37642),f312(f312(f169(x37641),x37643),x37644)),f312(f312(f169(x37642),x37643),x37645)),f312(f312(f169(f860(x37641,x37642)),x37643),f312(f312(f177(x37641,x37642),x37644),x37645)))
% 155.90/155.60 [3765]E(f312(f312(f177(x37651,x37652),f312(f312(f134(x37651),x37653),x37654)),f312(f312(f134(x37652),x37653),x37655)),f312(f312(f134(f860(x37651,x37652)),x37653),f312(f312(f177(x37651,x37652),x37654),x37655)))
% 155.90/155.60 [3780]E(f312(f312(f155(x37801,f312(f312(f147(x37801),x37802),x37803)),f312(a126,x37804)),x37805),f312(f312(f147(x37801),x37802),f312(f312(f155(x37801,x37803),x37804),x37805)))
% 155.90/155.60 [3783]E(f312(f221(f857(x37831),x37832,f192(x37831),x37833),f312(f312(f16(f857(x37832),x37834),f192(x37832)),x37835)),f192(x37831))
% 155.90/155.60 [3785]E(f312(f312(f129(x37851),f312(f312(f150(x37852,x37851),x37853),x37854)),f312(f312(f150(x37852,x37851),x37853),x37855)),f312(f312(f150(x37852,x37851),x37853),f312(f312(f129(x37852),x37854),x37855)))
% 155.90/155.60 [3790]E(f312(f312(x37901,x37902),f312(f312(f241(x37903,x37904,x37901),x37902),x37905)),f312(f312(f241(x37903,x37904,x37901),x37902),f312(a126,x37905)))
% 155.90/155.60 [3818]E(f160(x38181,x38182,x38183,f312(f312(f147(x38181),x38184),x38185)),f312(f312(f129(x38182),f312(x38183,x38184)),f160(x38181,x38182,x38183,x38185)))
% 155.90/155.60 [3830]E(f312(f312(f267(x38301,x38302,x38303),f312(f265(x38302,x38301),x38304)),f312(f265(x38303,x38302),x38305)),f312(f265(x38303,x38301),f312(f312(f267(x38303,x38302,x38301),x38305),x38304)))
% 155.90/155.60 [3864]E(f312(f312(f312(f184(f854(x38641),f854(x38641)),x38642),f164(x38641)),f312(f312(f150(x38643,x38641),x38644),x38645)),f312(f312(f150(x38643,x38641),x38644),f312(f312(f312(f184(f854(x38643),f854(x38643)),x38642),f164(x38643)),x38645)))
% 155.90/155.60 [3865]E(f312(f312(f251(x38651,x38652,x38651,x38653),f312(f239(x38652,x38651),x38654)),x38655),f312(x38655,x38654))
% 155.90/155.60 [3893]E(f151(x38931,x38932,f312(f312(f150(x38933,x38931),x38934),x38935)),f151(x38933,f312(f82(x38931,a853,x38933,x38932),x38934),x38935))
% 155.90/155.60 [3954]E(f312(f312(f82(f857(x39541),f857(x39542),x39543,f312(f193(x39541,x39542),x39544)),f312(f16(f857(x39541),x39543),f192(x39541))),x39545),f192(x39542))
% 155.90/155.60 [3955]E(f172(f860(x39551,x39552),f312(f82(x39552,a846,f860(x39551,x39552),x39553),f248(x39551,x39552)),f312(f312(f177(x39551,x39552),x39554),x39555)),f312(f312(f177(x39551,x39552),x39554),f172(x39552,x39553,x39555)))
% 155.90/155.60 [3960]E(f312(f290(x39601,x39602,f312(f312(f8(x39603,x39602,x39601),x39604),x39605)),f235(f861(x39601,a846))),f312(f290(x39603,x39602,x39604),f312(f290(x39601,x39603,x39605),f235(f861(x39601,a846)))))
% 155.90/155.60 [3973]E(f172(f860(x39731,x39732),f312(f82(x39731,a846,f860(x39731,x39732),x39733),f246(x39731,x39732)),f312(f312(f177(x39731,x39732),x39734),x39735)),f312(f312(f177(x39731,x39732),f172(x39731,x39733,x39734)),x39735))
% 155.90/155.60 [3994]E(f312(f312(f124(f861(x39941,a846)),f312(f291(x39941,x39942,x39943),f312(f312(f289(x39942),x39944),f189(f861(x39942,a846))))),f312(f291(x39941,x39942,x39943),x39945)),f312(f291(x39941,x39942,x39943),f312(f312(f289(x39942),x39944),x39945)))
% 155.90/155.60 [4054]E(f312(f312(f129(f860(x40541,x40542)),f312(f312(f150(x40542,f860(x40541,x40542)),f312(f239(x40541,x40542),x40543)),x40544)),f68(x40541,x40542,x40545,x40544)),f68(x40541,x40542,f312(f312(f147(x40541),x40543),x40545),x40544))
% 155.90/155.60 [4055]E(f312(f312(f150(x40551,x40552),x40553),f172(x40551,f312(f82(x40552,a846,x40551,x40554),x40553),x40555)),f172(x40552,x40554,f312(f312(f150(x40551,x40552),x40553),x40555)))
% 155.90/155.60 [4062]E(f312(f138(x40621,x40622,f312(f7(x40622,x40621,x40621),f312(f7(x40621,x40622,x40621),x40623)),x40624),f312(f165(x40622),f312(f165(x40622),x40625))),f312(f138(x40621,x40622,x40623,x40624),x40625))
% 155.90/155.60 [4063]E(f312(f312(f312(f81(x40631,f857(x40632)),f183(x40631,x40632,x40633,x40634)),x40635),f312(x40633,x40635)),f183(x40631,x40632,x40633,f312(f312(f289(x40631),x40635),x40634)))
% 155.90/155.60 [4073]E(f312(f299(x40731,x40732,x40733,f312(f16(x40732,x40731),x40734),f312(f16(x40732,x40733),x40734)),x40735),x40734)
% 155.90/155.60 [4129]E(f312(f221(f854(x41291),x41291,f159(x41292,x41291,x41293,x41294),f312(f312(f7(x41291,f854(x41291),f854(x41291)),f147(x41291)),f159(x41292,x41291,x41293,x41294))),f312(x41293,x41295)),f159(x41292,x41291,x41293,f312(f312(f147(x41292),x41295),x41294)))
% 155.90/155.60 [4166]P22(f312(f312(f227(f861(x41661,a846)),f312(f290(x41662,x41661,x41663),f312(f312(f115(f861(x41662,a846)),x41664),x41665))),f312(f312(f115(f861(x41661,a846)),f312(f290(x41662,x41661,x41663),x41664)),f312(f290(x41662,x41661,x41663),x41665))))
% 155.90/155.60 [4167]P22(f312(f312(f227(f861(x41671,a846)),f312(f264(x41672,x41671,x41673),f312(f312(f115(f861(x41672,a846)),x41674),x41675))),f312(f312(f115(f861(x41671,a846)),f312(f264(x41672,x41671,x41673),x41674)),f312(f264(x41672,x41671,x41673),x41675))))
% 155.90/155.60 [4269]E(f312(f248(x42691,x42692),f312(f250(x42693,x42691,x42692,x42692,x42694,f39(x42692)),x42695)),f312(f248(x42693,x42692),x42695))
% 155.90/155.60 [4270]E(f312(f246(x42701,x42702),f312(f250(x42701,x42701,x42703,x42702,f39(x42701),x42704),x42705)),f312(f246(x42701,x42703),x42705))
% 155.90/155.60 [4348]P18(x43481,x43482,f312(f312(f289(f852(x43481)),f312(f312(f312(f100(x43481),f312(f312(f7(x43481,f861(a848,a848),f861(a848,a846)),f312(f312(f8(f861(a848,a846),f861(f861(a848,a848),f861(a848,a846)),x43481),f8(a848,a846,a848)),x43483)),f312(f312(f18(a848,a853,a848),f312(f312(f7(a848,a851,f861(a853,a848)),a201),x43484)),x43485))),f28(x43484,x43485)),x43483)),f189(f861(f852(x43481),a846))))
% 155.90/155.60 [4350]E(f312(f138(f861(x43501,f857(x43502)),f860(x43501,x43502),f312(f312(f8(f861(x43501,f861(x43502,f861(x43501,f857(x43502)))),f861(f860(x43501,x43502),f861(x43501,f857(x43502))),f861(x43501,f857(x43502))),f249(x43501,x43502,f861(x43501,f857(x43502)))),f312(f312(f7(f861(x43501,f857(x43502)),f861(x43502,f857(x43502)),f861(x43501,f861(x43502,f861(x43501,f857(x43502))))),f312(f312(f8(f861(x43501,f861(f861(x43502,f857(x43502)),f861(x43502,f861(x43501,f857(x43502))))),f861(f861(x43502,f857(x43502)),f861(x43501,f861(x43502,f861(x43501,f857(x43502))))),f861(x43501,f857(x43502))),f7(x43501,f861(x43502,f857(x43502)),f861(x43502,f861(x43501,f857(x43502))))),f312(f312(f8(f861(x43501,f861(f857(x43502),f861(x43501,f857(x43502)))),f861(x43501,f861(f861(x43502,f857(x43502)),f861(x43502,f861(x43501,f857(x43502))))),f861(x43501,f857(x43502))),f312(f8(f861(f857(x43502),f861(x43501,f857(x43502))),f861(f861(x43502,f857(x43502)),f861(x43502,f861(x43501,f857(x43502)))),x43501),f8(f857(x43502),f861(x43501,f857(x43502)),x43502))),f81(x43501,f857(x43502))))),f219(x43502))),x43503),f312(f312(f177(x43501,x43502),x43504),x43505)),f182(x43501,x43502,x43503,x43504,x43505))
% 155.90/155.60 [4352]P18(x43521,x43522,f312(f312(f289(f852(x43521)),f312(f312(f312(f100(x43521),f312(f312(f7(x43521,f861(a848,a846),f861(a848,a846)),f312(f312(f8(f861(a848,f861(a846,a846)),f861(f861(a848,a846),f861(a848,a846)),x43521),f18(a848,a846,a846)),f312(f312(f8(f861(a848,a846),f861(a848,f861(a846,a846)),x43521),f312(f8(a846,f861(a846,a846),a848),a310)),x43523))),f312(f312(f8(a846,a846,a848),a307),x43524))),f35(x43524,x43525)),x43523)),f189(f861(f852(x43521),a846))))
% 155.90/155.60 [3501]E(f105(x35011,x35012,f312(f312(f312(f100(x35011),x35013),x35014),x35015)),f2(a853))
% 155.90/155.60 [3593]E(f312(f312(f312(f312(f81(x35931,x35932),x35933),x35934),x35935),x35934),x35935)
% 155.90/155.60 [3819]E(f312(f312(f50(x38191,f861(x38192,a846)),f312(f312(f289(x38191),x38193),x38194)),x38195),f312(f312(f124(f861(x38192,a846)),f312(x38195,x38193)),f312(f312(f50(x38191,f861(x38192,a846)),x38194),x38195)))
% 155.90/155.60 [3820]E(f312(f312(f51(x38201,f861(x38202,a846)),f312(f312(f289(x38201),x38203),x38204)),x38205),f312(f312(f115(f861(x38202,a846)),f312(x38205,x38203)),f312(f312(f51(x38201,f861(x38202,a846)),x38204),x38205)))
% 155.90/155.60 [3886]E(f312(f312(f124(f861(x38861,a846)),f312(f290(x38862,x38861,x38863),x38864)),f312(f290(x38862,x38861,x38863),x38865)),f312(f290(x38862,x38861,x38863),f312(f312(f124(f861(x38862,a846)),x38864),x38865)))
% 155.90/155.60 [3887]E(f312(f312(f21(f861(x38871,a846)),f312(f291(x38871,x38872,x38873),x38874)),f312(f291(x38871,x38872,x38873),x38875)),f312(f291(x38871,x38872,x38873),f312(f312(f21(f861(x38872,a846)),x38874),x38875)))
% 155.90/155.60 [3888]E(f312(f312(f124(f861(x38881,a846)),f312(f291(x38881,x38882,x38883),x38884)),f312(f291(x38881,x38882,x38883),x38885)),f312(f291(x38881,x38882,x38883),f312(f312(f124(f861(x38882,a846)),x38884),x38885)))
% 155.90/155.60 [3889]E(f312(f312(f115(f861(x38891,a846)),f312(f291(x38891,x38892,x38893),x38894)),f312(f291(x38891,x38892,x38893),x38895)),f312(f291(x38891,x38892,x38893),f312(f312(f115(f861(x38892,a846)),x38894),x38895)))
% 155.90/155.60 [3890]E(f312(f312(f124(f861(x38901,a846)),f312(f264(x38902,x38901,x38903),x38904)),f312(f264(x38902,x38901,x38903),x38905)),f312(f264(x38902,x38901,x38903),f312(f312(f124(f861(x38902,a846)),x38904),x38905)))
% 155.90/155.60 [3892]E(f183(x38921,x38922,f183(x38921,x38922,x38923,x38924),x38925),f183(x38921,x38922,x38923,f312(f312(f115(f861(x38921,a846)),x38924),x38925)))
% 155.90/155.60 [3951]E(f312(f312(f155(x39511,f312(f312(f129(x39511),x39512),f312(f312(f147(x39511),x39513),x39514))),f312(f190(f854(x39511)),x39512)),x39515),f312(f312(f129(x39511),x39512),f312(f312(f147(x39511),x39515),x39514)))
% 155.90/155.60 [3958]E(f312(f312(f51(x39581,f861(x39582,a846)),x39583),f312(f312(f8(f861(x39582,a846),f861(x39582,a846),x39581),f312(f289(x39582),x39584)),x39585)),f312(f312(f289(x39582),x39584),f312(f312(f51(x39581,f861(x39582,a846)),x39583),x39585)))
% 155.90/155.60 [4028]E(f183(x40281,x40282,f312(f312(f312(f81(x40281,f857(x40282)),x40283),x40284),f312(f219(x40282),x40285)),f312(f88(f861(x40281,a846)),f312(f312(f289(x40281),x40284),f189(f861(x40281,a846))))),f183(x40281,x40282,x40283,f312(f88(f861(x40281,a846)),f312(f312(f289(x40281),x40284),f189(f861(x40281,a846))))))
% 155.90/155.60 [4119]E(f312(f312(f150(x41191,x41192),x41193),f312(f132(x41191,f312(f82(x41192,a846,x41191,x41194),x41193)),x41195)),f312(f132(x41192,x41194),f312(f312(f150(x41191,x41192),x41193),x41195)))
% 155.90/155.60 [4123]E(f312(f190(f854(x41231)),f312(f132(x41231,x41232),f312(f312(f150(x41233,x41231),x41234),x41235))),f312(f190(f854(x41233)),f312(f132(x41233,f312(f82(x41231,a846,x41233,x41232),x41234)),x41235)))
% 155.90/155.60 [4261]E(f312(f312(f124(f861(x42611,a846)),f312(f312(f21(f861(x42611,a846)),f179(x42611,x42612,x42613)),f312(f233(x42611),f312(f312(f7(x42611,f861(x42611,a846),a846),f314(x42611)),f312(f312(f21(f861(x42611,a846)),x42614),f179(x42611,x42612,x42615)))))),f312(f233(x42611),f312(f312(f7(x42611,f861(x42611,a846),a846),f314(x42611)),f312(f312(f115(f861(x42611,a846)),x42614),f179(x42611,x42612,x42615))))),f179(x42611,x42612,f85(x42611,f857(x42612),x42613,x42615,x42614)))
% 155.90/155.60 [4329]E(f312(f152(f854(f860(x43291,x43292)),x43292,f127(f860(x43291,x43292)),f312(f312(f7(x43292,f861(f854(x43292),f854(f860(x43291,x43292))),f861(f854(x43292),f854(f860(x43291,x43292)))),f312(f312(f8(f861(f854(f860(x43291,x43292)),f854(f860(x43291,x43292))),f861(f861(f854(x43292),f854(f860(x43291,x43292))),f861(f854(x43292),f854(f860(x43291,x43292)))),x43292),f8(f854(f860(x43291,x43292)),f854(f860(x43291,x43292)),f854(x43292))),f312(f312(f8(f860(x43291,x43292),f861(f854(f860(x43291,x43292)),f854(f860(x43291,x43292))),x43292),f147(f860(x43291,x43292))),f312(f239(x43291,x43292),x43293)))),f312(f177(x43291,x43292),x43294))),x43295),f312(f312(f177(x43291,x43292),f312(f312(f147(x43291),x43293),x43294)),x43295))
% 155.90/155.60 [3814]E(f312(f312(f155(x38141,f312(f312(f155(x38141,x38142),x38143),x38144)),x38143),x38145),f312(f312(f155(x38141,x38142),x38143),x38145))
% 155.90/155.60 [3866]E(f312(f236(x38661,x38662),f312(f312(f289(f860(x38661,x38662)),f312(f312(f239(x38661,x38662),x38663),x38664)),x38665)),f312(f312(f289(x38662),x38664),f312(f236(x38661,x38662),x38665)))
% 155.90/155.60 [3867]E(f312(f238(x38671,x38672),f312(f312(f289(f860(x38671,x38672)),f312(f312(f239(x38671,x38672),x38673),x38674)),x38675)),f312(f312(f289(x38671),x38673),f312(f238(x38671,x38672),x38675)))
% 155.90/155.60 [3944]E(f312(f312(f21(f861(f860(x39441,x39442),a846)),f312(f312(f247(x39441,x39442),x39443),x39444)),f312(f312(f247(x39441,x39442),x39445),x39444)),f312(f312(f247(x39441,x39442),f312(f312(f21(f861(x39441,a846)),x39443),x39445)),x39444))
% 155.90/155.60 [3945]E(f312(f312(f124(f861(f860(x39451,x39452),a846)),f312(f312(f247(x39451,x39452),x39453),x39454)),f312(f312(f247(x39451,x39452),x39455),x39454)),f312(f312(f247(x39451,x39452),f312(f312(f124(f861(x39451,a846)),x39453),x39455)),x39454))
% 155.90/155.60 [3946]E(f312(f312(f115(f861(f860(x39461,x39462),a846)),f312(f312(f247(x39461,x39462),x39463),x39464)),f312(f312(f247(x39461,x39462),x39465),x39464)),f312(f312(f247(x39461,x39462),f312(f312(f115(f861(x39461,a846)),x39463),x39465)),x39464))
% 155.90/155.60 [4008]E(f312(f312(f124(f861(x40081,a846)),f312(f312(f50(x40082,f861(x40081,a846)),x40083),x40084)),f312(f312(f50(x40082,f861(x40081,a846)),x40085),x40084)),f312(f312(f50(x40082,f861(x40081,a846)),f312(f312(f124(f861(x40082,a846)),x40083),x40085)),x40084))
% 155.90/155.60 [4009]E(f312(f312(f115(f861(x40091,a846)),f312(f312(f51(x40092,f861(x40091,a846)),x40093),x40094)),f312(f312(f51(x40092,f861(x40091,a846)),x40095),x40094)),f312(f312(f51(x40092,f861(x40091,a846)),f312(f312(f124(f861(x40092,a846)),x40093),x40095)),x40094))
% 155.90/155.60 [4023]E(f312(f312(f50(x40231,f861(x40232,a846)),x40233),f312(f312(f8(f861(x40232,a846),f861(x40232,a846),x40231),f312(f21(f861(x40232,a846)),x40234)),x40235)),f312(f312(f21(f861(x40232,a846)),x40234),f312(f312(f51(x40231,f861(x40232,a846)),x40233),x40235)))
% 155.90/155.60 [4024]E(f312(f312(f50(x40241,f861(x40242,a846)),x40243),f312(f312(f8(f861(x40242,a846),f861(x40242,a846),x40241),f312(f115(f861(x40242,a846)),x40244)),x40245)),f312(f312(f115(f861(x40242,a846)),x40244),f312(f312(f50(x40241,f861(x40242,a846)),x40243),x40245)))
% 155.90/155.60 [4025]E(f312(f312(f51(x40251,f861(x40252,a846)),x40253),f312(f312(f8(f861(x40252,a846),f861(x40252,a846),x40251),f312(f124(f861(x40252,a846)),x40254)),x40255)),f312(f312(f124(f861(x40252,a846)),x40254),f312(f312(f51(x40251,f861(x40252,a846)),x40253),x40255)))
% 155.90/155.60 [4060]E(f180(x40601,x40602,x40603,f312(f173(x40601,x40602),f312(f165(f860(x40601,x40602)),f312(f312(f177(x40601,x40602),x40604),x40605)))),f182(x40601,x40602,x40603,x40604,x40605))
% 155.90/155.60 [4083]E(f186(f854(x40831),f312(f312(f147(x40831),x40832),x40833),f312(f312(f8(f854(x40831),f854(x40831),a853),f312(f147(x40831),x40834)),f312(f312(f7(a853,x40831,f854(x40831)),f155(x40831,x40833)),x40832)),x40835),f312(f312(f155(x40831,f312(f312(f147(x40831),x40834),x40833)),x40835),x40832))
% 155.90/155.60 [4087]E(f312(f312(f50(x40871,f861(f860(x40872,x40873),a846)),x40874),f312(f312(f8(f861(f860(x40873,x40872),a846),f861(f860(x40872,x40873),a846),x40871),f265(x40873,x40872)),x40875)),f312(f265(x40873,x40872),f312(f312(f50(x40871,f861(f860(x40873,x40872),a846)),x40874),x40875)))
% 155.90/155.60 [4088]E(f312(f312(f51(x40881,f861(f860(x40882,x40883),a846)),x40884),f312(f312(f8(f861(f860(x40883,x40882),a846),f861(f860(x40882,x40883),a846),x40881),f265(x40883,x40882)),x40885)),f312(f265(x40883,x40882),f312(f312(f51(x40881,f861(f860(x40883,x40882),a846)),x40884),x40885)))
% 155.90/155.60 [4140]E(f179(x41401,x41402,f312(f312(f18(x41401,f857(x41403),f857(x41402)),f312(f312(f8(f861(x41403,x41402),f861(f857(x41403),f857(x41402)),x41401),f193(x41403,x41402)),x41404)),x41405)),f179(x41401,x41403,x41405))
% 155.90/155.60 [4193]P22(f312(f312(f227(f861(x41931,a846)),f312(f312(f21(f861(x41931,a846)),f312(f290(x41932,x41931,x41933),x41934)),f312(f290(x41932,x41931,x41933),x41935))),f312(f290(x41932,x41931,x41933),f312(f312(f21(f861(x41932,a846)),x41934),x41935))))
% 155.90/155.60 [4333]E(f312(f152(f854(f860(x43331,x43332)),x43331,f127(f860(x43331,x43332)),f312(f312(f7(x43331,f861(f854(x43331),f854(f860(x43331,x43332))),f861(f854(x43331),f854(f860(x43331,x43332)))),f312(f312(f8(f861(f854(f860(x43331,x43332)),f854(f860(x43331,x43332))),f861(f861(f854(x43331),f854(f860(x43331,x43332))),f861(f854(x43331),f854(f860(x43331,x43332)))),x43331),f8(f854(f860(x43331,x43332)),f854(f860(x43331,x43332)),f854(x43331))),f312(f312(f8(f860(x43331,x43332),f861(f854(f860(x43331,x43332)),f854(f860(x43331,x43332))),x43331),f147(f860(x43331,x43332))),f312(f312(f7(x43331,x43332,f860(x43331,x43332)),f239(x43331,x43332)),x43333)))),f312(f312(f7(f854(x43331),f854(x43332),f854(f860(x43331,x43332))),f177(x43331,x43332)),x43334))),x43335),f312(f312(f177(x43331,x43332),x43335),f312(f312(f147(x43332),x43333),x43334)))
% 155.90/155.60 [4048]E(f312(f312(f124(f861(x40481,a846)),f312(f264(x40482,x40481,x40483),x40484)),f312(f264(x40482,x40481,x40485),x40484)),f312(f264(x40482,x40481,f312(f312(f124(f861(f860(x40482,x40481),a846)),x40483),x40485)),x40484))
% 155.90/155.60 [4090]E(f312(f312(f129(f860(x40901,x40902)),f312(f312(f177(x40901,x40902),x40903),f312(f312(f169(x40902),f312(f190(f854(x40901)),x40903)),x40904))),f312(f312(f177(x40901,x40902),x40905),f312(f312(f134(x40902),f312(f190(f854(x40901)),x40903)),x40904))),f312(f312(f177(x40901,x40902),f312(f312(f129(x40901),x40903),x40905)),x40904))
% 155.90/155.60 [4196]E(f312(f312(f247(x41961,x41962),x41963),f312(f312(f18(x41961,f861(x41962,a846),f861(x41962,a846)),f312(f312(f8(f861(x41962,a846),f861(f861(x41962,a846),f861(x41962,a846)),x41961),f21(f861(x41962,a846))),x41964)),x41965)),f312(f312(f21(f861(f860(x41961,x41962),a846)),f312(f312(f247(x41961,x41962),x41963),x41964)),f312(f312(f247(x41961,x41962),x41963),x41965)))
% 155.90/155.60 [4197]E(f312(f312(f247(x41971,x41972),x41973),f312(f312(f18(x41971,f861(x41972,a846),f861(x41972,a846)),f312(f312(f8(f861(x41972,a846),f861(f861(x41972,a846),f861(x41972,a846)),x41971),f124(f861(x41972,a846))),x41974)),x41975)),f312(f312(f124(f861(f860(x41971,x41972),a846)),f312(f312(f247(x41971,x41972),x41973),x41974)),f312(f312(f247(x41971,x41972),x41973),x41975)))
% 155.90/155.60 [4198]E(f312(f312(f247(x41981,x41982),x41983),f312(f312(f18(x41981,f861(x41982,a846),f861(x41982,a846)),f312(f312(f8(f861(x41982,a846),f861(f861(x41982,a846),f861(x41982,a846)),x41981),f115(f861(x41982,a846))),x41984)),x41985)),f312(f312(f115(f861(f860(x41981,x41982),a846)),f312(f312(f247(x41981,x41982),x41983),x41984)),f312(f312(f247(x41981,x41982),x41983),x41985)))
% 155.90/155.60 [4202]E(f312(f312(f50(x42021,f861(x42022,a846)),x42023),f312(f312(f7(x42021,f861(x42022,a846),f861(x42022,a846)),f312(f312(f8(f861(x42022,a846),f861(f861(x42022,a846),f861(x42022,a846)),x42021),f21(f861(x42022,a846))),x42024)),x42025)),f312(f312(f21(f861(x42022,a846)),f312(f312(f50(x42021,f861(x42022,a846)),x42023),x42024)),x42025))
% 155.90/155.60 [4203]E(f312(f312(f50(x42031,f861(x42032,a846)),x42033),f312(f312(f7(x42031,f861(x42032,a846),f861(x42032,a846)),f312(f312(f8(f861(x42032,a846),f861(f861(x42032,a846),f861(x42032,a846)),x42031),f115(f861(x42032,a846))),x42034)),x42035)),f312(f312(f115(f861(x42032,a846)),f312(f312(f50(x42031,f861(x42032,a846)),x42033),x42034)),x42035))
% 155.90/155.60 [4204]E(f312(f312(f51(x42041,f861(x42042,a846)),x42043),f312(f312(f7(x42041,f861(x42042,a846),f861(x42042,a846)),f312(f312(f8(f861(x42042,a846),f861(f861(x42042,a846),f861(x42042,a846)),x42041),f124(f861(x42042,a846))),x42044)),x42045)),f312(f312(f124(f861(x42042,a846)),f312(f312(f51(x42041,f861(x42042,a846)),x42043),x42044)),x42045))
% 155.90/155.60 [4208]E(f312(f312(f50(x42081,f861(x42082,a846)),x42083),f312(f312(f18(x42081,f861(x42082,a846),f861(x42082,a846)),f312(f312(f8(f861(x42082,a846),f861(f861(x42082,a846),f861(x42082,a846)),x42081),f124(f861(x42082,a846))),x42084)),x42085)),f312(f312(f124(f861(x42082,a846)),f312(f312(f50(x42081,f861(x42082,a846)),x42083),x42084)),f312(f312(f50(x42081,f861(x42082,a846)),x42083),x42085)))
% 155.90/155.60 [4209]E(f312(f312(f51(x42091,f861(x42092,a846)),x42093),f312(f312(f18(x42091,f861(x42092,a846),f861(x42092,a846)),f312(f312(f8(f861(x42092,a846),f861(f861(x42092,a846),f861(x42092,a846)),x42091),f115(f861(x42092,a846))),x42094)),x42095)),f312(f312(f115(f861(x42092,a846)),f312(f312(f51(x42091,f861(x42092,a846)),x42093),x42094)),f312(f312(f51(x42091,f861(x42092,a846)),x42093),x42095)))
% 155.90/155.60 [4223]E(f312(f312(f50(x42231,f861(x42232,a846)),x42233),f312(f312(f18(x42231,f861(x42232,a846),f861(x42232,a846)),f312(f312(f8(f861(x42232,a846),f861(f861(x42232,a846),f861(x42232,a846)),x42231),f124(f861(x42232,a846))),x42234)),x42235)),f312(f312(f124(f861(x42232,a846)),f48(f861(x42232,a846),f312(f290(x42231,f861(x42232,a846),x42234),x42233))),f48(f861(x42232,a846),f312(f290(x42231,f861(x42232,a846),x42235),x42233))))
% 155.90/155.60 [4224]E(f312(f312(f51(x42241,f861(x42242,a846)),x42243),f312(f312(f18(x42241,f861(x42242,a846),f861(x42242,a846)),f312(f312(f8(f861(x42242,a846),f861(f861(x42242,a846),f861(x42242,a846)),x42241),f115(f861(x42242,a846))),x42244)),x42245)),f312(f312(f115(f861(x42242,a846)),f49(f861(x42242,a846),f312(f290(x42241,f861(x42242,a846),x42244),x42243))),f49(f861(x42242,a846),f312(f290(x42241,f861(x42242,a846),x42245),x42243))))
% 155.90/155.60 [4257]E(f312(f312(f134(x42571),f312(f190(f854(x42571)),f172(x42571,x42572,f312(f312(f150(x42573,x42571),x42574),x42575)))),f312(f312(f150(x42573,x42571),x42574),x42575)),f312(f312(f150(x42573,x42571),x42574),f312(f312(f134(x42573),f312(f190(f854(x42573)),f172(x42573,f312(f82(x42571,a846,x42573,x42572),x42574),x42575))),x42575)))
% 155.90/155.60 [4130]E(f312(f312(f129(f860(x41301,x41302)),f312(f312(f177(x41301,x41302),f312(f312(f169(x41301),f312(f190(f854(x41302)),x41303)),x41304)),x41303)),f312(f312(f177(x41301,x41302),f312(f312(f134(x41301),f312(f190(f854(x41302)),x41303)),x41304)),x41305)),f312(f312(f177(x41301,x41302),x41304),f312(f312(f129(x41302),x41303),x41305)))
% 155.90/155.60 [4249]E(f94(x42491,f312(f312(f18(x42491,a846,a846),f312(f312(f8(a846,f861(a846,a846),x42491),a310),f312(f312(f7(x42491,f861(x42491,a846),a846),f314(x42491)),x42492))),f312(f312(f7(x42491,x42493,a846),f312(f312(f8(x42493,f861(x42493,a846),x42491),a309),x42494)),x42495))),f312(f86(x42491,x42493,x42492,x42494),x42495))
% 155.90/155.60 [4299]E(f312(f312(f95(a1,x42991),f312(f117(a1),f312(f312(f89(a1),x42992),a111))),f312(f312(f18(a1,x42991,x42991),f312(f312(f7(a1,x42991,f861(x42991,x42991)),f312(f312(f8(a846,f861(x42991,f861(x42991,x42991)),a1),f108(x42991)),a194)),f186(x42991,x42993,x42994,x42995))),f312(f312(f8(a853,x42991,a1),x42994),f312(f312(f7(a1,a853,a853),f312(f312(f8(a853,f861(a853,a853),a1),f89(a853)),a118)),x42995)))),f186(x42991,x42993,x42994,f312(f312(f89(a853),f312(f117(a853),x42992)),x42995)))
% 155.90/155.60 [4330]E(f312(f173(x43301,x43302),f312(f312(f150(f860(x43301,x43303),f860(x43301,x43302)),f312(f249(x43301,x43303,f860(x43301,x43302)),f312(f312(f7(x43301,f861(x43303,x43302),f861(x43303,f860(x43301,x43302))),f312(f312(f8(f861(x43302,f860(x43301,x43302)),f861(f861(x43303,x43302),f861(x43303,f860(x43301,x43302))),x43301),f8(x43302,f860(x43301,x43302),x43303)),f239(x43301,x43302))),x43304))),x43305)),f312(f82(f857(x43303),f857(x43302),x43301,f312(f193(x43303,x43302),x43304)),f312(f173(x43301,x43303),x43305)))
% 155.90/155.60 [4292]E(f179(x42921,x42922,f312(f312(f18(x42921,f857(x42922),f857(x42922)),f312(f312(f18(x42921,f857(x42922),f861(f857(x42922),f857(x42922))),f312(f312(f8(a846,f861(f857(x42922),f861(f857(x42922),f857(x42922))),x42921),f108(f857(x42922))),x42923)),x42924)),x42925)),f312(f312(f124(f861(x42921,a846)),f312(f312(f115(f861(x42921,a846)),f179(x42921,x42922,x42924)),f312(f233(x42921),x42923))),f312(f312(f115(f861(x42921,a846)),f179(x42921,x42922,x42925)),f312(f233(x42921),f312(f312(f8(a846,a846,x42921),a307),x42923)))))
% 155.90/155.60 [4328]E(f312(f312(f95(a1,x43281),f312(f117(a1),f312(f312(f89(a1),x43282),a111))),f312(f312(f18(a1,x43281,x43281),f312(f312(f7(a1,x43281,f861(x43281,x43281)),f312(f312(f8(a846,f861(x43281,f861(x43281,x43281)),a1),f108(x43281)),a194)),f312(f185(x43281,x43283,x43284),x43285))),f312(f312(f18(a1,x43281,x43281),f312(f312(f8(a853,f861(x43281,x43281),a1),x43284),f312(f312(f7(a1,a853,a853),f312(f312(f8(a853,f861(a853,a853),a1),f89(a853)),a118)),x43285))),f312(f312(f8(a853,x43281,a1),f185(x43281,x43283,x43284)),f312(f312(f7(a1,a853,a853),f312(f312(f8(a853,f861(a853,a853),a1),f89(a853)),a118)),x43285))))),f312(f185(x43281,x43283,x43284),f312(f312(f89(a853),f312(f117(a853),x43282)),x43285)))
% 155.90/155.60 [4376]E(f312(f233(f860(x43761,x43762)),f312(f249(x43761,x43762,a846),f312(f312(f8(f861(x43762,f861(x43763,a846)),f861(x43762,a846),x43761),f312(f8(f861(x43763,a846),a846,x43762),f96(x43763))),f312(f312(f7(x43761,f861(x43762,f861(x43763,a846)),f861(x43762,f861(x43763,a846))),f312(f312(f8(f861(f861(x43763,a846),f861(x43763,a846)),f861(f861(x43762,f861(x43763,a846)),f861(x43762,f861(x43763,a846))),x43761),f8(f861(x43763,a846),f861(x43763,a846),x43762)),f312(f312(f8(f861(x43763,f861(a846,a846)),f861(f861(x43763,a846),f861(x43763,a846)),x43761),f18(x43763,a846,a846)),f312(f312(f8(f861(x43763,a846),f861(x43763,f861(a846,a846)),x43761),f312(f8(a846,f861(a846,a846),x43763),a310)),f312(f312(f7(x43761,f861(f860(x43761,x43763),a846),f861(x43763,a846)),f312(f312(f8(f861(x43763,f861(f861(f860(x43761,x43763),a846),a846)),f861(f861(f860(x43761,x43763),a846),f861(x43763,a846)),x43761),f7(x43763,f861(f860(x43761,x43763),a846),a846)),f312(f312(f8(f861(x43763,f860(x43761,x43763)),f861(x43763,f861(f861(f860(x43761,x43763),a846),a846)),x43761),f312(f8(f860(x43761,x43763),f861(f861(f860(x43761,x43763),a846),a846),x43763),f314(f860(x43761,x43763)))),f239(x43761,x43763)))),x43764))))),f312(f312(f7(x43762,f861(f860(x43763,x43762),a846),f861(x43763,a846)),f312(f312(f8(f861(x43763,f861(f861(f860(x43763,x43762),a846),a846)),f861(f861(f860(x43763,x43762),a846),f861(x43763,a846)),x43762),f7(x43763,f861(f860(x43763,x43762),a846),a846)),f312(f312(f8(f861(x43763,f860(x43763,x43762)),f861(x43763,f861(f861(f860(x43763,x43762),a846),a846)),x43762),f312(f8(f860(x43763,x43762),f861(f861(f860(x43763,x43762),a846),a846),x43763),f314(f860(x43763,x43762)))),f312(f7(x43763,x43762,f860(x43763,x43762)),f239(x43763,x43762))))),x43765))))),f312(f312(f267(x43761,x43763,x43762),x43764),x43765))
% 155.90/155.60 [4477]~E(f32(x44771,x44772,x44773),f33(x44774,x44775,x44776))
% 155.90/155.60 [4480]~E(f31(x44801,x44802,x44803),f33(x44804,x44805,x44806))
% 155.90/155.60 [4481]~E(f31(x44811,x44812,x44813),f32(x44814,x44815,x44816))
% 155.90/155.60 [3974]E(f213(x39741,x39742,x39743,x39744,f209(x39741,x39742,x39745,x39746)),f312(f312(x39744,x39745),x39746))
% 155.90/155.60 [3975]E(f214(x39751,x39752,x39753,x39754,f209(x39751,x39752,x39755,x39756)),f312(f312(x39754,x39755),x39756))
% 155.90/155.60 [4117]E(f182(x41171,x41172,f180(x41171,x41172,x41173,x41174),x41175,x41176),f180(x41171,x41172,x41173,f182(x41171,x41172,x41174,x41175,x41176)))
% 155.90/155.60 [4239]E(f312(f82(f860(x42391,x42392),x42392,f860(x42393,x42394),f248(x42391,x42392)),f250(x42393,x42391,x42394,x42392,x42395,x42396)),f312(f82(x42394,x42392,f860(x42393,x42394),x42396),f248(x42393,x42394)))
% 155.90/155.60 [4240]E(f312(f82(f860(x42401,x42402),x42401,f860(x42403,x42404),f246(x42401,x42402)),f250(x42403,x42401,x42404,x42402,x42405,x42406)),f312(f82(x42403,x42401,f860(x42403,x42404),x42405),f246(x42403,x42404)))
% 155.90/155.60 [3841]E(f312(f312(f82(x38411,x38412,x38413,x38414),x38415),x38416),f312(x38414,f312(x38415,x38416)))
% 155.90/155.60 [4036]E(f215(x40361,x40362,x40363,x40364,f209(x40361,x40362,x40365,x40366)),f312(f312(f89(a853),f312(f312(f89(a853),f312(x40363,x40365)),f312(x40364,x40366))),f312(a126,f2(a853))))
% 155.90/155.60 [3636]E(f312(f312(f249(x36361,x36362,x36363),x36364),f312(f312(f239(x36361,x36362),x36365),x36366)),f312(f312(x36364,x36365),x36366))
% 155.90/155.60 [3695]E(f312(f312(f312(f8(x36951,x36952,x36953),x36954),x36955),x36956),f312(x36954,f312(x36955,x36956)))
% 155.90/155.60 [3696]E(f312(f312(f312(f7(x36961,x36962,x36963),x36964),x36965),x36966),f312(f312(x36964,x36966),x36965))
% 155.90/155.60 [3714]E(f312(f312(f312(f18(x37141,x37142,x37143),x37144),x37145),x37146),f312(f312(x37144,x37146),f312(x37145,x37146)))
% 155.90/155.60 [3736]E(f312(f152(x37361,x37362,x37363,x37364),f312(f312(f147(x37362),x37365),x37366)),f312(f312(x37364,x37365),x37366))
% 155.90/155.60 [3845]E(f312(f312(f147(f860(x38451,x38452)),f312(f312(f239(x38451,x38452),x38453),x38454)),f312(f312(f177(x38451,x38452),x38455),x38456)),f312(f312(f177(x38451,x38452),f312(f312(f147(x38451),x38453),x38455)),f312(f312(f147(x38452),x38454),x38456)))
% 155.90/155.60 [3847]E(f312(f312(f150(x38471,x38472),x38473),f312(f312(f155(x38471,x38474),x38475),x38476)),f312(f312(f155(x38472,f312(f312(f150(x38471,x38472),x38473),x38474)),x38475),f312(x38473,x38476)))
% 155.90/155.60 [3891]E(f312(f138(x38911,x38912,x38913,x38914),f312(f312(f147(x38912),x38915),x38916)),f312(f138(x38911,x38912,x38913,f312(f312(x38913,x38914),x38915)),x38916))
% 155.90/155.60 [3915]E(f252(x39151,x39152,x39153,x39154,f312(f312(f239(x39151,x39152),x39155),x39156)),f312(f312(x39154,x39155),x39156))
% 155.90/155.60 [3999]E(f312(f312(f50(x39991,f861(x39992,a846)),x39993),f312(f82(x39994,f861(x39992,a846),x39991,x39995),x39996)),f312(f312(f50(x39994,f861(x39992,a846)),f312(f290(x39991,x39994,x39996),x39993)),x39995))
% 155.90/155.60 [4051]E(f312(f312(f193(x40511,x40512),x40513),f312(f312(f193(x40514,x40511),x40515),x40516)),f312(f312(f193(x40514,x40512),f312(f82(x40511,x40512,x40514,x40513),x40515)),x40516))
% 155.90/155.60 [4053]E(f312(f312(f150(x40531,x40532),x40533),f312(f312(f150(x40534,x40531),x40535),x40536)),f312(f312(f150(x40534,x40532),f312(f82(x40531,x40532,x40534,x40533),x40535)),x40536))
% 155.90/155.60 [4058]E(f312(f290(x40581,x40582,f312(f82(x40583,x40582,x40581,x40584),x40585)),x40586),f312(f290(x40583,x40582,x40584),f312(f290(x40581,x40583,x40585),x40586)))
% 155.90/155.60 [4059]E(f312(f291(x40591,x40592,f312(f82(x40593,x40592,x40591,x40594),x40595)),x40596),f312(f291(x40591,x40593,x40595),f312(f291(x40593,x40592,x40594),x40596)))
% 155.90/155.60 [4089]E(f180(x40891,x40892,x40893,f312(f312(f312(f81(x40891,f857(x40892)),x40894),x40895),f312(f219(x40892),x40896))),f312(f312(f312(f81(x40891,f857(x40892)),f180(x40891,x40892,x40893,x40894)),x40895),f312(f219(x40892),x40896)))
% 155.90/155.60 [4091]E(f312(f138(x40911,x40912,x40913,f312(f138(x40911,x40912,x40913,x40914),x40915)),x40916),f312(f138(x40911,x40912,x40913,x40914),f312(f312(f129(x40912),x40915),x40916)))
% 155.90/155.60 [4229]E(f312(f250(x42291,x42291,x42292,x42293,f39(x42291),x42294),f312(f312(f239(x42291,x42292),x42295),x42296)),f312(f312(f239(x42291,x42293),x42295),f312(x42294,x42296)))
% 155.90/155.60 [4230]E(f312(f250(x42301,x42302,x42303,x42303,x42304,f39(x42303)),f312(f312(f239(x42301,x42303),x42305),x42306)),f312(f312(f239(x42302,x42303),f312(x42304,x42305)),x42306))
% 155.90/155.60 [4315]E(f312(f312(f150(f860(x43151,x43152),f860(x43151,x43153)),f312(f249(x43151,x43152,f860(x43151,x43153)),f312(f312(f7(x43151,f861(x43152,x43153),f861(x43152,f860(x43151,x43153))),f312(f312(f8(f861(x43153,f860(x43151,x43153)),f861(f861(x43152,x43153),f861(x43152,f860(x43151,x43153))),x43151),f8(x43153,f860(x43151,x43153),x43152)),f239(x43151,x43153))),x43154))),f312(f312(f177(x43151,x43152),x43155),x43156)),f312(f312(f177(x43151,x43153),x43155),f312(f312(f150(x43152,x43153),x43154),x43156)))
% 155.90/155.60 [3701]E(f106(x37011,x37012,x37013,f312(f312(f312(f100(x37011),x37014),x37015),x37016)),f312(f312(f312(x37013,x37014),x37015),x37016))
% 155.90/155.60 [3702]E(f107(x37021,x37022,x37023,f312(f312(f312(f100(x37021),x37024),x37025),x37026)),f312(f312(f312(x37023,x37024),x37025),x37026))
% 155.90/155.60 [3901]E(f312(f312(f82(x39011,x39012,x39013,f312(f16(x39012,x39011),x39014)),x39015),x39016),x39014)
% 155.90/155.60 [3935]E(f312(f290(x39351,x39352,x39353),f312(f290(x39354,x39351,x39355),x39356)),f312(f290(x39354,x39352,f312(f312(f8(x39351,x39352,x39354),x39353),x39355)),x39356))
% 155.90/155.60 [3940]E(f312(f312(f50(x39401,f861(x39402,a846)),f312(f290(x39403,x39401,x39404),x39405)),x39406),f312(f312(f50(x39403,f861(x39402,a846)),x39405),f312(f312(f8(x39401,f861(x39402,a846),x39403),x39406),x39404)))
% 155.90/155.60 [3941]E(f312(f312(f51(x39411,f861(x39412,a846)),f312(f290(x39413,x39411,x39414),x39415)),x39416),f312(f312(f51(x39413,f861(x39412,a846)),x39415),f312(f312(f8(x39411,f861(x39412,a846),x39413),x39416),x39414)))
% 155.90/155.60 [3942]E(f312(f312(f50(x39421,f861(x39422,a846)),x39423),f312(f312(f8(x39424,f861(x39422,a846),x39421),x39425),x39426)),f312(f312(f50(x39424,f861(x39422,a846)),f312(f290(x39421,x39424,x39426),x39423)),x39425))
% 155.90/155.60 [3943]E(f312(f312(f51(x39431,f861(x39432,a846)),x39433),f312(f312(f8(x39434,f861(x39432,a846),x39431),x39435),x39436)),f312(f312(f51(x39434,f861(x39432,a846)),f312(f290(x39431,x39434,x39436),x39433)),x39435))
% 155.90/155.60 [4001]E(f312(f312(f50(x40011,f861(x40012,a846)),x40013),f312(f312(f8(f861(x40014,a846),f861(x40012,a846),x40011),f290(x40014,x40012,x40015)),x40016)),f312(f290(x40014,x40012,x40015),f312(f312(f50(x40011,f861(x40014,a846)),x40013),x40016)))
% 155.90/155.60 [4002]E(f312(f312(f50(x40021,f861(x40022,a846)),x40023),f312(f312(f8(f861(x40024,a846),f861(x40022,a846),x40021),f291(x40022,x40024,x40025)),x40026)),f312(f291(x40022,x40024,x40025),f312(f312(f50(x40021,f861(x40024,a846)),x40023),x40026)))
% 155.90/155.60 [4003]E(f312(f312(f51(x40031,f861(x40032,a846)),x40033),f312(f312(f8(f861(x40034,a846),f861(x40032,a846),x40031),f291(x40032,x40034,x40035)),x40036)),f312(f291(x40032,x40034,x40035),f312(f312(f51(x40031,f861(x40034,a846)),x40033),x40036)))
% 155.90/155.60 [4004]E(f312(f312(f50(x40041,f861(x40042,a846)),x40043),f312(f312(f8(f861(x40044,a846),f861(x40042,a846),x40041),f264(x40044,x40042,x40045)),x40046)),f312(f264(x40044,x40042,x40045),f312(f312(f50(x40041,f861(x40044,a846)),x40043),x40046)))
% 155.90/155.60 [4098]E(f312(f138(x40981,x40982,f312(f7(x40982,x40981,x40981),x40983),x40984),f312(f165(x40982),f312(f312(f147(x40982),x40985),x40986))),f312(f312(x40983,x40985),f312(f138(x40981,x40982,f312(f7(x40982,x40981,x40981),x40983),x40984),f312(f165(x40982),x40986))))
% 155.90/155.60 [4153]E(f312(f312(f18(f860(x41531,x41532),x41532,x41533),f312(f312(f8(x41534,f861(x41532,x41533),f860(x41531,x41532)),x41535),f312(f312(f8(x41531,x41534,f860(x41531,x41532)),x41536),f246(x41531,x41532)))),f248(x41531,x41532)),f312(f249(x41531,x41532,x41533),f312(f312(f8(x41534,f861(x41532,x41533),x41531),x41535),x41536)))
% 155.90/155.60 [4160]E(f312(f138(x41601,x41602,f312(f7(x41602,x41601,x41601),x41603),f312(f138(x41601,x41602,f312(f7(x41602,x41601,x41601),x41603),x41604),f312(f165(x41602),x41605))),f312(f165(x41602),x41606)),f312(f138(x41601,x41602,f312(f7(x41602,x41601,x41601),x41603),x41604),f312(f165(x41602),f312(f312(f129(x41602),x41606),x41605))))
% 155.90/155.60 [4162]E(f312(f312(f150(f860(x41621,x41622),f860(x41623,x41622)),f312(f249(x41621,x41622,f860(x41623,x41622)),f312(f312(f8(x41623,f861(x41622,f860(x41623,x41622)),x41621),f239(x41623,x41622)),x41624))),f312(f312(f177(x41621,x41622),x41625),x41626)),f312(f312(f177(x41623,x41622),f312(f312(f150(x41621,x41623),x41624),x41625)),x41626))
% 155.90/155.60 [4212]P22(f312(f312(f227(f861(x42121,a846)),f312(f264(x42122,x42121,x42123),f312(f312(f51(x42124,f861(x42122,a846)),x42125),x42126))),f312(f312(f51(x42124,f861(x42121,a846)),x42125),f312(f312(f8(f861(x42122,a846),f861(x42121,a846),x42124),f264(x42122,x42121,x42123)),x42126))))
% 155.90/155.60 [4016]E(f312(f312(f177(x40161,x40162),f312(f312(f155(x40161,x40163),x40164),f312(f246(x40161,x40162),x40165))),f312(f312(f155(x40162,x40166),x40164),f312(f248(x40161,x40162),x40165))),f312(f312(f155(f860(x40161,x40162),f312(f312(f177(x40161,x40162),x40163),x40166)),x40164),x40165))
% 155.90/155.60 [4079]E(f312(f312(f124(f861(f860(x40791,x40792),a846)),f312(f312(f267(x40791,x40793,x40792),x40794),x40795)),f312(f312(f267(x40791,x40793,x40792),x40794),x40796)),f312(f312(f267(x40791,x40793,x40792),x40794),f312(f312(f124(f861(f860(x40793,x40792),a846)),x40795),x40796)))
% 155.90/155.60 [4174]E(f312(f312(f289(f860(x41741,x41742)),f312(f312(f239(x41741,x41742),x41743),x41744)),f312(f312(f124(f861(f860(x41741,x41742),a846)),f312(f312(f247(x41741,x41742),x41745),f312(f16(f861(x41742,a846),x41741),f312(f312(f289(x41742),x41744),x41746)))),f312(f312(f247(x41741,x41742),f312(f312(f289(x41741),x41743),x41745)),f312(f16(f861(x41742,a846),x41741),x41746)))),f312(f312(f247(x41741,x41742),f312(f312(f289(x41741),x41743),x41745)),f312(f16(f861(x41742,a846),x41741),f312(f312(f289(x41742),x41744),x41746))))
% 155.90/155.60 [4178]E(f312(f312(f197(x41781,x41782),x41783),f312(f312(f7(x41781,f861(x41784,f857(x41782)),f857(x41782)),f312(f312(f8(f857(x41784),f861(f861(x41784,f857(x41782)),f857(x41782)),x41781),f197(x41784,x41782)),x41785)),x41786)),f312(f312(f197(x41784,x41782),f312(f312(f197(x41781,x41784),x41783),x41785)),x41786))
% 155.90/155.60 [4252]E(f312(f312(f115(f861(x42521,a846)),f312(f291(x42521,x42522,f312(f82(f860(x42522,x42523),x42522,x42521,f246(x42522,x42523)),x42524)),x42525)),f312(f291(x42521,x42523,f312(f82(f860(x42522,x42523),x42523,x42521,f248(x42522,x42523)),x42524)),x42526)),f312(f291(x42521,f860(x42522,x42523),x42524),f312(f312(f247(x42522,x42523),x42525),f312(f16(f861(x42523,a846),x42522),x42526))))
% 155.90/155.60 [3998]E(f312(f312(f312(f81(x39981,x39982),f312(f312(f312(f81(x39981,x39982),x39983),x39984),x39985)),x39984),x39986),f312(f312(f312(f81(x39981,x39982),x39983),x39984),x39986))
% 155.90/155.60 [4103]E(f312(f312(f124(f861(f860(x41031,x41032),a846)),f312(f312(f267(x41031,x41033,x41032),x41034),x41035)),f312(f312(f267(x41031,x41033,x41032),x41036),x41035)),f312(f312(f267(x41031,x41033,x41032),f312(f312(f124(f861(f860(x41031,x41033),a846)),x41034),x41036)),x41035))
% 155.90/155.60 [4237]E(f312(f312(f50(x42371,f861(x42372,a846)),x42373),f312(f312(f7(x42371,f861(x42374,f861(x42372,a846)),f861(x42372,a846)),f312(f312(f8(f861(x42374,a846),f861(f861(x42374,f861(x42372,a846)),f861(x42372,a846)),x42371),f50(x42374,f861(x42372,a846))),x42375)),x42376)),f312(f312(f50(x42374,f861(x42372,a846)),f312(f312(f50(x42371,f861(x42374,a846)),x42373),x42375)),x42376))
% 155.90/155.60 [4238]E(f312(f312(f51(x42381,f861(x42382,a846)),x42383),f312(f312(f7(x42381,f861(x42384,f861(x42382,a846)),f861(x42382,a846)),f312(f312(f8(f861(x42384,a846),f861(f861(x42384,f861(x42382,a846)),f861(x42382,a846)),x42381),f51(x42384,f861(x42382,a846))),x42385)),x42386)),f312(f312(f51(x42384,f861(x42382,a846)),f312(f312(f50(x42381,f861(x42384,a846)),x42383),x42385)),x42386))
% 155.90/155.60 [4287]E(f312(f249(x42871,x42872,f860(x42873,x42874)),f312(f312(f7(x42871,f861(x42872,x42874),f861(x42872,f860(x42873,x42874))),f312(f312(f8(f861(x42874,f860(x42873,x42874)),f861(f861(x42872,x42874),f861(x42872,f860(x42873,x42874))),x42871),f8(x42874,f860(x42873,x42874),x42872)),f312(f312(f8(x42873,f861(x42874,f860(x42873,x42874)),x42871),f239(x42873,x42874)),x42875))),x42876)),f250(x42871,x42873,x42872,x42874,x42875,x42876))
% 155.90/155.60 [4211]E(f312(f312(f312(f81(x42111,f857(x42112)),f183(x42111,x42112,x42113,f312(f312(f21(f861(x42111,a846)),x42114),f312(f312(f289(x42111),x42115),f189(f861(x42111,a846)))))),x42115),x42116),f312(f312(f312(f81(x42111,f857(x42112)),f183(x42111,x42112,x42113,x42114)),x42115),x42116))
% 155.90/155.60 [4311]E(f312(f290(x43111,x43112,f312(f312(f18(x43111,x43112,x43112),f312(f312(f18(x43111,x43112,f861(x43112,x43112)),f312(f312(f8(a846,f861(x43112,f861(x43112,x43112)),x43111),f108(x43112)),x43113)),x43114)),x43115)),x43116),f312(f312(f124(f861(x43112,a846)),f312(f290(x43111,x43112,x43114),f312(f312(f115(f861(x43111,a846)),x43116),f312(f233(x43111),x43113)))),f312(f290(x43111,x43112,x43115),f312(f312(f115(f861(x43111,a846)),x43116),f312(f233(x43111),f312(f312(f8(a846,a846,x43111),a307),x43113))))))
% 155.90/155.60 [4320]E(f312(f290(x43201,f860(x43202,x43203),f312(f312(f18(x43201,x43203,f860(x43202,x43203)),f312(f312(f8(x43202,f861(x43203,f860(x43202,x43203)),x43201),f239(x43202,x43203)),x43204)),x43205)),x43206),f312(f312(f247(x43202,x43203),f312(f290(x43201,x43202,x43204),x43206)),f312(f312(f8(f861(x43201,a846),f861(x43203,a846),x43202),f290(x43201,x43203,x43205)),f312(f312(f7(x43202,f861(x43201,a846),f861(x43201,a846)),f312(f312(f8(f861(x43201,a846),f861(f861(x43201,a846),f861(x43201,a846)),x43202),f115(f861(x43201,a846))),f312(f312(f8(f861(x43202,a846),f861(x43201,a846),x43202),f291(x43201,x43202,x43204)),f312(f312(f7(x43202,f861(x43202,a846),f861(x43202,a846)),f289(x43202)),f189(f861(x43202,a846)))))),x43206))))
% 155.90/155.60 [4271]E(f312(f248(x42711,x42712),f312(f250(x42713,x42711,x42714,x42712,x42715,x42716),x42717)),f312(x42716,f312(f248(x42713,x42714),x42717)))
% 155.90/155.60 [4272]E(f312(f246(x42721,x42722),f312(f250(x42723,x42721,x42724,x42722,x42725,x42726),x42727)),f312(x42725,f312(f246(x42723,x42724),x42727)))
% 155.90/155.60 [3976]E(f312(f312(f177(x39761,x39762),f312(f312(f155(x39761,x39763),x39764),x39765)),f312(f312(f155(x39762,x39766),x39764),x39767)),f312(f312(f155(f860(x39761,x39762),f312(f312(f177(x39761,x39762),x39763),x39766)),x39764),f312(f312(f239(x39761,x39762),x39765),x39767)))
% 155.90/155.60 [4045]E(f312(f312(f312(f251(x40451,x40452,x40453,x40454),x40455),x40456),x40457),f312(f312(f249(x40452,x40453,x40454),x40456),f312(x40455,x40457)))
% 155.90/155.60 [4057]E(f312(f312(f312(f251(x40571,x40572,x40573,x40574),x40575),x40576),x40577),f312(f312(x40576,f312(f246(x40572,x40573),f312(x40575,x40577))),f312(f248(x40572,x40573),f312(x40575,x40577))))
% 155.90/155.60 [4093]E(f182(x40931,x40932,f312(f312(f312(f81(x40931,f857(x40932)),x40933),x40934),f312(f219(x40932),x40935)),x40936,x40937),f182(x40931,x40932,x40933,f312(f312(f147(x40931),x40934),x40936),f312(f312(f147(x40932),x40935),x40937)))
% 155.90/155.60 [4110]E(f312(f82(x41101,x41102,x41103,x41104),f312(f82(x41105,x41101,x41103,x41106),x41107)),f312(f82(x41105,x41102,x41103,f312(f82(x41101,x41102,x41105,x41104),x41106)),x41107))
% 155.90/155.60 [4169]E(f312(f82(f857(x41691),f857(x41692),x41693,f312(f193(x41691,x41692),x41694)),f312(f312(f312(f81(x41693,f857(x41691)),x41695),x41696),f312(f219(x41691),x41697))),f312(f312(f312(f81(x41693,f857(x41692)),f312(f82(f857(x41691),f857(x41692),x41693,f312(f193(x41691,x41692),x41694)),x41695)),x41696),f312(f219(x41692),f312(x41694,x41697))))
% 155.90/155.60 [4294]E(f312(f250(x42941,x42942,x42943,x42943,x42944,f39(x42943)),f312(f250(x42941,x42941,x42945,x42943,f39(x42941),x42946),x42947)),f312(f312(f239(x42942,x42943),f312(x42944,f312(f246(x42941,x42945),x42947))),f312(x42946,f312(f248(x42941,x42945),x42947))))
% 155.90/155.60 [4295]E(f312(f250(x42951,x42951,x42952,x42953,f39(x42951),x42954),f312(f250(x42955,x42951,x42952,x42952,x42956,f39(x42952)),x42957)),f312(f312(f239(x42951,x42953),f312(x42956,f312(f246(x42955,x42952),x42957))),f312(x42954,f312(f248(x42955,x42952),x42957))))
% 155.90/155.60 [4309]E(f312(f250(x43091,x43092,x43093,x43093,x43094,f39(x43093)),f312(f250(x43095,x43091,x43093,x43093,x43096,f39(x43093)),x43097)),f312(f250(x43095,x43092,x43093,x43093,f312(f82(x43091,x43092,x43095,x43094),x43096),f39(x43093)),x43097))
% 155.90/155.60 [4310]E(f312(f250(x43101,x43101,x43102,x43103,f39(x43101),x43104),f312(f250(x43101,x43101,x43105,x43102,f39(x43101),x43106),x43107)),f312(f250(x43101,x43101,x43105,x43103,f39(x43101),f312(f82(x43102,x43103,x43105,x43104),x43106)),x43107))
% 155.90/155.60 [4317]E(f312(f250(x43171,x43172,x43173,x43173,x43174,f39(x43173)),f312(f250(x43171,x43171,x43175,x43173,f39(x43171),x43176),x43177)),f312(f250(x43172,x43172,x43175,x43173,f39(x43172),x43176),f312(f250(x43171,x43172,x43175,x43175,x43174,f39(x43175)),x43177)))
% 155.90/155.60 [4013]E(f312(f312(f267(x40131,x40132,x40133),f312(f312(f267(x40131,x40134,x40132),x40135),x40136)),x40137),f312(f312(f267(x40131,x40134,x40133),x40135),f312(f312(f267(x40134,x40132,x40133),x40136),x40137)))
% 155.90/155.60 [4084]E(f312(f312(f249(x40841,x40842,x40843),f312(f82(x40844,f861(x40842,x40843),x40841,x40845),x40846)),x40847),f312(f312(x40845,f312(x40846,f312(f246(x40841,x40842),x40847))),f312(f248(x40841,x40842),x40847)))
% 155.90/155.60 [4133]E(f312(f82(x41331,x41332,x41333,x41334),f312(f312(f312(f81(x41333,x41331),x41335),x41336),x41337)),f312(f312(f312(f81(x41333,x41332),f312(f82(x41331,x41332,x41333,x41334),x41335)),x41336),f312(x41334,x41337)))
% 155.90/155.60 [4165]E(f312(f138(x41651,x41652,f312(f7(x41652,x41651,x41651),x41653),x41654),f312(f165(x41652),f312(f312(f150(x41655,x41652),x41656),x41657))),f312(f138(x41651,x41655,f312(f7(x41655,x41651,x41651),f312(f82(x41652,f861(x41651,x41651),x41655,x41653),x41656)),x41654),f312(f165(x41655),x41657)))
% 155.90/155.60 [4170]E(f299(x41701,f857(x41702),x41703,f312(f82(f857(x41704),f857(x41702),x41701,f312(f193(x41704,x41702),x41705)),x41706),f312(f82(f857(x41704),f857(x41702),x41703,f312(f193(x41704,x41702),x41705)),x41707)),f312(f82(f857(x41704),f857(x41702),f859(x41701,x41703),f312(f193(x41704,x41702),x41705)),f299(x41701,f857(x41704),x41703,x41706,x41707)))
% 155.90/155.60 [4111]E(f312(f312(f50(x41111,f861(f860(x41112,x41113),a846)),x41114),f312(f312(f8(f861(f860(x41115,x41113),a846),f861(f860(x41112,x41113),a846),x41111),f312(f267(x41112,x41115,x41113),x41116)),x41117)),f312(f312(f267(x41112,x41115,x41113),x41116),f312(f312(f50(x41111,f861(f860(x41115,x41113),a846)),x41114),x41117)))
% 155.90/155.60 [4258]E(f312(f312(f50(x42581,f861(f860(x42582,x42583),a846)),x42584),f312(f312(f7(x42581,f861(f860(x42585,x42583),a846),f861(f860(x42582,x42583),a846)),f312(f312(f8(f861(f860(x42582,x42585),a846),f861(f861(f860(x42585,x42583),a846),f861(f860(x42582,x42583),a846)),x42581),f267(x42582,x42585,x42583)),x42586)),x42587)),f312(f312(f267(x42582,x42585,x42583),f312(f312(f50(x42581,f861(f860(x42582,x42585),a846)),x42584),x42586)),x42587))
% 155.90/155.60 [4259]E(f312(f138(x42591,x42592,f312(f312(f7(x42591,f861(x42592,x42593),f861(x42592,x42591)),f312(f312(f8(f861(x42593,x42591),f861(f861(x42592,x42593),f861(x42592,x42591)),x42591),f8(x42593,x42591,x42592)),x42594)),x42595),x42596),x42597),f312(f138(x42591,x42593,x42594,x42596),f312(f312(f150(x42592,x42593),x42595),x42597)))
% 155.90/155.60 [4318]E(f312(f312(f51(x43181,f861(x43182,a846)),x43183),f312(f312(f8(f861(x43184,f861(x43182,a846)),f861(x43182,a846),x43181),f312(f51(x43184,f861(x43182,a846)),x43185)),f312(f312(f7(x43181,f861(x43184,f861(x43182,a846)),f861(x43184,f861(x43182,a846))),f312(f312(f8(f861(f861(x43182,a846),f861(x43182,a846)),f861(f861(x43184,f861(x43182,a846)),f861(x43184,f861(x43182,a846))),x43181),f8(f861(x43182,a846),f861(x43182,a846),x43184)),f312(f312(f8(f861(x43182,a846),f861(f861(x43182,a846),f861(x43182,a846)),x43181),f124(f861(x43182,a846))),x43186))),x43187))),f312(f312(f124(f861(x43182,a846)),f312(f312(f51(x43181,f861(x43182,a846)),x43183),x43186)),f312(f312(f51(x43184,f861(x43182,a846)),x43185),x43187)))
% 155.90/155.60 [4319]E(f312(f312(f50(x43191,f861(x43192,a846)),x43193),f312(f312(f8(f861(x43194,f861(x43192,a846)),f861(x43192,a846),x43191),f312(f50(x43194,f861(x43192,a846)),x43195)),f312(f312(f7(x43191,f861(x43194,f861(x43192,a846)),f861(x43194,f861(x43192,a846))),f312(f312(f8(f861(f861(x43192,a846),f861(x43192,a846)),f861(f861(x43194,f861(x43192,a846)),f861(x43194,f861(x43192,a846))),x43191),f8(f861(x43192,a846),f861(x43192,a846),x43194)),f312(f312(f8(f861(x43192,a846),f861(f861(x43192,a846),f861(x43192,a846)),x43191),f115(f861(x43192,a846))),x43196))),x43197))),f312(f312(f115(f861(x43192,a846)),f312(f312(f50(x43191,f861(x43192,a846)),x43193),x43196)),f312(f312(f50(x43194,f861(x43192,a846)),x43195),x43197)))
% 155.90/155.60 [4231]E(f312(f250(x42311,x42312,x42313,x42314,x42315,x42316),f312(f312(f239(x42311,x42313),x42317),x42318)),f312(f312(f239(x42312,x42314),f312(x42315,x42317)),f312(x42316,x42318)))
% 155.90/155.60 [4327]E(f312(f312(f150(f860(x43271,x43272),f860(x43273,x43274)),f312(f249(x43271,x43272,f860(x43273,x43274)),f312(f312(f7(x43271,f861(x43272,x43274),f861(x43272,f860(x43273,x43274))),f312(f312(f8(f861(x43274,f860(x43273,x43274)),f861(f861(x43272,x43274),f861(x43272,f860(x43273,x43274))),x43271),f8(x43274,f860(x43273,x43274),x43272)),f312(f312(f8(x43273,f861(x43274,f860(x43273,x43274)),x43271),f239(x43273,x43274)),x43275))),x43276))),f312(f312(f177(x43271,x43272),x43277),x43278)),f312(f312(f177(x43273,x43274),f312(f312(f150(x43271,x43273),x43275),x43277)),f312(f312(f150(x43272,x43274),x43276),x43278)))
% 155.90/155.60 [4331]E(f312(f312(f150(f860(x43311,x43312),x43313),f312(f249(x43311,x43312,x43313),f312(f312(f8(f861(x43312,f860(x43311,x43314)),f861(x43312,x43313),x43311),f312(f8(f860(x43311,x43314),x43313,x43312),x43315)),f312(f312(f7(x43311,f861(x43312,x43314),f861(x43312,f860(x43311,x43314))),f312(f312(f8(f861(x43314,f860(x43311,x43314)),f861(f861(x43312,x43314),f861(x43312,f860(x43311,x43314))),x43311),f8(x43314,f860(x43311,x43314),x43312)),f239(x43311,x43314))),x43316)))),f312(f312(f177(x43311,x43312),x43317),x43318)),f312(f312(f150(f860(x43311,x43314),x43313),x43315),f312(f312(f177(x43311,x43314),x43317),f312(f312(f150(x43312,x43314),x43316),x43318))))
% 155.90/155.60 [4263]E(f312(f312(f150(f860(x42631,x42632),x42633),f312(f249(x42631,x42632,x42633),f312(f312(f8(f861(x42632,f860(x42634,x42632)),f861(x42632,x42633),x42631),f312(f8(f860(x42634,x42632),x42633,x42632),x42635)),f312(f312(f8(x42634,f861(x42632,f860(x42634,x42632)),x42631),f239(x42634,x42632)),x42636)))),f312(f312(f177(x42631,x42632),x42637),x42638)),f312(f312(f150(f860(x42634,x42632),x42633),x42635),f312(f312(f177(x42634,x42632),f312(f312(f150(x42631,x42634),x42636),x42637)),x42638)))
% 155.90/155.60 [4222]E(f312(f312(f249(x42221,x42222,x42223),f312(f312(f8(f861(x42222,f860(x42224,x42225)),f861(x42222,x42223),x42221),f312(f8(f860(x42224,x42225),x42223,x42222),f312(f249(x42224,x42225,x42223),x42226))),x42227)),x42228),f312(f312(f249(x42224,x42225,x42223),x42226),f312(f312(f249(x42221,x42222,f860(x42224,x42225)),x42227),x42228)))
% 155.90/155.60 [4332]E(f312(f312(f50(f860(x43321,x43322),f861(f860(x43323,x43324),a846)),f312(f312(f247(x43321,x43322),x43325),f312(f16(f861(x43322,a846),x43321),x43326))),f312(f249(x43321,x43322,f861(f860(x43323,x43324),a846)),f312(f312(f7(x43321,f861(x43322,f861(x43323,f861(x43324,a846))),f861(x43322,f861(f860(x43323,x43324),a846))),f312(f312(f8(f861(f861(x43323,f861(x43324,a846)),f861(f860(x43323,x43324),a846)),f861(f861(x43322,f861(x43323,f861(x43324,a846))),f861(x43322,f861(f860(x43323,x43324),a846))),x43321),f8(f861(x43323,f861(x43324,a846)),f861(f860(x43323,x43324),a846),x43322)),f312(f312(f8(f861(x43323,a846),f861(f861(x43323,f861(x43324,a846)),f861(f860(x43323,x43324),a846)),x43321),f247(x43323,x43324)),x43327))),f312(f312(f8(f861(x43324,a846),f861(x43323,f861(x43324,a846)),x43322),f16(f861(x43324,a846),x43323)),x43328)))),f312(f312(f247(x43323,x43324),f312(f312(f50(x43321,f861(x43323,a846)),x43325),x43327)),f312(f16(f861(x43324,a846),x43323),f312(f312(f50(x43322,f861(x43324,a846)),x43326),x43328))))
% 155.90/155.60 [4361]E(f37(x43611,x43612,x43613,x43614,x43615,x43616,x43617,x43618,x43619,a23),x43612)
% 155.90/155.60 [4362]E(f38(x43621,x43622,x43623,x43624,x43625,x43626,x43627,x43628,x43629,a23),x43622)
% 155.90/155.60 [4276]E(f312(f312(f251(x42761,x42762,x42763,x42764),f312(f312(f251(x42761,x42765,x42766,f860(x42762,x42763)),x42767),x42768)),x42769),f312(f312(f251(x42761,x42765,x42766,x42764),x42767),f312(f312(f7(x42765,f861(x42762,f861(x42763,x42764)),f861(x42766,x42764)),f312(f312(f8(f861(x42766,f860(x42762,x42763)),f861(f861(x42762,f861(x42763,x42764)),f861(x42766,x42764)),x42765),f251(x42766,x42762,x42763,x42764)),x42768)),x42769)))
% 155.90/155.60 [4363]E(f37(x43631,x43632,x43633,x43634,x43635,x43636,x43637,x43638,x43639,f312(a27,x436310)),f312(x43638,x436310))
% 155.90/155.60 [4364]E(f38(x43641,x43642,x43643,x43644,x43645,x43646,x43647,x43648,x43649,f312(a27,x436410)),f312(x43648,x436410))
% 155.90/155.61 [4306]E(f312(f82(f860(x43061,x43062),f860(x43063,x43064),f860(x43065,x43066),f250(x43061,x43063,x43062,x43064,x43067,x43068)),f250(x43065,x43061,x43066,x43062,x43069,x430610)),f250(x43065,x43063,x43066,x43064,f312(f82(x43061,x43063,x43065,x43067),x43069),f312(f82(x43062,x43064,x43066,x43068),x430610)))
% 155.90/155.61 [4365]E(f37(x43651,x43652,x43653,x43654,x43655,x43656,x43657,x43658,x43659,f36(x436510,x436511)),f312(f312(x43655,x436510),x436511))
% 155.90/155.61 [4366]E(f37(x43661,x43662,x43663,x43664,x43665,x43666,x43667,x43668,x43669,f35(x436610,x436611)),f312(f312(x43667,x436610),x436611))
% 155.90/155.61 [4367]E(f37(x43671,x43672,x43673,x43674,x43675,x43676,x43677,x43678,x43679,f28(x436710,x436711)),f312(f312(x43673,x436710),x436711))
% 155.90/155.61 [4368]E(f38(x43681,x43682,x43683,x43684,x43685,x43686,x43687,x43688,x43689,f28(x436810,x436811)),f312(f312(x43683,x436810),x436811))
% 155.90/155.61 [4374]E(f312(f312(f312(x43741,x43742),x43743),f38(x43744,x43745,x43746,x43747,x43748,x43749,x43741,x437410,x437411,x43743)),f38(x43744,x43745,x43746,x43747,x43748,x43749,x43741,x437410,x437411,f35(x43742,x43743)))
% 155.90/155.61 [4378]E(f312(f312(f312(f312(x43781,x43782),x43783),f38(x43784,x43785,x43786,x43787,x43781,x43788,x43789,x437810,x437811,x43782)),f38(x43784,x43785,x43786,x43787,x43781,x43788,x43789,x437810,x437811,x43783)),f38(x43784,x43785,x43786,x43787,x43781,x43788,x43789,x437810,x437811,f36(x43782,x43783)))
% 155.90/155.61 [4312]E(f312(f250(x43121,x43122,x43123,x43124,x43125,x43126),f312(f250(x43127,x43121,x43128,x43123,x43129,x431210),x431211)),f312(f250(x43127,x43122,x43128,x43124,f312(f82(x43121,x43122,x43127,x43125),x43129),f312(f82(x43123,x43124,x43128,x43126),x431210)),x431211))
% 155.90/155.61 [4375]E(f312(f312(f312(f312(x43751,x43752),x43753),x43754),f38(x43755,x43756,x43757,x43751,x43758,x43759,x437510,x437511,x437512,x43754)),f38(x43755,x43756,x43757,x43751,x43758,x43759,x437510,x437511,x437512,f32(x43752,x43753,x43754)))
% 155.90/155.61 [4379]E(f312(f312(f312(f312(f312(x43791,x43792),x43793),x43794),f38(x43795,x43796,x43797,x43798,x43799,x43791,x437910,x437911,x437912,x43793)),f38(x43795,x43796,x43797,x43798,x43799,x43791,x437910,x437911,x437912,x43794)),f38(x43795,x43796,x43797,x43798,x43799,x43791,x437910,x437911,x437912,f33(x43792,x43793,x43794)))
% 155.90/155.61 [4369]E(f37(x43691,x43692,x43693,x43694,x43695,x43696,x43697,x43698,x43699,f33(x436910,x436911,x436912)),f312(f312(f312(x43696,x436910),x436911),x436912))
% 155.90/155.61 [4370]E(f37(x43701,x43702,x43703,x43704,x43705,x43706,x43707,x43708,x43709,f32(x437010,x437011,x437012)),f312(f312(f312(x43704,x437010),x437011),x437012))
% 155.90/155.61 [4371]E(f37(x43711,x43712,x43713,x43714,x43715,x43716,x43717,x43718,x43719,f31(x437110,x437111,x437112)),f312(f312(f312(x43719,x437110),x437111),x437112))
% 155.90/155.61 [4372]E(f38(x43721,x43722,x43723,x43724,x43725,x43726,x43727,x43728,x43729,f31(x437210,x437211,x437212)),f312(f312(f312(x43729,x437210),x437211),x437212))
% 155.90/155.61 [4509]~E(a522,a580)+~P1(a5000)
% 155.90/155.61 [6371]P4(a5000)+P22(f312(f312(f314(f860(a849,a847)),a584),f312(f168(f860(a849,a847)),a29)))
% 155.90/155.61 [8358]P4(a5000)+~P22(f312(f312(f249(a849,a847,a846),f312(f16(f861(a847,a846),a849),a24)),a584))
% 155.90/155.61 [4511]~E(f649(x45111),x45111)+~P1(a5000)
% 155.90/155.61 [4512]~E(f760(x45121),x45121)+E(x45121,a865)
% 155.90/155.61 [4515]~P62(x45151)+P62(f857(x45151))
% 155.90/155.61 [4516]~P63(x45161)+P63(f857(x45161))
% 155.90/155.61 [4519]~P137(x45191)+~E(f87(x45191),f2(x45191))
% 155.90/155.61 [4521]~E(x45211,f2(a113))+E(f312(a20,x45211),f2(a1))
% 155.90/155.61 [4522]~E(x45221,f2(a1))+E(f91(a1,x45221),f2(a1))
% 155.90/155.61 [4529]~P23(x45291)+P35(x45291,f2(x45291))
% 155.90/155.61 [4531]~P103(x45311)+P33(x45311,f127(x45311))
% 155.90/155.61 [4541]P22(x45411)+P22(f312(a307,x45411))
% 155.90/155.61 [4584]~P23(x45841)+~P35(x45841,f87(x45841))
% 155.90/155.61 [4634]~P22(x46341)+~P22(f312(a307,x46341))
% 155.90/155.61 [4659]E(f312(a118,x46591),f2(a853))+~P22(f312(a194,x46591))
% 155.90/155.61 [4723]~P98(x47231)+P11(x47231,x47231,f124(x47231))
% 155.90/155.61 [4724]~P99(x47241)+P11(x47241,x47241,f115(x47241))
% 155.90/155.61 [4725]~P93(x47251)+P11(x47251,x47251,f90(x47251))
% 155.90/155.61 [4726]~P103(x47261)+P11(x47261,x47261,f225(x47261))
% 155.90/155.61 [4727]~P103(x47271)+P11(x47271,x47271,f226(x47271))
% 155.90/155.61 [4526]~E(x45261,f2(a853))+E(f312(f114(a1),x45261),f2(a1))
% 155.90/155.61 [4534]~P90(x45341)+E(f312(f117(x45341),a92),f2(x45341))
% 155.90/155.61 [4537]~E(f581(x45371),f2(a853))+E(f312(f162(a853),x45371),f2(a853))
% 155.90/155.61 [4538]~P104(x45381)+E(f229(x45381,f227(x45381)),f225(x45381))
% 155.90/155.61 [4539]~P104(x45391)+E(f230(x45391,f227(x45391)),f226(x45391))
% 155.90/155.61 [4540]~P85(x45401)+E(f91(x45401,f2(x45401)),f2(x45401))
% 155.90/155.61 [4549]~P23(x45491)+E(f312(f114(x45491),f2(a853)),f2(x45491))
% 155.90/155.61 [4550]~P23(x45501)+E(f312(f114(x45501),f87(a853)),f87(x45501))
% 155.90/155.61 [4551]~P111(x45511)+E(f312(f116(x45511),f2(a1)),f2(x45511))
% 155.90/155.61 [4552]~P111(x45521)+E(f312(f116(x45521),f87(a1)),f87(x45521))
% 155.90/155.61 [4553]E(x45531,f2(a853))+~E(f312(f114(a1),x45531),f2(a1))
% 155.90/155.61 [4578]~P71(x45781)+E(f312(f88(x45781),f2(x45781)),f2(x45781))
% 155.90/155.61 [4579]~P88(x45791)+E(f312(f88(x45791),f189(x45791)),f235(x45791))
% 155.90/155.61 [4580]~P88(x45801)+E(f312(f88(x45801),f235(x45801)),f189(x45801))
% 155.90/155.61 [4581]~P83(x45811)+E(f312(f84(x45811),f2(x45811)),f2(x45811))
% 155.90/155.61 [4582]~P112(x45821)+E(f312(f84(x45821),f87(x45821)),f87(x45821))
% 155.90/155.61 [4583]~P25(x45831)+E(f312(f162(x45831),f127(x45831)),f2(x45831))
% 155.90/155.61 [4600]E(x46001,f2(a1))+E(f312(f47(a1,x46001),x46001),f87(a1))
% 155.90/155.61 [4605]~P40(x46051)+P43(f312(f168(a1),x46051))
% 155.90/155.61 [4639]~P90(x46391)+E(f312(f88(x46391),f87(x46391)),f312(f117(x46391),a111))
% 155.90/155.61 [4656]~P90(x46561)+P35(x46561,f312(f117(x46561),a92))
% 155.90/155.61 [4675]~P63(x46751)+E(f312(f168(x46751),f64(x46751)),f235(f861(x46751,a846)))
% 155.90/155.61 [4685]P40(x46851)+~P43(f312(f168(a1),x46851))
% 155.90/155.61 [4686]~P63(x46861)+P22(f312(f133(x46861),f64(x46861)))
% 155.90/155.61 [4728]E(f312(f114(a1),f312(a118,x47281)),x47281)+P22(f312(a194,x47281))
% 155.90/155.61 [4743]~P104(x47431)+E(f101(x47431,x47431,f5(x47431)),f102(x47431))
% 155.90/155.61 [4795]~P109(x47951)+E(f241(x47951,f87(x47951),f90(x47951)),f240(x47951))
% 155.90/155.61 [4825]~P90(x48251)+~P35(x48251,f312(f117(x48251),a111))
% 155.90/155.61 [4835]E(f312(a30,x48351),f192(a847))+P22(f312(a24,f312(a27,x48351)))
% 155.90/155.61 [4892]E(x48921,a865)+P22(f312(f312(f195(a862),a863),f760(x48921)))
% 155.90/155.61 [4961]E(f312(f84(a1),x49611),x49611)+P22(f312(f312(f228(a1),x49611),f2(a1)))
% 155.90/155.61 [4982]~E(f312(a118,x49821),f2(a853))+P22(f312(f312(f227(a1),x49821),f2(a1)))
% 155.90/155.61 [5045]~P22(f312(a194,x50451))+P22(f312(f312(f228(a1),x50451),f2(a1)))
% 155.90/155.61 [5087]~P111(x50871)+P22(f312(f312(f314(x50871),f2(x50871)),f123(x50871)))
% 155.90/155.61 [5088]~P23(x50881)+P22(f312(f312(f314(x50881),f2(x50881)),f187(x50881)))
% 155.90/155.61 [5089]~P111(x50891)+P22(f312(f312(f314(x50891),f87(x50891)),f123(x50891)))
% 155.90/155.61 [5090]~P23(x50901)+P22(f312(f312(f314(x50901),f87(x50901)),f187(x50901)))
% 155.90/155.61 [5091]~P117(x50911)+P22(f312(f312(f228(x50911),f2(x50911)),f87(x50911)))
% 155.90/155.61 [5092]~P117(x50921)+P22(f312(f312(f227(x50921),f2(x50921)),f87(x50921)))
% 155.90/155.61 [5095]E(f312(f219(a847),f394(x50951)),f312(a30,x50951))+~P22(f312(a24,f312(a27,x50951)))
% 155.90/155.61 [5096]E(f312(f219(a847),f429(x50961)),f312(a30,x50961))+~P22(f312(a24,f312(a27,x50961)))
% 155.90/155.61 [5151]E(x51511,f2(a853))+~P22(f312(f312(f227(a853),x51511),f2(a853)))
% 155.90/155.61 [5193]E(f312(a118,x51931),f2(a853))+~P22(f312(f312(f227(a1),x51931),f2(a1)))
% 155.90/155.61 [5251]P22(f312(a194,x52511))+~P22(f312(f312(f228(a1),x52511),f2(a1)))
% 155.90/155.61 [5273]P43(x52731)+~P22(f312(f312(f227(a1),f2(a1)),f318(x52731)))
% 155.90/155.61 [5279]E(f312(f84(a1),x52791),f312(f88(a1),x52791))+~P22(f312(f312(f228(a1),x52791),f2(a1)))
% 155.90/155.61 [5447]~P117(x54471)+~P22(f312(f312(f228(x54471),f87(x54471)),f2(x54471)))
% 155.90/155.61 [5448]~P117(x54481)+~P22(f312(f312(f227(x54481),f87(x54481)),f2(x54481)))
% 155.90/155.61 [5458]~E(x54581,f2(a1))+P22(f312(f312(f228(a1),f312(f84(a1),x54581)),f87(a1)))
% 155.90/155.61 [5459]~E(x54591,f2(a853))+P22(f312(f312(f227(a1),f312(f114(a1),x54591)),f2(a1)))
% 155.90/155.61 [5585]~P25(x55851)+E(f138(x55851,x55851,f89(x55851),f2(x55851)),f162(x55851))
% 155.90/155.61 [5743]~P100(x57431)+P19(a853,x57431,f114(x57431),f235(f861(a853,a846)))
% 155.90/155.61 [5944]E(x59441,f2(a853))+~P22(f312(f312(f227(a1),f312(f114(a1),x59441)),f2(a1)))
% 155.90/155.61 [5945]E(x59451,f2(a1))+~P22(f312(f312(f228(a1),f312(f84(a1),x59451)),f87(a1)))
% 155.90/155.61 [6719]~P22(f312(f312(f228(a1),x67191),f2(a1)))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x67191),x67191)),f2(a1)))
% 155.90/155.61 [7260]P22(f312(f312(f228(a1),x72601),f2(a1)))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x72601),x72601)),f2(a1)))
% 155.90/155.61 [7808]E(x78081,f312(a3,f2(a853)))+P22(f312(f312(f228(a853),f312(f312(f21(a853),f312(a19,x78081)),f312(a126,f2(a853)))),f312(a19,x78081)))
% 155.90/155.61 [8581]~P22(f312(f312(f228(a1),x85811),f2(a1)))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85811),x85811)),a111)),f2(a1)))
% 155.90/155.61 [8669]~P22(f312(f312(f228(a1),x86691),f2(a1)))+P22(f312(f312(f228(a1),f312(f312(f89(a1),f312(f312(f89(a1),f87(a1)),x86691)),x86691)),f2(a1)))
% 155.90/155.61 [8988]P22(f312(f312(f228(a1),x89881),f2(a1)))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89881),x89881)),a111)),f2(a1)))
% 155.90/155.61 [9050]P22(f312(f312(f228(a1),x90501),f2(a1)))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),f312(f312(f89(a1),f87(a1)),x90501)),x90501)),f2(a1)))
% 155.90/155.61 [4627]~E(a92,x46271)+E(f312(f312(f89(a1),x46271),x46271),a92)
% 155.90/155.61 [4628]~E(x46281,a92)+E(f312(f312(f89(a1),x46281),x46281),a92)
% 155.90/155.61 [4772]E(x47721,a92)+~E(f312(f312(f89(a1),x47721),x47721),a92)
% 155.90/155.61 [4773]E(a92,x47731)+~E(f312(f312(f89(a1),x47731),x47731),a92)
% 155.90/155.61 [4785]~P103(x47851)+E(f135(x47851,f189(f861(x47851,a846))),f127(x47851))
% 155.90/155.61 [4786]~P31(x47861)+E(f48(x47861,f189(f861(x47861,a846))),f189(x47861))
% 155.90/155.61 [4787]~P31(x47871)+E(f48(x47871,f235(f861(x47871,a846))),f235(x47871))
% 155.90/155.61 [4788]~P31(x47881)+E(f49(x47881,f189(f861(x47881,a846))),f235(x47881))
% 155.90/155.61 [4789]~P31(x47891)+E(f49(x47891,f235(f861(x47891,a846))),f189(x47891))
% 155.90/155.61 [4922]E(x49221,f2(a853))+P22(f312(f312(f228(a853),f2(a853)),x49221))
% 155.90/155.61 [4940]~P32(x49401)+P22(f312(f312(f227(a1),f2(a1)),x49401))
% 155.90/155.61 [4973]~E(f312(f117(a853),x49731),f2(a853))+P22(f312(f312(f227(a1),x49731),a92))
% 155.90/155.61 [4978]P43(x49781)+P22(f312(f312(f314(a1),f318(x49781)),x49781))
% 155.90/155.61 [4979]E(x49791,f312(a3,f2(a853)))+P22(f312(f312(f227(a113),f87(a113)),x49791))
% 155.90/155.61 [5018]P22(f312(a194,x50181))+P22(f312(f312(f227(a1),f2(a1)),x50181))
% 155.90/155.61 [5069]E(f312(f114(a1),f312(a118,x50691)),f2(a1))+P22(f312(f312(f227(a1),f2(a1)),x50691))
% 155.90/155.61 [5137]E(f312(f114(a1),f312(f117(a853),x51371)),f312(f117(a1),x51371))+P22(f312(a194,f312(f117(a1),x51371)))
% 155.90/155.61 [5157]E(f312(f117(a853),x51571),f2(a853))+~P22(f312(a194,f312(f117(a1),x51571)))
% 155.90/155.61 [5158]E(f312(f117(a853),x51581),f2(a853))+~P22(f312(f312(f227(a1),x51581),a92))
% 155.90/155.61 [5190]P32(x51901)+~P22(f312(f312(f227(a1),f2(a1)),x51901))
% 155.90/155.61 [5258]E(f312(a126,f786(x52581)),x52581)+~P22(f312(f312(f228(a853),f2(a853)),x52581))
% 155.90/155.61 [5267]E(f312(a126,f312(f117(a853),x52671)),f87(a853))+~P22(f312(a194,f312(f117(a1),x52671)))
% 155.90/155.61 [5275]E(f312(f114(a1),f834(x52751)),x52751)+~P22(f312(f312(f228(a1),f2(a1)),x52751))
% 155.90/155.61 [5282]~E(x52821,f312(a3,f2(a853)))+~P22(f312(f312(f227(a113),f87(a113)),x52821))
% 155.90/155.61 [5289]E(f312(f114(a1),f312(f117(a853),x52891)),f2(a1))+~P22(f312(a194,f312(f117(a1),x52891)))
% 155.90/155.61 [5312]E(f312(f162(a853),x53121),f2(a853))+P22(f312(f312(f314(a853),f581(x53121)),f312(f168(a853),x53121)))
% 155.90/155.61 [5332]E(f312(f114(a1),f312(a118,x53321)),x53321)+~P22(f312(f312(f227(a1),f2(a1)),x53321))
% 155.90/155.61 [5341]~P22(f312(a194,x53411))+~P22(f312(f312(f227(a1),f2(a1)),x53411))
% 155.90/155.61 [5440]E(f312(f312(f89(a853),f87(a853)),f312(f117(a853),x54401)),f87(a853))+~P22(f312(f312(f228(a1),x54401),a92))
% 155.90/155.61 [5500]E(x55001,f2(a853))+~P22(f312(f312(f228(a853),x55001),f312(a126,f2(a853))))
% 155.90/155.61 [5542]E(f312(f312(f89(a853),f312(f117(a853),x55421)),f87(a853)),f87(a853))+~P22(f312(f312(f228(a1),x55421),a92))
% 155.90/155.61 [5543]E(f312(f312(f21(a853),f312(f117(a853),x55431)),f87(a853)),f2(a853))+~P22(f312(f312(f227(a1),x55431),a92))
% 155.90/155.61 [5555]~P43(x55551)+E(f312(f53(a853),f312(f290(a1,a853,a118),x55551)),f312(f53(a1),x55551))
% 155.90/155.61 [5586]~P103(x55861)+E(f229(x55861,f312(f7(x55861,x55861,a846),f227(x55861))),f226(x55861))
% 155.90/155.61 [5587]~P103(x55871)+E(f230(x55871,f312(f7(x55871,x55871,a846),f227(x55871))),f225(x55871))
% 155.90/155.61 [5597]E(f54(a853,f312(a126,f2(a853)),f312(f117(a853),x55971)),f312(a126,f2(a853)))+~P22(f312(a194,f312(f117(a1),x55971)))
% 155.90/155.61 [5605]P22(f312(f312(f228(a1),f2(a1)),x56051))+~P22(f312(f312(f227(a1),f87(a1)),x56051))
% 155.90/155.61 [5606]~P22(f312(f312(f228(a1),f2(a1)),x56061))+P22(f312(f312(f227(a1),f87(a1)),x56061))
% 155.90/155.61 [5612]E(f312(a126,f312(f312(f21(a853),x56121),f87(a853))),x56121)+~P22(f312(f312(f228(a853),f2(a853)),x56121))
% 155.90/155.61 [5671]P22(f312(f312(f228(a853),f2(a853)),f834(x56711)))+~P22(f312(f312(f228(a1),f2(a1)),x56711))
% 155.90/155.61 [5724]E(f54(a1,f312(f117(a1),a111),x57241),f312(f312(f21(a1),x57241),f87(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x57241))
% 155.90/155.61 [5754]~P22(f312(f312(f228(a1),a92),x57541))+P22(f312(f312(f228(a853),f2(a853)),f312(f117(a853),x57541)))
% 155.90/155.61 [5806]P22(f312(f312(f228(a853),f2(a853)),f312(a118,x58061)))+~P22(f312(f312(f228(a1),f2(a1)),x58061))
% 155.90/155.61 [5854]~P22(f312(f312(f228(a853),f2(a853)),x58541))+P22(f312(f312(f228(a1),f2(a1)),f312(f114(a1),x58541)))
% 155.90/155.61 [5892]~P22(f312(f312(f228(a853),f2(a853)),f312(a118,x58921)))+P22(f312(f312(f228(a1),f2(a1)),x58921))
% 155.90/155.61 [5912]~P43(x59121)+E(f312(f290(a853,a1,f114(a1)),f312(f290(a1,a853,a118),x59121)),x59121)
% 155.90/155.61 [5925]P22(f312(f312(f228(a1),a92),x59251))+~P22(f312(f312(f228(a853),f2(a853)),f312(f117(a853),x59251)))
% 155.90/155.61 [5969]~P63(x59691)+E(f312(f312(f147(f857(x59691)),f192(x59691)),f312(f312(f150(x59691,f857(x59691)),f219(x59691)),f64(x59691))),f64(f857(x59691)))
% 155.90/155.61 [5979]P22(f312(f312(f228(a853),f2(a853)),x59791))+~P22(f312(f312(f228(a1),f2(a1)),f312(f114(a1),x59791)))
% 155.90/155.61 [6086]E(f312(f290(a853,a1,f114(a1)),f312(f279(a853),f312(a118,x60861))),f312(f282(a1,f2(a1)),x60861))+~P22(f312(f312(f227(a1),f2(a1)),x60861))
% 155.90/155.61 [6101]~P117(x61011)+P22(f312(f312(f228(x61011),f2(x61011)),f312(f312(f89(x61011),f87(x61011)),f87(x61011))))
% 155.90/155.61 [6154]P22(f312(f312(f228(a853),f312(a126,f2(a853))),f312(a118,x61541)))+~P22(f312(f312(f228(a1),f87(a1)),x61541))
% 155.90/155.61 [6246]E(x62461,f2(a1))+P22(f312(f57(f2(a1),x62461),f312(f312(f239(a1,a1),f2(a1)),f2(a1))))
% 155.90/155.61 [6410]~P22(f312(f312(f228(a853),f312(a126,f2(a853))),f312(a118,x64101)))+P22(f312(f312(f228(a1),f87(a1)),x64101))
% 155.90/155.61 [6824]~P101(x68241)+P41(x68241,f312(f233(f860(x68241,x68241)),f312(f249(x68241,x68241,a846),f228(x68241))))
% 155.90/155.61 [5487]E(f312(f117(a853),f312(f312(f21(a1),x54871),a111)),f312(a126,f312(f117(a853),x54871)))+P22(f312(a194,f312(f117(a1),x54871)))
% 155.90/155.61 [5503]~P40(x55031)+E(f312(f312(f150(a853,a1),f114(a1)),f312(f312(f150(a1,a853),a118),x55031)),x55031)
% 155.90/155.61 [5613]E(f312(f47(a1,f312(f117(a1),a111)),x56131),f312(f117(a1),a111))+~P22(f312(f312(f228(a1),f2(a1)),x56131))
% 155.90/155.61 [5619]E(f312(f88(a1),f312(f114(a1),f312(a126,f835(x56191)))),x56191)+~P22(f312(f312(f228(a1),x56191),f2(a1)))
% 155.90/155.61 [5630]E(f312(f312(f89(a853),f87(a853)),f312(f117(a853),x56301)),f312(f117(a853),f312(f312(f21(a1),x56301),a111)))+P22(f312(f312(f228(a1),x56301),a92))
% 155.90/155.61 [5750]E(f312(f312(f89(a853),f312(f117(a853),x57501)),f87(a853)),f312(f117(a853),f312(f312(f21(a1),x57501),a111)))+P22(f312(f312(f228(a1),x57501),a92))
% 155.90/155.61 [5751]E(f312(f312(f21(a853),f312(f117(a853),x57511)),f87(a853)),f312(f117(a853),f312(f312(f89(a1),x57511),a111)))+P22(f312(f312(f227(a1),x57511),a92))
% 155.90/155.61 [5794]E(f312(a118,f312(f312(f89(a1),f87(a1)),x57941)),f312(a126,f312(a118,x57941)))+~P22(f312(f312(f227(a1),f2(a1)),x57941))
% 155.90/155.61 [5829]E(f312(a126,f312(f312(f21(a853),x58291),f312(a126,f2(a853)))),x58291)+~P22(f312(f312(f228(a853),f2(a853)),x58291))
% 155.90/155.61 [6035]E(f54(a853,f312(a126,f2(a853)),f312(f117(a853),x60351)),f312(a118,f54(a1,f87(a1),f312(f117(a1),x60351))))+P22(f312(a194,f312(f117(a1),x60351)))
% 155.90/155.61 [6077]~P22(f312(f312(f228(a1),a92),x60771))+P22(f312(f312(f228(a1),a92),f312(f312(f89(a1),x60771),x60771)))
% 155.90/155.61 [6078]~P22(f312(f312(f228(a1),a111),x60781))+P22(f312(f312(f228(a1),a111),f312(f312(f89(a1),x60781),x60781)))
% 155.90/155.61 [6079]~P22(f312(f312(f227(a1),a92),x60791))+P22(f312(f312(f227(a1),a92),f312(f312(f89(a1),x60791),x60791)))
% 155.90/155.61 [6080]~P22(f312(f312(f228(a1),a111),x60801))+P22(f312(f312(f227(a1),a111),f312(f312(f89(a1),x60801),x60801)))
% 155.90/155.61 [6259]~P22(f312(f70(x62591),f235(f861(x62591,a846))))+P22(f312(f70(f857(x62591)),f235(f861(f857(x62591),a846))))
% 155.90/155.61 [6326]E(f312(f246(a1,a1),f55(f87(a1),f312(f117(a1),x63261))),f312(f47(a1,f87(a1)),f312(f117(a1),x63261)))+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x63261)))
% 155.90/155.61 [6344]~P22(f312(f312(f227(a1),f2(a1)),x63441))+P22(f312(f312(f228(a1),f2(a1)),f312(f312(f89(a1),f87(a1)),x63441)))
% 155.90/155.61 [6370]E(f312(f248(a1,a1),f55(f87(a1),f312(f117(a1),x63701))),f54(a1,f87(a1),f312(f117(a1),x63701)))+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x63701)))
% 155.90/155.61 [6382]P22(f312(f70(x63821),f235(f861(x63821,a846))))+~P22(f312(f70(f857(x63821)),f235(f861(f857(x63821),a846))))
% 155.90/155.61 [6411]P22(f312(f312(f228(a1),a92),x64111))+~P22(f312(f312(f228(a1),a92),f312(f312(f89(a1),x64111),x64111)))
% 155.90/155.61 [6412]P22(f312(f312(f228(a1),a111),x64121))+~P22(f312(f312(f228(a1),a111),f312(f312(f89(a1),x64121),x64121)))
% 155.90/155.61 [6413]P22(f312(f312(f228(a1),a111),x64131))+~P22(f312(f312(f227(a1),a111),f312(f312(f89(a1),x64131),x64131)))
% 155.90/155.61 [6414]P22(f312(f312(f227(a1),a92),x64141))+~P22(f312(f312(f227(a1),a92),f312(f312(f89(a1),x64141),x64141)))
% 155.90/155.61 [6723]~P22(f312(f70(x67231),f235(f861(x67231,a846))))+P22(f312(f312(f228(a853),f2(a853)),f312(f53(x67231),f235(f861(x67231,a846)))))
% 155.90/155.61 [7302]P22(f312(f70(a853),x73021))+~P22(f312(f70(a1),f312(f290(a853,a1,f114(a1)),x73021)))
% 155.90/155.61 [5416]~E(a111,x54161)+E(f312(f312(f21(a1),f312(f312(f89(a1),x54161),x54161)),a111),a111)
% 155.90/155.61 [5417]~E(x54171,a111)+E(f312(f312(f21(a1),f312(f312(f89(a1),x54171),x54171)),a111),a111)
% 155.90/155.61 [5917]E(x59171,a111)+~E(f312(f312(f21(a1),f312(f312(f89(a1),x59171),x59171)),a111),a111)
% 155.90/155.61 [5918]E(a111,x59181)+~E(f312(f312(f21(a1),f312(f312(f89(a1),x59181),x59181)),a111),a111)
% 155.90/155.61 [6310]~E(f312(f117(a853),x63101),f2(a853))+P22(f312(a194,f312(f117(a1),f312(f312(f89(a1),x63101),a111))))
% 155.90/155.61 [6655]~P22(f312(a194,f312(f117(a1),x66551)))+P22(f312(a194,f312(f117(a1),f312(f312(f89(a1),x66551),x66551))))
% 155.90/155.61 [6656]~P22(f312(f312(f228(a1),x66561),a92))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x66561),x66561)),a92))
% 155.90/155.61 [6657]~P22(f312(f312(f227(a1),x66571),a111))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x66571),x66571)),a111))
% 155.90/155.61 [6658]~P22(f312(f312(f227(a1),x66581),a92))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x66581),x66581)),a92))
% 155.90/155.61 [6659]~P22(f312(f312(f227(a1),x66591),a111))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x66591),x66591)),a111))
% 155.90/155.61 [6976]E(f312(f117(a853),x69761),f2(a853))+~P22(f312(a194,f312(f117(a1),f312(f312(f89(a1),x69761),a111))))
% 155.90/155.61 [7209]~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x72091)))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),f312(f312(f89(a1),x72091),x72091))))
% 155.90/155.61 [7210]P22(f312(a194,f312(f117(a1),x72101)))+~P22(f312(a194,f312(f117(a1),f312(f312(f89(a1),x72101),x72101))))
% 155.90/155.61 [7211]P22(f312(f312(f228(a1),x72111),a92))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x72111),x72111)),a92))
% 155.90/155.61 [7212]P22(f312(f312(f227(a1),x72121),a92))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x72121),x72121)),a92))
% 155.90/155.61 [7213]P22(f312(f312(f227(a1),x72131),a111))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x72131),x72131)),a111))
% 155.90/155.61 [7214]P22(f312(f312(f227(a1),x72141),a111))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x72141),x72141)),a111))
% 155.90/155.61 [7579]E(f312(a121,f541(x75791)),x75791)+~P22(f312(f312(f314(f861(f860(a853,a853),a846)),x75791),a112))
% 155.90/155.61 [6231]~P90(x62311)+E(f312(f117(x62311),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f87(x62311))
% 155.90/155.61 [6703]~P22(f312(a194,f312(f117(a1),x67031)))+E(f312(f117(a853),f312(f312(f21(a1),f312(f312(f89(a1),x67031),x67031)),a111)),f2(a853))
% 155.90/155.61 [7728]~P22(f312(f312(f228(a1),f312(f117(a1),x77281)),f2(a1)))+E(f312(f246(a1,a1),f312(a59,f58(f312(f88(a1),f87(a1)),f312(f88(a1),f312(f117(a1),x77281))))),f312(f47(a1,f87(a1)),f312(f117(a1),x77281)))
% 155.90/155.61 [7770]~P22(f312(f312(f228(a1),f312(f117(a1),x77701)),f2(a1)))+E(f312(f248(a1,a1),f312(a59,f58(f312(f88(a1),f87(a1)),f312(f88(a1),f312(f117(a1),x77701))))),f54(a1,f87(a1),f312(f117(a1),x77701)))
% 155.90/155.61 [7813]~P22(f312(f312(f227(a1),a92),x78131))+P22(f312(f312(f228(a1),a92),f312(f312(f21(a1),f312(f312(f89(a1),x78131),x78131)),a111)))
% 155.90/155.61 [7814]~P22(f312(f312(f228(a1),a111),x78141))+P22(f312(f312(f228(a1),a111),f312(f312(f21(a1),f312(f312(f89(a1),x78141),x78141)),a111)))
% 155.90/155.61 [7815]~P22(f312(f312(f227(a1),a92),x78151))+P22(f312(f312(f227(a1),a92),f312(f312(f21(a1),f312(f312(f89(a1),x78151),x78151)),a111)))
% 155.90/155.61 [7816]~P22(f312(f312(f227(a1),a111),x78161))+P22(f312(f312(f227(a1),a111),f312(f312(f21(a1),f312(f312(f89(a1),x78161),x78161)),a111)))
% 155.90/155.61 [8123]~P90(x81231)+~P35(x81231,f312(f117(x81231),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))
% 155.90/155.61 [8307]P22(f312(f312(f228(a1),a111),x83071))+~P22(f312(f312(f228(a1),a111),f312(f312(f21(a1),f312(f312(f89(a1),x83071),x83071)),a111)))
% 155.90/155.61 [8308]P22(f312(f312(f227(a1),a92),x83081))+~P22(f312(f312(f228(a1),a92),f312(f312(f21(a1),f312(f312(f89(a1),x83081),x83081)),a111)))
% 155.90/155.61 [8309]P22(f312(f312(f227(a1),a92),x83091))+~P22(f312(f312(f227(a1),a92),f312(f312(f21(a1),f312(f312(f89(a1),x83091),x83091)),a111)))
% 155.90/155.61 [8310]P22(f312(f312(f227(a1),a111),x83101))+~P22(f312(f312(f227(a1),a111),f312(f312(f21(a1),f312(f312(f89(a1),x83101),x83101)),a111)))
% 155.90/155.61 [8625]E(f312(f117(a853),f312(f312(f21(a1),f312(f312(f89(a1),x86251),x86251)),a111)),f312(f312(f95(a853,a853),f312(f117(a853),x86251)),f312(f312(f8(a853,a853,a853),a126),f312(f312(f18(a853,a853,a853),f89(a853)),f5(a853)))))+P22(f312(a194,f312(f117(a1),x86251)))
% 155.90/155.61 [9463]E(x94631,f189(f861(f860(a853,a853),a846)))+P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),x94631),f189(f861(f860(a853,a853),a846)))),a77))
% 155.90/155.61 [8558]~P22(f312(a194,f312(f117(a1),x85581)))+P22(f312(a194,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85581),x85581)),a111))))
% 155.90/155.61 [8559]~P22(f312(f312(f228(a1),x85591),a92))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85591),x85591)),a111)),a92))
% 155.90/155.61 [8560]~P22(f312(f312(f228(a1),x85601),a111))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85601),x85601)),a111)),a111))
% 155.90/155.61 [8561]~P22(f312(f312(f228(a1),x85611),a92))+P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85611),x85611)),a111)),a92))
% 155.90/155.61 [8562]~P22(f312(f312(f227(a1),x85621),a111))+P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x85621),x85621)),a111)),a111))
% 155.90/155.61 [8662]~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x86621)))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x86621),x86621)),a111))))
% 155.90/155.61 [8815]~P90(x88151)+E(f312(f312(f89(x88151),f87(x88151)),f87(x88151)),f312(f117(x88151),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))))
% 155.90/155.61 [8973]P22(f312(a194,f312(f117(a1),x89731)))+~P22(f312(a194,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89731),x89731)),a111))))
% 155.90/155.61 [8974]P22(f312(f312(f228(a1),x89741),a92))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89741),x89741)),a111)),a92))
% 155.90/155.61 [8975]P22(f312(f312(f228(a1),x89751),a92))+~P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89751),x89751)),a111)),a92))
% 155.90/155.61 [8976]P22(f312(f312(f228(a1),x89761),a111))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89761),x89761)),a111)),a111))
% 155.90/155.61 [8977]P22(f312(f312(f227(a1),x89771),a111))+~P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89771),x89771)),a111)),a111))
% 155.90/155.61 [9511]~P22(f312(f70(f860(a853,a853)),x95111))+P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),f189(f861(f860(a853,a853),a846))),x95111)),a78))
% 155.90/155.61 [9296]~P23(x92961)+E(f312(f312(f240(x92961),f2(x92961)),f312(f117(a853),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(x92961))
% 155.90/155.61 [9297]~P23(x92971)+E(f312(f312(f240(x92971),f87(x92971)),f312(f117(a853),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(x92971))
% 155.90/155.61 [9729]~P22(f312(f312(f228(a853),f87(a853)),x97291))+P22(f312(f312(f228(a853),f2(a853)),f312(f47(a853,x97291),f312(f117(a853),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))))))
% 155.90/155.61 [9743]~P22(f312(f312(f228(a853),f2(a853)),x97431))+P22(f312(f312(f228(a853),f2(a853)),f312(f47(a853,f312(f312(f89(a853),x97431),f87(a853))),f312(f117(a853),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))))))
% 155.90/155.61 [9783]~E(f54(a853,x97831,f312(f117(a853),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(a853))+P22(f312(f312(f228(a853),f2(a853)),f54(a853,x97831,f312(f117(a853),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))))))
% 155.90/155.61 [9807]E(f54(a853,x98071,f312(f117(a853),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(a853))+~P22(f312(f312(f228(a853),f2(a853)),f54(a853,x98071,f312(f117(a853),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))))))
% 155.90/155.61 [4557]~P41(x45571,x45572)+P57(x45571,x45572)
% 155.90/155.61 [4558]~P46(x45581,x45582)+P57(x45581,x45582)
% 155.90/155.61 [4513]E(x45131,x45132)+~E(f40(x45131),f40(x45132))
% 155.90/155.61 [4514]E(x45141,x45142)+~E(f41(x45141),f41(x45142))
% 155.90/155.61 [4517]~E(x45171,x45172)+E(f257(x45171,x45172),f87(a113))
% 155.90/155.61 [4520]E(f199(x45201,x45202),x45201)+~E(x45202,f2(a853))
% 155.90/155.61 [4525]P42(x45251,x45252)+~E(x45252,f192(x45251))
% 155.90/155.61 [4528]~E(x45282,f127(x45281))+E(f148(x45281,x45282),f127(x45281))
% 155.90/155.61 [4532]~P42(x45322,x45321)+E(x45321,f192(x45322))
% 155.90/155.61 [4548]~E(f148(x45482,x45481),f127(x45482))+E(x45481,f127(x45482))
% 155.90/155.61 [4562]~P24(x45622)+P24(f861(x45621,x45622))
% 155.90/155.61 [4563]~P73(x45632)+P73(f861(x45631,x45632))
% 155.90/155.61 [4564]~P79(x45642)+P79(f861(x45641,x45642))
% 155.90/155.61 [4565]~P87(x45652)+P87(f861(x45651,x45652))
% 155.90/155.61 [4566]~P88(x45662)+P88(f861(x45661,x45662))
% 155.90/155.61 [4567]~P87(x45672)+P98(f861(x45671,x45672))
% 155.90/155.61 [4568]~P95(x45682)+P94(f861(x45681,x45682))
% 155.90/155.61 [4569]~P87(x45692)+P99(f861(x45691,x45692))
% 155.90/155.61 [4570]~P96(x45702)+P96(f861(x45701,x45702))
% 155.90/155.61 [4571]~P102(x45712)+P102(f861(x45711,x45712))
% 155.90/155.61 [4572]~P106(x45722)+P106(f861(x45721,x45722))
% 155.90/155.61 [4573]~P104(x45732)+P104(f861(x45731,x45732))
% 155.90/155.61 [4574]~P105(x45742)+P105(f861(x45741,x45742))
% 155.90/155.61 [4575]~P95(x45752)+P97(f861(x45751,x45752))
% 155.90/155.61 [4576]~P31(x45762)+P31(f861(x45761,x45762))
% 155.90/155.61 [4577]~P95(x45772)+P95(f861(x45771,x45772))
% 155.90/155.61 [4589]E(x45891,x45892)+~E(f312(a27,x45891),f312(a27,x45892))
% 155.90/155.61 [4591]E(x45911,x45912)+~E(f312(a126,x45911),f312(a126,x45912))
% 155.90/155.61 [4592]E(x45921,x45922)+~E(f312(a121,x45921),f312(a121,x45922))
% 155.90/155.61 [4593]E(x45931,x45932)+~E(f312(a3,x45931),f312(a3,x45932))
% 155.90/155.61 [4595]E(x45951,x45952)+~E(f312(a19,x45951),f312(a19,x45952))
% 155.90/155.61 [4703]~P60(x47031)+E(f54(x47031,x47032,x47032),f2(x47031))
% 155.90/155.61 [4734]~P41(x47341,x47342)+P41(f854(x47341),f142(x47341,x47342))
% 155.90/155.61 [4735]~P41(x47351,x47352)+P41(f854(x47351),f141(x47351,x47352))
% 155.90/155.61 [4830]~P41(x48301,x48302)+P41(f861(x48301,a846),f305(x48301,x48302))
% 155.90/155.61 [4831]~P41(x48311,x48312)+P41(f861(x48311,a846),f303(x48311,x48312))
% 155.90/155.61 [4946]~P32(x49461)+P43(f283(a1,x49461,x49462))
% 155.90/155.61 [5048]~P41(x50481,x50482)+P59(x50481,f76(x50481,x50481,x50482))
% 155.90/155.61 [5548]~P76(x55481)+P19(x55481,x55481,f88(x55481),x55482)
% 155.90/155.61 [4543]~E(x45432,f127(x45431))+E(f312(f164(x45431),x45432),f127(x45431))
% 155.90/155.61 [4544]~E(x45442,f127(x45441))+E(f312(f165(x45441),x45442),f127(x45441))
% 155.90/155.61 [4599]E(x45991,f312(a118,x45992))+~E(f312(f114(a1),x45991),x45992)
% 155.90/155.61 [4603]E(x46031,f127(x46032))+~E(f312(f164(x46032),x46031),f127(x46032))
% 155.90/155.61 [4604]E(x46041,f127(x46042))+~E(f312(f165(x46042),x46041),f127(x46042))
% 155.90/155.61 [4615]~E(x46152,f2(a1))+E(f312(f47(a1,x46151),x46152),f2(a1))
% 155.90/155.61 [4624]~P90(x46241)+E(f312(f117(x46241),x46242),f312(f116(x46241),x46242))
% 155.90/155.61 [4631]~E(x46312,f192(x46311))+E(f218(x46311,x46312),f189(f861(x46311,a846)))
% 155.90/155.61 [4633]~P62(x46331)+P22(f312(f70(x46331),x46332))
% 155.90/155.61 [4640]E(x46401,f192(x46402))+E(f312(f219(x46402),f363(x46402,x46401)),x46401)
% 155.90/155.61 [4641]E(x46411,f192(x46412))+E(f312(f219(x46412),f494(x46412,x46411)),x46411)
% 155.90/155.61 [4642]E(x46421,f192(x46422))+E(f312(f219(x46422),f523(x46422,x46421)),x46421)
% 155.90/155.61 [4643]~E(f611(x46432,x46431),f127(x46431))+E(f175(x46431,x46432),f127(f854(x46431)))
% 155.90/155.61 [4645]~P60(x46451)+E(f312(f47(x46451,x46452),f87(x46451)),x46452)
% 155.90/155.61 [4652]~E(x46522,f127(x46521))+E(f312(f168(x46521),x46522),f189(f861(x46521,a846)))
% 155.90/155.61 [4653]~E(x46532,f127(x46531))+E(f189(f861(x46531,a846)),f312(f168(x46531),x46532))
% 155.90/155.61 [4655]E(x46551,x46552)+~E(f312(f114(a1),x46551),f312(f114(a1),x46552))
% 155.90/155.61 [4658]~P60(x46581)+E(f312(f47(x46581,x46582),f2(x46581)),f2(x46581))
% 155.90/155.61 [4660]E(f207(x46601,x46602),f2(a853))+P22(f312(f70(x46601),x46602))
% 155.90/155.61 [4680]~P112(x46801)+E(f91(x46801,f91(x46801,x46802)),f91(x46801,x46802))
% 155.90/155.61 [4694]~P107(x46941)+E(f312(f312(f240(x46941),x46942),f87(a853)),x46942)
% 155.90/155.61 [4695]~P78(x46951)+E(f312(f312(f240(x46951),x46952),f87(a853)),x46952)
% 155.90/155.61 [4697]E(x46971,x46972)+E(f257(x46971,x46972),f312(f312(f89(a113),x46972),f87(a113)))
% 155.90/155.61 [4700]E(f312(f53(x47001),x47002),f2(a853))+P22(f312(f70(x47001),x47002))
% 155.90/155.61 [4704]~E(f148(x47041,x47042),x47042)+P22(f312(f133(x47041),x47042))
% 155.90/155.61 [4707]~P25(x47071)+E(f312(f312(f89(x47071),x47072),f2(x47071)),x47072)
% 155.90/155.61 [4708]~P107(x47081)+E(f312(f312(f89(x47081),x47082),f2(x47081)),x47082)
% 155.90/155.61 [4709]~P26(x47091)+E(f312(f312(f89(x47091),x47092),f2(x47091)),x47092)
% 155.90/155.61 [4710]~P71(x47101)+E(f312(f312(f21(x47101),x47102),f2(x47101)),x47102)
% 155.90/155.61 [4711]~P94(x47111)+E(f312(f312(f124(x47111),x47112),f189(x47111)),x47112)
% 155.90/155.61 [4712]~P97(x47121)+E(f312(f312(f115(x47121),x47122),f235(x47121)),x47122)
% 155.90/155.61 [4713]~P107(x47131)+E(f312(f312(f90(x47131),x47132),f87(x47131)),x47132)
% 155.90/155.61 [4714]~P78(x47141)+E(f312(f312(f90(x47141),x47142),f87(x47141)),x47142)
% 155.90/155.61 [4715]~P72(x47151)+E(f312(f312(f90(x47151),x47152),f87(x47151)),x47152)
% 155.90/155.61 [4716]~P114(x47161)+E(f312(f312(f268(x47161),x47162),f87(x47161)),x47162)
% 155.90/155.61 [4717]~P107(x47171)+E(f312(f312(f240(x47171),x47172),f2(a853)),f87(x47171))
% 155.90/155.61 [4718]~P109(x47181)+E(f312(f312(f240(x47181),x47182),f2(a853)),f87(x47181))
% 155.90/155.61 [4719]~E(x47192,f189(f861(x47191,a846)))+E(f312(f53(x47191),x47192),f2(a853))
% 155.90/155.61 [4729]~P60(x47291)+E(f54(x47291,x47292,f2(x47291)),x47292)
% 155.90/155.61 [4736]~P97(x47361)+E(f312(f312(f124(x47361),x47362),f235(x47361)),f235(x47361))
% 155.90/155.61 [4737]~P94(x47371)+E(f312(f312(f115(x47371),x47372),f189(x47371)),f189(x47371))
% 155.90/155.61 [4738]~P107(x47381)+E(f312(f312(f90(x47381),x47382),f2(x47381)),f2(x47381))
% 155.90/155.61 [4739]~P126(x47391)+E(f312(f312(f90(x47391),x47392),f2(x47391)),f2(x47391))
% 155.90/155.61 [4740]~P115(x47401)+E(f312(f312(f268(x47401),x47402),f2(x47401)),f2(x47401))
% 155.90/155.61 [4741]E(x47411,f192(x47412))+~E(f218(x47412,x47411),f189(f861(x47412,a846)))
% 155.90/155.61 [4744]~P60(x47441)+E(f54(x47441,x47442,f87(x47441)),f2(x47441))
% 155.90/155.61 [4745]~P60(x47451)+E(f54(x47451,f2(x47451),x47452),f2(x47451))
% 155.90/155.61 [4774]E(x47741,f2(a853))+E(f63(x47742,x47741,f127(x47742)),f127(f854(x47742)))
% 155.90/155.61 [4797]P41(x47971,x47972)+~E(f687(x47972,x47971),f189(f861(x47971,a846)))
% 155.90/155.61 [4798]E(x47981,f127(x47982))+~E(f312(f168(x47982),x47981),f189(f861(x47982,a846)))
% 155.90/155.61 [4799]E(x47991,f127(x47992))+~E(f189(f861(x47992,a846)),f312(f168(x47992),x47991))
% 155.90/155.61 [4802]~E(x48021,x48022)+P22(f312(f312(a309,x48021),x48022))
% 155.90/155.61 [4812]P22(x48121)+P22(f312(f312(a315,x48121),x48122))
% 155.90/155.61 [4813]E(x48131,f127(x48132))+E(f312(f312(f161(x48132),x48131),f2(a853)),f312(f137(x48132),x48131))
% 155.90/155.61 [4816]E(f148(x48161,x48162),x48162)+~P22(f312(f133(x48161),x48162))
% 155.90/155.61 [4821]~P22(x48212)+P22(f312(f312(a315,x48211),x48212))
% 155.90/155.61 [4822]~P22(x48222)+P22(f312(f312(a311,x48221),x48222))
% 155.90/155.61 [4823]~P22(x48231)+P22(f312(f312(a311,x48231),x48232))
% 155.90/155.61 [4833]~E(f582(x48332,x48331),f599(x48332,x48331))+P22(f312(f133(x48331),x48332))
% 155.90/155.61 [4841]E(f312(f233(x48411),x48412),f189(f861(x48411,a846)))+P22(f312(x48412,f538(x48412)))
% 155.90/155.61 [4842]E(f189(f861(x48421,a846)),f312(f233(x48421),x48422))+P22(f312(x48422,f539(x48422)))
% 155.90/155.61 [4909]~P112(x49091)+E(f312(f312(f90(x49091),x49092),f91(x49091,x49092)),f312(f84(x49091),x49092))
% 155.90/155.61 [4945]~P57(x49451,x49452)+P57(x49451,f312(f265(x49451,x49451),x49452))
% 155.90/155.61 [4962]~E(f312(a30,x49621),f312(f219(a847),x49622))+P22(f312(a24,f312(a27,x49621)))
% 155.90/155.61 [4967]E(x49671,x49672)+~P22(f312(f312(a309,x49671),x49672))
% 155.90/155.61 [4971]~P22(f312(a24,x49712))+P22(f312(a24,f35(x49711,x49712)))
% 155.90/155.61 [4980]P22(x49801)+~P22(f312(f312(a310,x49802),x49801))
% 155.90/155.61 [4981]P22(x49811)+~P22(f312(f312(a310,x49811),x49812))
% 155.90/155.61 [4985]~P106(x49851)+P22(f312(f312(f227(x49851),x49852),f235(x49851)))
% 155.90/155.61 [4989]E(x49891,x49892)+~E(f312(x49891,f364(x49892,x49891)),f312(x49892,f364(x49892,x49891)))
% 155.90/155.61 [5020]E(x50201,f2(a853))+E(f199(x50201,f54(a853,x50202,x50201)),f199(x50202,x50201))
% 155.90/155.61 [5025]~P103(x50251)+P33(x50251,f312(f312(f147(x50251),x50252),f127(x50251)))
% 155.90/155.61 [5046]~E(x50461,x50462)+P22(f312(f312(f228(a853),x50461),f312(a126,x50462)))
% 155.90/155.61 [5056]~E(x50561,f2(a853))+P22(f312(f312(f228(a853),x50561),f312(a126,x50562)))
% 155.90/155.61 [5068]P22(f312(x50681,x50682))+P22(f312(f312(f227(a1),f2(a1)),f320(x50681)))
% 155.90/155.61 [5105]P22(f312(a24,x51051))+~P22(f312(a24,f35(x51052,x51051)))
% 155.90/155.61 [5107]P22(f312(a24,x51071))+~P22(f312(a24,f36(x51072,x51071)))
% 155.90/155.61 [5109]P22(f312(a24,x51091))+~P22(f312(a24,f36(x51091,x51092)))
% 155.90/155.61 [5141]P57(x51411,x51412)+~P57(x51411,f312(f265(x51411,x51411),x51412))
% 155.90/155.61 [5144]~E(f54(a853,x51442,x51441),f2(a853))+E(f312(f312(f90(a853),x51441),f325(x51441,x51442)),x51442)
% 155.90/155.61 [5145]~E(f54(a1,x51452,x51451),f2(a1))+E(f312(f312(f90(a1),x51451),f326(x51451,x51452)),x51452)
% 155.90/155.61 [5170]~P22(f312(x51701,x51702))+P22(f312(f312(f227(a1),f2(a1)),f319(x51701)))
% 155.90/155.61 [5182]E(f312(f312(f21(a853),f312(a118,x51821)),f312(a118,x51822)),f312(a118,x51821))+~P22(f312(a194,x51822))
% 155.90/155.61 [5211]E(f258(x52111,x52112),f87(a113))+~P22(f312(f312(f227(a113),x52111),f87(a113)))
% 155.90/155.61 [5299]E(f312(f312(f161(x52991),x52992),f582(x52992,x52991)),f312(f312(f161(x52991),x52992),f599(x52992,x52991)))+P22(f312(f133(x52991),x52992))
% 155.90/155.61 [5342]~P22(f312(x53421,f99(x53422,x53421)))+P22(f312(x53421,f612(x53422,x53421)))
% 155.90/155.61 [5406]P59(x54061,x54062)+~P22(f312(f300(x54061,x54062),f553(x54062,x54061)))
% 155.90/155.61 [5556]~E(f312(a126,f54(a853,x55561,x55562)),x55562)+E(f54(a853,f312(a126,x55561),x55562),f2(a853))
% 155.90/155.61 [5615]~P111(x56151)+P22(f312(f312(f314(x56151),f312(f114(x56151),x56152)),f123(x56151)))
% 155.90/155.61 [5616]~P23(x56161)+P22(f312(f312(f314(x56161),f312(f114(x56161),x56162)),f187(x56161)))
% 155.90/155.61 [5617]~P90(x56171)+P22(f312(f312(f314(x56171),f312(f117(x56171),x56172)),f123(x56171)))
% 155.90/155.61 [5618]~P111(x56181)+P22(f312(f312(f314(x56181),f312(f116(x56181),x56182)),f123(x56181)))
% 155.90/155.61 [5753]E(f312(a126,f54(a853,x57531,x57532)),x57532)+E(f54(a853,f312(a126,x57531),x57532),f312(a126,f54(a853,x57531,x57532)))
% 155.90/155.61 [6135]~E(x61351,f2(a1))+E(f312(f312(f239(a1,a1),f312(f47(a1,x61351),x61352)),f54(a1,x61351,x61352)),f312(f312(f239(a1,a1),f2(a1)),f2(a1)))
% 155.90/155.61 [6166]P41(x61661,x61662)+~P22(f312(f312(f314(x61661),f554(x61662,x61661)),f301(x61661,x61662)))
% 155.90/155.61 [6202]~P117(x62021)+~P22(f312(f312(f228(x62021),f312(f114(x62021),x62022)),f2(x62021)))
% 155.90/155.61 [6203]~P83(x62031)+~P22(f312(f312(f228(x62031),f312(f84(x62031),x62032)),f2(x62031)))
% 155.90/155.61 [6288]P22(f312(f312(f228(a1),x62881),f54(a1,x62882,x62881)))+~P22(f312(f312(f228(a1),x62881),f2(a1)))
% 155.90/155.61 [6384]E(f312(f312(f289(a853),f312(a126,x63841)),f283(a853,x63842,x63841)),f283(a853,x63842,f312(a126,x63841)))+~P22(f312(f312(f227(a853),x63842),f312(a126,x63841)))
% 155.90/155.61 [6469]~P103(x64691)+P33(x64691,f144(x64691,x64691,f5(x64691),x64692))
% 155.90/155.61 [6601]E(f312(f164(x66011),x66012),x66012)+~P22(f312(f312(f227(a853),f312(f190(f854(x66011)),x66012)),f87(a853)))
% 155.90/155.61 [6616]~P83(x66161)+P22(f312(f312(f227(x66161),f312(f88(x66161),f312(f84(x66161),x66162))),f2(x66161)))
% 155.90/155.61 [6652]~P41(x66521,x66522)+P41(x66521,f312(f312(f267(x66521,x66521,x66521),x66522),f287(x66521,x66522)))
% 155.90/155.61 [6865]~P22(f312(f312(f228(a1),x68652),f2(a1)))+P22(f312(f312(f227(a1),f54(a1,x68651,x68652)),f2(a1)))
% 155.90/155.61 [7257]~P23(x72571)+E(f191(x72571,f312(f312(f7(x72571,x72571,x72571),f89(x72571)),f87(x72571)),x72572,f2(x72571)),f312(f114(x72571),x72572))
% 155.90/155.61 [7283]~P119(x72831)+~P22(f312(f312(f228(x72831),f312(f312(f90(x72831),x72832),x72832)),f2(x72831)))
% 155.90/155.61 [9903]~P112(x99031)+~P22(f312(f312(f228(x99031),f312(f312(f240(x99031),x99032),f312(f117(a853),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(x99031)))
% 155.90/155.61 [4601]~E(x46012,f127(x46011))+E(f312(f190(f854(x46011)),x46012),f2(a853))
% 155.90/155.61 [4644]~E(x46441,f2(a853))+E(f312(f312(f89(a853),x46441),x46442),x46442)
% 155.90/155.61 [4646]~E(x46462,f2(a853))+E(f312(f312(f90(a853),x46461),x46462),f2(a853))
% 155.90/155.61 [4648]~E(x46481,f2(a853))+E(f312(f312(f90(a853),x46481),x46482),f2(a853))
% 155.90/155.61 [4649]~E(x46492,f2(a853))+E(f312(f312(f240(a853),x46491),x46492),f87(a853))
% 155.90/155.61 [4661]E(x46611,f127(x46612))+~E(f312(f190(f854(x46612)),x46611),f2(a853))
% 155.90/155.61 [4662]~P87(x46621)+E(f312(f312(f124(x46621),x46622),x46622),x46622)
% 155.90/155.61 [4664]~P98(x46641)+E(f312(f312(f124(x46641),x46642),x46642),x46642)
% 155.90/155.61 [4665]~P87(x46651)+E(f312(f312(f115(x46651),x46652),x46652),x46652)
% 155.90/155.61 [4667]~P99(x46671)+E(f312(f312(f115(x46671),x46672),x46672),x46672)
% 155.90/155.61 [4669]~P93(x46691)+E(f312(f312(f90(x46691),x46692),x46692),x46692)
% 155.90/155.61 [4671]~P103(x46711)+E(f312(f312(f225(x46711),x46712),x46712),x46712)
% 155.90/155.61 [4673]~P103(x46731)+E(f312(f312(f226(x46731),x46732),x46732),x46732)
% 155.90/155.61 [4692]~P60(x46921)+E(f312(f47(x46921,f2(x46921)),x46922),f2(x46921))
% 155.90/155.61 [4693]~P71(x46931)+E(f312(f312(f21(x46931),x46932),x46932),f2(x46931))
% 155.90/155.61 [4705]~P71(x47051)+E(f312(f88(x47051),f312(f88(x47051),x47052)),x47052)
% 155.90/155.61 [4706]~P88(x47061)+E(f312(f88(x47061),f312(f88(x47061),x47062)),x47062)
% 155.90/155.61 [4722]~E(x47222,f2(a853))+E(f312(f312(f240(a853),x47221),x47222),f312(a126,f2(a853)))
% 155.90/155.61 [4753]~P25(x47531)+E(f312(f312(f89(x47531),f2(x47531)),x47532),x47532)
% 155.90/155.61 [4754]~P107(x47541)+E(f312(f312(f89(x47541),f2(x47541)),x47542),x47542)
% 155.90/155.61 [4755]~P26(x47551)+E(f312(f312(f89(x47551),f2(x47551)),x47552),x47552)
% 155.90/155.61 [4756]~P94(x47561)+E(f312(f312(f124(x47561),f189(x47561)),x47562),x47562)
% 155.90/155.61 [4757]~P97(x47571)+E(f312(f312(f115(x47571),f235(x47571)),x47572),x47572)
% 155.90/155.61 [4758]~P107(x47581)+E(f312(f312(f90(x47581),f87(x47581)),x47582),x47582)
% 155.90/155.61 [4759]~P78(x47591)+E(f312(f312(f90(x47591),f87(x47591)),x47592),x47592)
% 155.90/155.61 [4760]~P72(x47601)+E(f312(f312(f90(x47601),f87(x47601)),x47602),x47602)
% 155.90/155.61 [4779]~P97(x47791)+E(f312(f312(f124(x47791),f235(x47791)),x47792),f235(x47791))
% 155.90/155.61 [4780]~P94(x47801)+E(f312(f312(f115(x47801),f189(x47801)),x47802),f189(x47801))
% 155.90/155.61 [4781]~P107(x47811)+E(f312(f312(f90(x47811),f2(x47811)),x47812),f2(x47811))
% 155.90/155.61 [4782]~P126(x47821)+E(f312(f312(f90(x47821),f2(x47821)),x47822),f2(x47821))
% 155.90/155.61 [4783]~P78(x47831)+E(f312(f312(f240(x47831),f87(x47831)),x47832),f87(x47831))
% 155.90/155.61 [4784]~P114(x47841)+E(f312(f312(f268(x47841),f2(x47841)),x47842),f2(x47841))
% 155.90/155.61 [4792]E(x47921,f127(x47922))+E(f140(x47922,f312(f165(x47922),x47921)),f312(f137(x47922),x47921))
% 155.90/155.61 [4793]E(x47931,f127(x47932))+E(f312(f137(x47932),f312(f165(x47932),x47931)),f140(x47932,x47931))
% 155.90/155.61 [4794]E(x47941,f2(a853))+~E(f312(f312(f89(a853),x47942),x47941),x47942)
% 155.90/155.61 [4800]~P111(x48001)+E(f312(f116(x48001),f312(f114(a1),x48002)),f312(f114(x48001),x48002))
% 155.90/155.61 [4801]~P90(x48011)+E(f312(f116(x48011),f312(f117(a1),x48012)),f312(f117(x48011),x48012))
% 155.90/155.61 [4808]E(x48081,f2(a853))+~E(f312(f312(f89(a853),x48082),x48081),f2(a853))
% 155.90/155.61 [4809]E(x48091,f2(a853))+~E(f312(f312(f89(a853),x48091),x48092),f2(a853))
% 155.90/155.61 [4810]E(x48101,f87(a853))+~E(f312(f312(f90(a853),x48102),x48101),f87(a853))
% 155.90/155.61 [4811]E(x48111,f87(a853))+~E(f312(f312(f90(a853),x48111),x48112),f87(a853))
% 155.90/155.61 [4826]~P83(x48261)+E(f312(f84(x48261),f312(f88(x48261),x48262)),f312(f84(x48261),x48262))
% 155.90/155.61 [4827]~P112(x48271)+E(f312(f84(x48271),f312(f114(x48271),x48272)),f312(f114(x48271),x48272))
% 155.90/155.61 [4828]~P83(x48281)+E(f312(f84(x48281),f312(f84(x48281),x48282)),f312(f84(x48281),x48282))
% 155.90/155.61 [4829]~P26(x48291)+E(f312(f162(x48291),f312(f165(x48291),x48292)),f312(f162(x48291),x48292))
% 155.90/155.61 [4834]~E(x48341,f312(a126,f2(a853)))+E(f312(f312(f240(a853),x48341),x48342),f312(a126,f2(a853)))
% 155.90/155.61 [4845]~P71(x48451)+E(f312(f312(f21(x48451),f2(x48451)),x48452),f312(f88(x48451),x48452))
% 155.90/155.61 [4846]~E(x48462,f2(a853))+E(f135(a853,f312(f282(a853,x48461),x48462)),f127(a853))
% 155.90/155.61 [4855]~P90(x48551)+E(f312(f312(f89(x48551),x48552),f312(f117(x48551),a92)),x48552)
% 155.90/155.61 [4856]E(x48561,f2(a1))+E(f55(f312(f84(a1),x48562),f312(f84(a1),x48561)),f61(x48562,x48561))
% 155.90/155.61 [4870]~E(x48701,x48702)+P22(f312(f312(f227(a853),x48701),x48702))
% 155.90/155.61 [4877]~E(x48771,f2(a113))+E(f312(f312(f89(a853),f312(a19,x48771)),x48772),x48772)
% 155.90/155.61 [4878]~E(f312(f117(a1),x48782),f312(f114(a1),x48781))+E(x48781,f312(a118,f312(f117(a1),x48782)))
% 155.90/155.61 [4879]~P31(x48791)+E(f109(x48791,f312(f16(x48791,x48791),x48792)),x48792)
% 155.90/155.61 [4888]~P32(x48881)+P32(f312(f312(f240(a1),x48881),x48882))
% 155.90/155.61 [4889]~P71(x48891)+E(f312(f312(f89(x48891),x48892),f312(f88(x48891),x48892)),f2(x48891))
% 155.90/155.61 [4890]~P88(x48901)+E(f312(f312(f124(x48901),x48902),f312(f88(x48901),x48902)),f235(x48901))
% 155.90/155.61 [4891]~P88(x48911)+E(f312(f312(f115(x48911),x48912),f312(f88(x48911),x48912)),f189(x48911))
% 155.90/155.61 [4917]E(x49171,f2(a853))+~E(f312(f88(a1),f312(f114(a1),x49172)),f312(f114(a1),x49171))
% 155.90/155.61 [4918]E(x49181,f2(a853))+~E(f312(f88(a1),f312(f114(a1),x49181)),f312(f114(a1),x49182))
% 155.90/155.61 [4923]E(f196(x49231,x49232),f2(a1))+P22(f312(f312(f227(a1),x49232),x49231))
% 155.90/155.61 [4924]E(f174(x49241,x49242),f127(a1))+P22(f312(f312(f227(a1),x49241),x49242))
% 155.90/155.61 [4937]E(x49371,f312(a126,f2(a853)))+~E(f312(f312(f90(a853),x49372),x49371),f312(a126,f2(a853)))
% 155.90/155.61 [4938]E(x49381,f312(a126,f2(a853)))+~E(f312(f312(f90(a853),x49381),x49382),f312(a126,f2(a853)))
% 155.90/155.61 [4939]~P102(x49391)+P22(f312(f312(f227(x49391),x49392),x49392))
% 155.90/155.61 [4942]~P90(x49421)+E(f312(f312(f90(x49421),x49422),f312(f117(x49421),a111)),f312(f88(x49421),x49422))
% 155.90/155.61 [4959]~P90(x49591)+E(f312(f88(x49591),f312(f117(x49591),x49592)),f312(f117(x49591),f312(f88(a1),x49592)))
% 155.90/155.61 [4960]~P111(x49601)+E(f312(f88(x49601),f312(f116(x49601),x49602)),f312(f116(x49601),f312(f88(a1),x49602)))
% 155.90/155.61 [4990]~E(x49901,f312(a126,x49902))+P22(f312(f312(f228(a853),f2(a853)),x49901))
% 155.90/155.61 [5007]~P103(x50071)+E(f312(f88(f861(x50071,a846)),f312(f281(x50071),x50072)),f312(f280(x50071),x50072))
% 155.90/155.61 [5008]~P103(x50081)+E(f312(f88(f861(x50081,a846)),f312(f280(x50081),x50082)),f312(f281(x50081),x50082))
% 155.90/155.61 [5009]~P103(x50091)+E(f312(f88(f861(x50091,a846)),f312(f234(x50091),x50092)),f312(f279(x50091),x50092))
% 155.90/155.61 [5010]~P103(x50101)+E(f312(f88(f861(x50101,a846)),f312(f279(x50101),x50102)),f312(f234(x50101),x50102))
% 155.90/155.61 [5019]~E(f312(f114(a1),x50192),x50191)+P22(f312(f312(f227(a1),f2(a1)),x50191))
% 155.90/155.61 [5028]~E(x50282,f2(a1))+E(f61(x50281,x50282),f312(f312(f239(a1,a1),f2(a1)),f312(f84(a1),x50281)))
% 155.90/155.61 [5029]~P24(x50291)+P22(f312(f312(f227(x50291),f189(x50291)),x50292))
% 155.90/155.61 [5061]E(x50611,x50612)+~E(f312(f312(f89(a1),x50611),x50611),f312(f312(f89(a1),x50612),x50612))
% 155.90/155.61 [5067]~P22(f312(x50671,x50672))+P22(f312(x50671,f312(a118,f319(x50671))))
% 155.90/155.61 [5093]~P112(x50931)+E(f312(f312(f90(x50931),f91(x50931,x50932)),f312(f84(x50931),x50932)),x50932)
% 155.90/155.61 [5094]E(x50941,x50942)+~P22(f312(f312(f195(a23),x50941),x50942))
% 155.90/155.61 [5103]~E(x51032,f2(a853))+E(f94(f860(a853,a853),f56(x51031,x51032)),f312(f312(f239(a853,a853),f2(a853)),x51031))
% 155.90/155.61 [5114]~E(x51141,x51142)+~P22(f312(f312(f228(a853),x51141),x51142))
% 155.90/155.61 [5115]~E(x51151,x51152)+~P22(f312(f312(f228(a1),x51151),x51152))
% 155.90/155.61 [5118]~P23(x51181)+E(f312(f312(f89(x51181),f87(x51181)),f312(f114(x51181),x51182)),f312(f114(x51181),f312(a126,x51182)))
% 155.90/155.61 [5122]~E(x51221,f2(a853))+~P22(f312(f312(f228(a853),x51222),x51221))
% 155.90/155.61 [5138]E(f148(x51381,x51382),x51382)+~E(f312(f190(f854(x51381)),f148(x51381,x51382)),f312(f190(f854(x51381)),x51382))
% 155.90/155.61 [5139]E(f312(f53(x51391),f312(f168(x51391),x51392)),f312(f190(f854(x51391)),x51392))+~P22(f312(f133(x51391),x51392))
% 155.90/155.61 [5149]~P22(f312(x51491,f819(x51491)))+P22(f312(x51491,f312(f114(a1),x51492)))
% 155.90/155.61 [5160]E(f174(x51601,x51602),f127(a1))+~P22(f312(f312(f228(a1),x51602),x51601))
% 155.90/155.61 [5161]E(f258(x51611,x51612),f87(a113))+~P22(f312(f312(f228(a113),x51612),x51611))
% 155.90/155.61 [5164]~P105(x51641)+E(f283(x51641,x51642,x51642),f312(f312(f289(x51641),x51642),f189(f861(x51641,a846))))
% 155.90/155.61 [5185]~E(f312(f312(f21(a853),x51851),x51852),f2(a853))+P22(f312(f312(f227(a853),x51851),x51852))
% 155.90/155.61 [5208]~E(x52082,f2(a853))+E(f63(x52081,x52082,f127(x52081)),f312(f312(f147(f854(x52081)),f127(x52081)),f127(f854(x52081))))
% 155.90/155.61 [5212]~P102(x52121)+~P22(f312(f312(f228(x52121),x52122),x52122))
% 155.90/155.61 [5215]~E(f54(a1,x52151,x52152),f2(a1))+E(f54(a1,x52151,f312(f88(a1),x52152)),f2(a1))
% 155.90/155.61 [5217]~E(f54(a1,x52171,x52172),f2(a1))+E(f54(a1,f312(f88(a1),x52171),x52172),f2(a1))
% 155.90/155.61 [5224]E(f312(f282(a853,x52241),f312(a126,x52242)),f189(f861(a853,a846)))+P22(f312(f312(f227(a853),x52241),x52242))
% 155.90/155.61 [5243]E(f135(a853,f312(f282(a853,x52431),x52432)),f127(a853))+P22(f312(f312(f228(a853),x52431),x52432))
% 155.90/155.61 [5248]~E(f312(f53(x52481),f312(f168(x52481),x52482)),f312(f190(f854(x52481)),x52482))+P22(f312(f133(x52481),x52482))
% 155.90/155.61 [5252]~P22(f312(f133(x52521),x52522))+P22(f312(f133(x52521),f312(f164(x52521),x52522)))
% 155.90/155.61 [5253]~P22(f312(f133(x52531),x52532))+P22(f312(f133(x52531),f312(f167(x52531),x52532)))
% 155.90/155.61 [5254]~P22(f312(f133(x52541),x52542))+P22(f312(f133(x52541),f312(f165(x52541),x52542)))
% 155.90/155.61 [5260]E(f312(f47(a853,x52601),x52602),f2(a853))+~P22(f312(f312(f228(a853),x52601),x52602))
% 155.90/155.61 [5261]P22(f312(x52611,x52612))+~P22(f312(x52611,f312(a118,f320(x52611))))
% 155.90/155.61 [5262]P22(f312(f312(f227(a853),x52622),x52621))+P22(f312(f312(f227(a853),x52621),x52622))
% 155.90/155.61 [5263]P22(f312(f312(f227(a1),x52632),x52631))+P22(f312(f312(f227(a1),x52631),x52632))
% 155.90/155.61 [5265]~P83(x52651)+P22(f312(f312(f227(x52651),x52652),f312(f84(x52651),x52652)))
% 155.90/155.61 [5268]P22(f312(x52681,f820(x52681)))+~P22(f312(x52681,f312(f114(a1),x52682)))
% 155.90/155.61 [5293]E(f312(f312(f21(a853),x52931),x52932),f2(a853))+~P22(f312(f312(f227(a853),x52931),x52932))
% 155.90/155.61 [5310]E(f54(a853,x53101,x53102),x53101)+~P22(f312(f312(f228(a853),x53101),x53102))
% 155.90/155.61 [5318]E(f54(a1,x53181,f312(f88(a1),x53182)),f269(x53181,x53182))+P22(f312(f312(f227(a1),f2(a1)),x53182))
% 155.90/155.61 [5330]E(f312(f312(f21(a1),x53301),x53302),f196(x53301,x53302))+~P22(f312(f312(f227(a1),x53302),x53301))
% 155.90/155.61 [5349]P22(f312(f312(f227(a1),f2(a1)),f819(x53491)))+P22(f312(x53491,f312(f114(a1),x53492)))
% 155.90/155.61 [5361]~P63(x53611)+P22(f312(f312(f314(x53611),x53612),f312(f168(x53611),f64(x53611))))
% 155.90/155.61 [5363]~P117(x53631)+P22(f312(f312(f227(x53631),f2(x53631)),f312(f114(x53631),x53632)))
% 155.90/155.61 [5364]~P83(x53641)+P22(f312(f312(f227(x53641),f2(x53641)),f312(f84(x53641),x53642)))
% 155.90/155.61 [5372]E(f312(f47(a1,x53721),x53722),f270(x53721,x53722))+~P22(f312(f312(f227(a1),f2(a1)),x53722))
% 155.90/155.61 [5392]E(f312(f312(f89(a853),x53921),f821(x53922,x53921)),x53922)+~P22(f312(f312(f227(a853),x53921),x53922))
% 155.90/155.61 [5404]~E(f312(f117(a1),x54041),f312(f114(a1),x54042))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x54041)))
% 155.90/155.61 [5407]E(f283(a1,x54071,x54072),f189(f861(a1,a846)))+~P22(f312(f312(f228(a1),x54072),x54071))
% 155.90/155.61 [5410]~P112(x54101)+E(f312(f312(f90(x54101),f312(f84(x54101),x54102)),f312(f84(x54101),x54102)),f312(f312(f90(x54101),x54102),x54102))
% 155.90/155.61 [5415]E(f135(a853,f312(f282(a853,x54151),f312(a126,x54152))),f127(a853))+P22(f312(f312(f227(a853),x54151),x54152))
% 155.90/155.61 [5438]P22(f312(f133(x54381),x54382))+~P22(f312(f133(x54381),f312(f164(x54381),x54382)))
% 155.90/155.61 [5439]P22(f312(f133(x54391),x54392))+~P22(f312(f133(x54391),f312(f165(x54391),x54392)))
% 155.90/155.61 [5460]P22(f312(f70(a853),x54601))+P22(f312(f312(f314(a853),f367(x54601,x54602)),x54601))
% 155.90/155.61 [5461]P22(f312(f70(a853),x54611))+P22(f312(f312(f314(a853),f371(x54611,x54612)),x54611))
% 155.90/155.61 [5462]P22(f312(f312(f228(a853),x54622),f312(a126,x54621)))+P22(f312(f312(f228(a853),x54621),x54622))
% 155.90/155.61 [5463]E(f54(a1,x54631,x54632),f269(x54631,x54632))+~P22(f312(f312(f227(a1),f2(a1)),x54632))
% 155.90/155.61 [5466]E(f135(a853,f312(f282(a853,x54661),x54662)),f127(a853))+~P22(f312(f312(f227(a853),x54662),x54661))
% 155.90/155.61 [5467]~P76(x54671)+E(f312(f290(x54671,x54671,f88(x54671)),f312(f281(x54671),x54672)),f312(f234(x54671),f312(f88(x54671),x54672)))
% 155.90/155.61 [5468]~P76(x54681)+E(f312(f290(x54681,x54681,f88(x54681)),f312(f280(x54681),x54682)),f312(f279(x54681),f312(f88(x54681),x54682)))
% 155.90/155.61 [5469]~P76(x54691)+E(f312(f290(x54691,x54691,f88(x54691)),f312(f234(x54691),x54692)),f312(f281(x54691),f312(f88(x54691),x54692)))
% 155.90/155.61 [5470]~P76(x54701)+E(f312(f290(x54701,x54701,f88(x54701)),f312(f279(x54701),x54702)),f312(f280(x54701),f312(f88(x54701),x54702)))
% 155.90/155.61 [5483]E(x54831,f189(f861(x54832,a846)))+P22(f312(f312(f314(x54832),f787(x54831,x54832)),x54831))
% 155.90/155.61 [5484]E(x54841,f189(f861(x54842,a846)))+P22(f312(f312(f314(x54842),f761(x54841,x54842)),x54841))
% 155.90/155.61 [5495]~P22(f312(f312(f228(a853),x54951),x54952))+P22(f312(f312(f227(a853),x54951),x54952))
% 155.90/155.61 [5496]~P22(f312(f312(f228(a1),x54961),x54962))+P22(f312(f312(f227(a1),x54961),x54962))
% 155.90/155.61 [5512]E(f55(x55121,x55122),f312(f312(f239(a1,a1),f2(a1)),x55121))+~P22(f312(f312(f228(a1),x55121),x55122))
% 155.90/155.61 [5514]E(f210(f312(f88(a1),x55141),f312(f88(a1),x55142)),f210(x55141,x55142))+~P22(f312(f312(f228(a1),x55142),f2(a1)))
% 155.90/155.61 [5526]E(x55261,x55262)+~E(f312(a3,f312(a126,f312(a19,x55261))),f312(a3,f312(a126,f312(a19,x55262))))
% 155.90/155.61 [5531]E(f55(x55311,x55312),f312(f312(f239(a1,a1),f2(a1)),x55311))+~P22(f312(f312(f227(a1),x55312),f2(a1)))
% 155.90/155.61 [5562]E(f54(a853,f312(f117(a853),x55621),f312(f117(a853),x55622)),f2(a853))+~P22(f312(a194,f312(f117(a1),x55621)))
% 155.90/155.61 [5580]P22(f312(f312(f227(a1),f2(a1)),f820(x55801)))+~P22(f312(x55801,f312(f114(a1),x55802)))
% 155.90/155.61 [5609]P43(f283(a1,x56091,x56092))+~P22(f312(f312(f227(a1),f2(a1)),x56091))
% 155.90/155.61 [5610]~P22(f312(f70(x56101),x56102))+P22(f312(f70(f861(x56101,a846)),f312(f288(x56101),x56102)))
% 155.90/155.61 [5624]E(f312(f47(a853,f312(f117(a853),x56241)),f312(f117(a853),x56242)),f2(a853))+~P22(f312(a194,f312(f117(a1),x56241)))
% 155.90/155.61 [5625]E(f312(f312(f89(a1),x56251),f312(f114(a1),f822(x56252,x56251))),x56252)+~P22(f312(f312(f227(a1),x56251),x56252))
% 155.90/155.61 [5633]P22(f312(f312(f227(a853),x56331),x56332))+P22(f312(f312(f227(a853),f312(a126,x56332)),x56331))
% 155.90/155.61 [5675]E(f312(f312(f90(a853),f312(f117(a853),x56751)),f312(f117(a853),x56752)),f2(a853))+~P22(f312(f312(f228(a1),x56751),a92))
% 155.90/155.61 [5677]P22(f312(f312(f228(a853),x56771),f312(a126,x56772)))+~P22(f312(f312(f228(a853),x56771),x56772))
% 155.90/155.61 [5679]P22(f312(f312(f228(a853),x56791),f312(a126,x56792)))+~P22(f312(f312(f227(a853),x56791),x56792))
% 155.90/155.61 [5681]P22(f312(f312(f227(a853),x56811),f312(a126,x56812)))+~P22(f312(f312(f227(a853),x56811),x56812))
% 155.90/155.61 [5684]~E(x56841,x56842)+P22(f312(f312(f228(a1),x56841),f312(f312(f89(a1),x56842),f87(a1))))
% 155.90/155.61 [5687]E(f54(a1,x56871,x56872),f2(a1))+E(f312(f312(f21(a1),x56872),f54(a1,x56871,x56872)),f54(a1,f312(f88(a1),x56871),x56872))
% 155.90/155.61 [5695]E(x56951,f127(x56952))+P22(f312(f312(f314(x56952),f140(x56952,x56951)),f312(f168(x56952),x56951)))
% 155.90/155.61 [5706]E(f94(f860(a853,a853),f56(x57061,x57062)),f312(f312(f239(a853,a853),f2(a853)),x57061))+~P22(f312(f312(f228(a853),x57061),x57062))
% 155.90/155.61 [5734]E(f312(f312(f89(a853),f312(f117(a853),x57341)),f312(f117(a853),x57342)),f312(f117(a853),x57342))+~P22(f312(f312(f228(a1),x57341),a92))
% 155.90/155.61 [5735]E(f312(f312(f21(a853),f312(f117(a853),x57351)),f312(f117(a853),x57352)),f312(f117(a853),x57351))+~P22(f312(f312(f228(a1),x57352),a92))
% 155.90/155.61 [5740]E(f312(a126,f312(f312(f89(a853),x57401),f818(x57402,x57401))),x57402)+~P22(f312(f312(f228(a853),x57401),x57402))
% 155.90/155.61 [5763]P22(f312(x57631,x57632))+~P22(f312(x57631,f312(a98,f583(x57632,x57631))))
% 155.90/155.61 [5771]~P22(f312(f312(f228(a853),x57711),f312(a126,x57712)))+P22(f312(f312(f227(a853),x57711),x57712))
% 155.90/155.61 [5817]E(f312(f312(f289(a853),x58171),f312(f282(a853,x58172),x58171)),f312(f282(a853,x58172),f312(a126,x58171)))+~P22(f312(f312(f227(a853),x58172),x58171))
% 155.90/155.61 [5822]E(x58221,f127(x58222))+E(f312(f312(f129(x58222),f128(x58222,x58221)),f312(f312(f147(x58222),f140(x58222,x58221)),f127(x58222))),x58221)
% 155.90/155.61 [5834]P22(f312(f70(x58341),x58342))+~P22(f312(f312(f228(a853),f2(a853)),f312(f53(x58341),x58342)))
% 155.90/155.61 [5836]~E(x58361,f189(f861(x58362,a846)))+~P22(f312(f312(f228(a853),f2(a853)),f312(f53(x58362),x58361)))
% 155.90/155.61 [5847]~P22(f312(f312(f228(a853),x58471),x58472))+P22(f312(f312(f227(a853),f312(a126,x58471)),x58472))
% 155.90/155.61 [5855]~P103(x58551)+E(f144(x58551,x58551,f5(x58551),f148(x58551,x58552)),f135(x58551,f312(f168(x58551),x58552)))
% 155.90/155.61 [5858]E(x58581,f127(x58582))+P22(f312(f312(f314(x58582),f312(f137(x58582),x58581)),f312(f168(x58582),x58581)))
% 155.90/155.61 [5864]~P117(x58641)+P22(f312(f312(f228(x58641),x58642),f312(f312(f89(x58641),x58642),f87(x58641))))
% 155.90/155.61 [5866]~P83(x58661)+P22(f312(f312(f227(x58661),f312(f88(x58661),x58662)),f312(f84(x58661),x58662)))
% 155.90/155.61 [5904]P22(f312(f70(a853),x59041))+~P22(f312(f312(f228(a853),f371(x59041,x59042)),x59042))
% 155.90/155.61 [5905]P22(f312(f70(a853),x59051))+~P22(f312(f312(f227(a853),f367(x59051,x59052)),x59052))
% 155.90/155.61 [5909]~P22(f312(f70(f860(x59091,x59091)),x59092))+P22(f312(f70(x59091),f312(f263(x59091),x59092)))
% 155.90/155.61 [5926]E(f312(f47(a853,f312(a118,x59261)),f312(a118,x59262)),f312(a118,f312(f47(a1,x59261),x59262)))+~P22(f312(f312(f227(a1),f2(a1)),x59261))
% 155.90/155.61 [5961]~P22(f312(f312(f228(a853),x59612),f312(a126,x59611)))+~P22(f312(f312(f228(a853),x59611),x59612))
% 155.90/155.61 [5962]~P105(x59621)+E(f312(f312(f115(f861(x59621,a846)),f312(f281(x59621),x59622)),f312(f234(x59621),x59622)),f312(f312(f289(x59621),x59622),f189(f861(x59621,a846))))
% 155.90/155.61 [5974]P22(f312(f70(x59741),x59742))+~P22(f312(f70(f861(x59741,a846)),f312(f288(x59741),x59742)))
% 155.90/155.61 [5997]P22(f312(f312(f228(a853),f312(a126,x59971)),f312(a126,x59972)))+~P22(f312(f312(f228(a853),x59971),x59972))
% 155.90/155.61 [5998]P22(f312(f312(f228(a853),f312(a19,x59981)),f312(a19,x59982)))+~P22(f312(f312(f228(a113),x59981),x59982))
% 155.90/155.61 [5999]P22(f312(f312(f228(a113),f312(a3,x59991)),f312(a3,x59992)))+~P22(f312(f312(f228(a853),x59991),x59992))
% 155.90/155.61 [6000]P22(f312(f312(f227(a853),f312(a126,x60001)),f312(a126,x60002)))+~P22(f312(f312(f227(a853),x60001),x60002))
% 155.90/155.61 [6001]P22(f312(f312(f227(a853),f312(a19,x60011)),f312(a19,x60012)))+~P22(f312(f312(f227(a113),x60011),x60012))
% 155.90/155.61 [6002]P22(f312(f312(f227(a113),f312(a3,x60021)),f312(a3,x60022)))+~P22(f312(f312(f227(a853),x60021),x60022))
% 155.90/155.61 [6005]E(x60051,x60052)+~E(f312(f290(a853,a1,f114(a1)),x60051),f312(f290(a853,a1,f114(a1)),x60052))
% 155.90/155.61 [6020]P22(f312(f312(f228(a853),x60201),x60202))+~P22(f312(f312(f228(a853),f312(a126,x60201)),x60202))
% 155.90/155.61 [6023]P22(f312(f312(f228(a853),x60231),x60232))+~P22(f312(f312(f227(a853),f312(a126,x60231)),x60232))
% 155.90/155.61 [6024]P22(f312(f312(f227(a853),x60241),x60242))+~P22(f312(f312(f227(a853),f312(a126,x60241)),x60242))
% 155.90/155.61 [6038]E(f54(a1,x60381,x60382),f2(a1))+E(f312(f312(f21(a1),f54(a1,x60381,x60382)),x60382),f54(a1,x60381,f312(f88(a1),x60382)))
% 155.90/155.61 [6104]E(f312(f53(f861(x61041,a846)),f312(f288(x61041),x61042)),f312(f312(f240(a853),f312(a126,f312(a126,f2(a853)))),f312(f53(x61041),x61042)))+~P22(f312(f70(x61041),x61042))
% 155.90/155.61 [6107]E(x61071,f127(x61072))+E(f312(f312(f161(x61072),x61071),f312(f312(f21(a853),f312(f190(f854(x61072)),x61071)),f87(a853))),f140(x61072,x61071))
% 155.90/155.61 [6132]E(x61321,f127(x61322))+E(f312(f312(f129(x61322),f312(f167(x61322),x61321)),f312(f312(f147(x61322),f312(f137(x61322),x61321)),f127(x61322))),f312(f164(x61322),x61321))
% 155.90/155.61 [6163]~P22(f312(f70(x61631),f48(f861(x61631,a846),x61632)))+P22(f312(f70(f861(x61631,a846)),x61632))
% 155.90/155.61 [6186]P22(f312(f312(f227(a853),f312(f117(a853),x61861)),f312(f117(a853),x61862)))+~P22(f312(f312(f227(a1),x61861),a92))
% 155.90/155.61 [6204]~P22(f312(f312(f228(a1),x62041),x62042))+P22(f312(f312(f228(a1),x62041),f312(f312(f89(a1),x62042),f87(a1))))
% 155.90/155.61 [6205]~P22(f312(f312(f227(a1),x62051),x62052))+P22(f312(f312(f228(a1),x62051),f312(f312(f89(a1),x62052),f87(a1))))
% 155.90/155.61 [6206]~P22(f312(f312(f228(a1),x62061),x62062))+P22(f312(f312(f227(a1),x62061),f312(f312(f21(a1),x62062),f87(a1))))
% 155.90/155.61 [6209]~P22(f312(f312(f228(a853),x62091),x62092))+P22(f312(f312(f228(a1),f312(f114(a1),x62091)),f312(f114(a1),x62092)))
% 155.90/155.61 [6210]~P22(f312(f312(f228(a1),x62101),x62102))+P22(f312(f312(f228(a1),f312(f117(a1),x62101)),f312(f117(a1),x62102)))
% 155.90/155.61 [6211]~P22(f312(f312(f227(a1),x62111),x62112))+P22(f312(f312(f227(a853),f312(f117(a853),x62111)),f312(f117(a853),x62112)))
% 155.90/155.61 [6213]~P22(f312(f312(f227(a853),x62131),x62132))+P22(f312(f312(f227(a1),f312(f114(a1),x62131)),f312(f114(a1),x62132)))
% 155.90/155.61 [6214]~P22(f312(f312(f227(a1),x62141),x62142))+P22(f312(f312(f227(a1),f312(f117(a1),x62141)),f312(f117(a1),x62142)))
% 155.90/155.61 [6229]~P22(f312(f312(f227(a853),x62291),x62292))+~P22(f312(f312(f227(a853),f312(a126,x62292)),x62291))
% 155.90/155.61 [6274]~P22(f312(f312(f228(a853),f312(a126,x62741)),f312(a126,x62742)))+P22(f312(f312(f228(a853),x62741),x62742))
% 155.90/155.61 [6275]~P22(f312(f312(f228(a113),f312(a3,x62751)),f312(a3,x62752)))+P22(f312(f312(f228(a853),x62751),x62752))
% 155.90/155.61 [6276]~P22(f312(f312(f228(a853),f312(a118,x62761)),f312(a118,x62762)))+P22(f312(f312(f228(a1),x62761),x62762))
% 155.90/155.61 [6277]~P22(f312(f312(f228(a853),f312(a19,x62771)),f312(a19,x62772)))+P22(f312(f312(f228(a113),x62771),x62772))
% 155.90/155.61 [6278]~P22(f312(f312(f227(a853),f312(a126,x62781)),f312(a126,x62782)))+P22(f312(f312(f227(a853),x62781),x62782))
% 155.90/155.61 [6279]~P22(f312(f312(f227(a113),f312(a3,x62791)),f312(a3,x62792)))+P22(f312(f312(f227(a853),x62791),x62792))
% 155.90/155.61 [6280]~P22(f312(f312(f227(a853),f312(a19,x62801)),f312(a19,x62802)))+P22(f312(f312(f227(a113),x62801),x62802))
% 155.90/155.61 [6318]~P22(f312(f312(f228(a853),f312(a118,x63182)),f312(a118,x63181)))+P22(f312(f312(f228(a1),f2(a1)),x63181))
% 155.90/155.61 [6350]P22(f312(f312(f227(a1),f2(a1)),f54(a1,x63501,x63502)))+~P22(f312(f312(f228(a1),f2(a1)),x63502))
% 155.90/155.61 [6503]P41(x65031,x65032)+~E(f312(f312(f267(x65031,x65031,x65031),x65032),x65032),f189(f861(f860(x65031,x65031),a846)))
% 155.90/155.61 [6515]~P41(x65151,x65152)+P41(x65151,f312(f312(f267(x65151,x65151,x65151),x65152),x65152))
% 155.90/155.61 [6527]P22(f312(f312(f228(a1),x65271),x65272))+~P22(f312(f312(f227(a1),x65271),f312(f312(f21(a1),x65272),f87(a1))))
% 155.90/155.61 [6528]P22(f312(f312(f227(a1),x65281),x65282))+~P22(f312(f312(f228(a1),x65281),f312(f312(f89(a1),x65282),f87(a1))))
% 155.90/155.61 [6531]P22(f312(f312(f228(a853),x65311),x65312))+~P22(f312(f312(f228(a1),f312(f114(a1),x65311)),f312(f114(a1),x65312)))
% 155.90/155.61 [6532]P22(f312(f312(f228(a1),x65321),x65322))+~P22(f312(f312(f228(a853),f312(f117(a853),x65321)),f312(f117(a853),x65322)))
% 155.90/155.61 [6533]P22(f312(f312(f228(a1),x65331),x65332))+~P22(f312(f312(f228(a1),f312(f117(a1),x65331)),f312(f117(a1),x65332)))
% 155.90/155.61 [6535]P22(f312(f312(f227(a853),x65351),x65352))+~P22(f312(f312(f227(a1),f312(f114(a1),x65351)),f312(f114(a1),x65352)))
% 155.90/155.61 [6536]P22(f312(f312(f227(a1),x65361),x65362))+~P22(f312(f312(f227(a1),f312(f117(a1),x65361)),f312(f117(a1),x65362)))
% 155.90/155.61 [6631]~E(f658(x66312,x66311),f127(x66311))+E(f312(f138(f854(x66311),f854(x66311),f129(x66311),f127(x66311)),x66312),f127(x66311))
% 155.90/155.61 [6632]~E(f659(x66322,x66321),f127(x66321))+E(f312(f138(f854(x66321),f854(x66321),f129(x66321),f127(x66321)),x66322),f127(x66321))
% 155.90/155.61 [6639]~P31(x66391)+E(f312(f138(x66391,x66391,f124(x66391),f189(x66391)),x66392),f48(x66391,f312(f168(x66391),x66392)))
% 155.90/155.61 [6640]~P31(x66401)+E(f312(f138(x66401,x66401,f115(x66401),f235(x66401)),x66402),f49(x66401,f312(f168(x66401),x66402)))
% 155.90/155.61 [6653]E(x66531,f2(a113))+E(f312(f312(f89(a853),f312(a19,f312(f312(f21(a113),x66531),f87(a113)))),f312(a126,x66532)),f312(f312(f89(a853),f312(a19,x66531)),x66532))
% 155.90/155.61 [6699]P22(f312(f312(f228(a1),f312(f312(f21(a1),x66991),x66992)),f2(a1)))+~P22(f312(f312(f228(a1),x66991),x66992))
% 155.90/155.61 [6725]~P103(x67251)+E(f312(f312(f124(f861(x67251,a846)),f312(f312(f289(x67251),x67252),f189(f861(x67251,a846)))),f312(f280(x67251),x67252)),f312(f234(x67251),x67252))
% 155.90/155.61 [6793]~P59(x67931,x67932)+P41(x67931,f312(f233(f860(x67931,x67931)),f312(f249(x67931,x67931,a846),x67932)))
% 155.90/155.61 [6794]~P59(x67941,x67942)+P57(x67941,f312(f233(f860(x67941,x67941)),f312(f249(x67941,x67941,a846),x67942)))
% 155.90/155.61 [6795]E(x67951,f189(f861(x67952,a846)))+~P22(f312(f312(f227(f861(x67952,a846)),x67951),f189(f861(x67952,a846))))
% 155.90/155.61 [6882]~P22(f312(f312(f228(a853),f2(a853)),x68822))+P22(f312(f312(f228(a853),f54(a853,x68821,x68822)),x68822))
% 155.90/155.61 [6884]~P22(f312(f312(f228(a1),f2(a1)),x68842))+P22(f312(f312(f228(a1),f54(a1,x68841,x68842)),x68842))
% 155.90/155.61 [6885]~P22(f312(f312(f228(a853),f2(a853)),x68852))+P22(f312(f312(f227(a853),f54(a853,x68851,x68852)),x68852))
% 155.90/155.61 [6886]~P22(f312(f312(f227(a1),f2(a1)),x68861))+P22(f312(f312(f227(a1),f54(a1,x68861,x68862)),x68861))
% 155.90/155.61 [6965]~P105(x69651)+E(f312(f312(f21(f861(x69651,a846)),f312(f312(f289(x69651),x69652),f189(f861(x69651,a846)))),f312(f279(x69651),x69652)),f312(f312(f289(x69651),x69652),f189(f861(x69651,a846))))
% 155.90/155.61 [7038]~P52(x70381,x70382)+P50(x70381,f235(f861(x70381,a846)),f312(f233(f860(x70381,x70381)),f312(f249(x70381,x70381,a846),x70382)))
% 155.90/155.61 [7039]P22(f312(x70391,x70392))+P22(f312(f312(f314(f861(f860(a853,a853),a846)),f583(x70392,x70391)),a112))
% 155.90/155.61 [7088]E(f312(f312(f129(a853),f135(a853,f312(f282(a853,x70881),x70882))),f312(f312(f147(a853),x70882),f127(a853))),f135(a853,f312(f282(a853,x70881),f312(a126,x70882))))+~P22(f312(f312(f227(a853),x70881),x70882))
% 155.90/155.61 [7218]E(x72181,f2(a853))+~E(f312(f138(a853,a853,f89(a853),x72181),x72182),f2(a853))
% 155.90/155.61 [7248]~P22(f312(f312(f228(a1),f312(f312(f21(a1),x72481),x72482)),f2(a1)))+P22(f312(f312(f228(a1),x72481),x72482))
% 155.90/155.61 [7275]P41(x72751,x72752)+~P41(x72751,f312(f312(f267(x72751,x72751,x72751),x72752),x72752))
% 155.90/155.61 [7305]~P22(f312(f312(f227(a853),f312(a126,x73051)),x73052))+P22(f186(a846,a224,f312(f227(a853),x73051),x73052))
% 155.90/155.61 [7459]P19(a853,a853,f312(f312(f7(a853,a853,a853),f21(a853)),x74591),x74592)+P22(f312(f312(f314(a853),f841(x74591,x74592)),x74592))
% 155.90/155.61 [7515]E(f312(f312(f312(f74(a853,x75151,f89(a853)),f312(f16(a853,x75151),f87(a853))),f2(a853)),x75152),f312(f53(x75151),x75152))+~P22(f312(f70(x75151),x75152))
% 155.90/155.61 [7556]P19(a853,a853,f312(f312(f7(a853,a853,a853),f21(a853)),x75561),x75562)+~P22(f312(f312(f227(a853),x75561),f841(x75561,x75562)))
% 155.90/155.61 [7613]P41(x76131,x76132)+P22(f312(f312(f227(f861(x76131,a846)),f687(x76132,x76131)),f312(f264(x76131,x76131,x76132),f687(x76132,x76131))))
% 155.90/155.61 [7618]P59(x76181,x76182)+~P41(x76181,f312(f233(f860(x76181,x76181)),f312(f249(x76181,x76181,a846),x76182)))
% 155.90/155.61 [7690]P22(f312(f312(f227(a853),f312(a126,x76901)),x76902))+~P22(f186(a846,a224,f312(f227(a853),x76901),x76902))
% 155.90/155.61 [7747]P22(f312(f312(f314(f860(a853,a853)),f312(f312(f239(a853,a853),x77471),x77472)),f287(a853,a302)))+~P22(f312(f312(f227(a853),x77471),x77472))
% 155.90/155.61 [7835]P52(x78351,x78352)+~P50(x78351,f235(f861(x78351,a846)),f312(f233(f860(x78351,x78351)),f312(f249(x78351,x78351,a846),x78352)))
% 155.90/155.61 [7894]~P22(f312(f133(x78941),x78942))+P22(f312(f133(f861(x78941,a846)),f312(f312(f150(f854(x78941),f861(x78941,a846)),f168(x78941)),f62(x78941,x78942))))
% 155.90/155.61 [8100]~P41(x81001,f312(f265(x81001,x81001),x81002))+P41(x81001,f312(f265(x81001,x81001),f312(f312(f267(x81001,x81001,x81001),x81002),f287(x81001,x81002))))
% 155.90/155.61 [8137]E(x81371,f2(a1))+P22(f312(f57(x81372,x81371),f312(f312(f239(a1,a1),f312(f47(a1,x81372),x81371)),f54(a1,x81372,x81371))))
% 155.90/155.61 [8222]P22(f312(f70(f860(x82221,x82221)),f312(f312(f267(x82221,x82221,x82221),x82222),f287(x82221,x82222))))+~P22(f312(f70(f860(x82221,x82221)),x82222))
% 155.90/155.61 [8267]~P22(f312(f312(f314(f860(a853,a853)),f312(f312(f239(a853,a853),x82671),x82672)),f287(a853,a302)))+P22(f312(f312(f227(a853),x82671),x82672))
% 155.90/155.61 [8284]~P25(x82841)+E(f312(f138(x82841,x82841,f312(f7(x82841,x82841,x82841),f89(x82841)),f2(x82841)),f312(f165(x82841),x82842)),f312(f138(x82841,x82841,f89(x82841),f2(x82841)),x82842))
% 155.90/155.61 [8470]~P103(x84701)+E(f312(f138(f854(x84701),x84701,f312(f7(x84701,f854(x84701),f854(x84701)),f145(x84701,x84701,f5(x84701))),f127(x84701)),x84702),f144(x84701,x84701,f5(x84701),x84702))
% 155.90/155.61 [8580]P22(f312(f312(f314(f860(a853,a853)),f312(f312(f239(a853,a853),x85801),x85802)),f312(f312(f267(a853,a853,a853),a302),f287(a853,a302))))+~P22(f312(f312(f228(a853),x85801),x85802))
% 155.90/155.61 [8623]~P22(f312(f70(f860(x86231,x86231)),f312(f312(f267(x86231,x86231,x86231),x86232),f287(x86231,x86232))))+P22(f312(f70(f860(x86231,x86231)),x86232))
% 155.90/155.61 [8875]P57(x88751,x88752)+P22(f312(f312(f314(f860(x88751,x88751)),f312(f312(f239(x88751,x88751),f750(x88752,x88751)),f750(x88752,x88751))),f312(f312(f267(x88751,x88751,x88751),x88752),f287(x88751,x88752))))
% 155.90/155.61 [8876]P57(x88761,x88762)+P22(f312(f312(f314(f860(x88761,x88761)),f312(f312(f239(x88761,x88761),f759(x88762,x88761)),f759(x88762,x88761))),f312(f312(f267(x88761,x88761,x88761),x88762),f287(x88761,x88762))))
% 155.90/155.61 [8991]~P22(f312(f312(f314(f860(a853,a853)),f312(f312(f239(a853,a853),x89911),x89912)),f312(f312(f267(a853,a853,a853),a302),f287(a853,a302))))+P22(f312(f312(f228(a853),x89911),x89912))
% 155.90/155.61 [5003]~P90(x50031)+E(f312(f312(f89(x50031),f312(f117(x50031),a92)),x50032),x50032)
% 155.90/155.61 [5034]~P30(x50341)+E(f312(f312(f89(x50341),f312(f88(x50341),x50342)),x50342),f2(x50341))
% 155.90/155.61 [5035]~P71(x50351)+E(f312(f312(f89(x50351),f312(f88(x50351),x50352)),x50352),f2(x50351))
% 155.90/155.61 [5036]~P88(x50361)+E(f312(f312(f124(x50361),f312(f88(x50361),x50362)),x50362),f235(x50361))
% 155.90/155.61 [5037]~P88(x50371)+E(f312(f312(f115(x50371),f312(f88(x50371),x50372)),x50372),f189(x50371))
% 155.90/155.61 [5071]~P90(x50711)+E(f312(f312(f90(x50711),f312(f117(x50711),a111)),x50712),f312(f88(x50711),x50712))
% 155.90/155.61 [5237]~P108(x52371)+E(f312(f312(f90(x52371),f312(f88(x52371),f87(x52371))),x52372),f312(f88(x52371),x52372))
% 155.90/155.61 [5278]E(f312(f84(a1),x52781),f87(a1))+~E(f312(f84(a1),f312(f312(f90(a1),x52781),x52782)),f87(a1))
% 155.90/155.61 [5366]~P90(x53661)+E(f312(f312(f89(x53661),f87(x53661)),f312(f117(x53661),x53662)),f312(f117(x53661),f312(f312(f21(a1),x53662),a111)))
% 155.90/155.61 [5419]~P87(x54191)+E(f11(x54191,f312(f312(f289(x54191),x54192),f189(f861(x54191,a846)))),x54192)
% 155.90/155.61 [5420]~P87(x54201)+E(f10(x54201,f312(f312(f289(x54201),x54202),f189(f861(x54201,a846)))),x54202)
% 155.90/155.61 [5421]~P103(x54211)+E(f14(x54211,f312(f312(f289(x54211),x54212),f189(f861(x54211,a846)))),x54212)
% 155.90/155.61 [5422]~P103(x54221)+E(f15(x54221,f312(f312(f289(x54221),x54222),f189(f861(x54221,a846)))),x54222)
% 155.90/155.61 [5423]~P31(x54231)+E(f48(x54231,f312(f312(f289(x54231),x54232),f189(f861(x54231,a846)))),x54232)
% 155.90/155.61 [5424]~P31(x54241)+E(f49(x54241,f312(f312(f289(x54241),x54242),f189(f861(x54241,a846)))),x54242)
% 155.90/155.61 [5446]E(f312(f312(f89(a853),x54461),f312(f312(f21(a853),x54462),x54461)),x54462)+P22(f312(f312(f228(a853),x54462),x54461))
% 155.90/155.61 [5476]E(x54761,f127(x54762))+P22(f312(f312(f228(a853),f2(a853)),f312(f190(f854(x54762)),x54761)))
% 155.90/155.61 [5599]E(f312(f88(a1),f312(f47(a1,x55991),f312(f88(a1),x55992))),f270(x55991,x55992))+P22(f312(f312(f227(a1),f2(a1)),x55992))
% 155.90/155.61 [5607]~P103(x56071)+E(f12(x56071,f226(x56071),f312(f312(f289(x56071),x56072),f189(f861(x56071,a846)))),x56072)
% 155.90/155.61 [5608]~P103(x56081)+E(f13(x56081,f225(x56081),f312(f312(f289(x56081),x56082),f189(f861(x56081,a846)))),x56082)
% 155.90/155.61 [5667]E(f312(f312(f89(a853),x56671),f312(f312(f21(a853),x56672),x56671)),x56672)+~P22(f312(f312(f227(a853),x56671),x56672))
% 155.90/155.61 [5668]E(f312(f312(f21(a853),x56681),f312(f312(f21(a853),x56681),x56682)),x56682)+~P22(f312(f312(f227(a853),x56682),x56681))
% 155.90/155.61 [5686]E(f54(a853,f312(f312(f21(a853),x56861),x56862),x56862),f54(a853,x56861,x56862))+P22(f312(f312(f228(a853),x56861),x56862))
% 155.90/155.61 [5697]~E(x56972,f2(a853))+P22(f312(f312(f228(a853),f2(a853)),f312(f312(f240(a853),x56971),x56972)))
% 155.90/155.61 [5744]~P90(x57441)+E(f312(f312(f89(x57441),f312(f88(x57441),f87(x57441))),f312(f117(x57441),x57442)),f312(f117(x57441),f312(f312(f89(a1),x57442),a111)))
% 155.90/155.61 [5745]E(f312(f312(f240(a853),f312(f117(a853),x57451)),x57452),f312(f312(f240(a853),f2(a853)),x57452))+~P22(f312(a194,f312(f117(a1),x57451)))
% 155.90/155.61 [5839]E(f312(f137(a853),f135(a853,f312(f282(a853,x58391),x58392))),x58391)+~P22(f312(f312(f228(a853),x58391),x58392))
% 155.90/155.61 [5859]E(f312(f312(f90(a853),f312(f117(a853),x58591)),f312(f117(a853),x58592)),f312(f117(a853),f312(f312(f90(a1),x58591),x58592)))+P22(f312(f312(f228(a1),x58591),a92))
% 155.90/155.61 [5865]~P119(x58651)+P22(f312(f312(f227(x58651),f2(x58651)),f312(f312(f90(x58651),x58652),x58652)))
% 155.90/155.61 [5877]E(f312(f312(f21(a853),f312(a126,x58771)),x58772),f312(a126,f312(f312(f21(a853),x58771),x58772)))+~P22(f312(f312(f227(a853),x58772),x58771))
% 155.90/155.61 [5880]E(f54(a853,f312(f312(f21(a853),x58801),x58802),x58802),f54(a853,x58801,x58802))+~P22(f312(f312(f227(a853),x58802),x58801))
% 155.90/155.61 [5940]E(f312(f312(f240(a853),f312(a118,x59401)),x59402),f312(a118,f312(f312(f240(a1),x59401),x59402)))+~P22(f312(f312(f227(a1),f2(a1)),x59401))
% 155.90/155.61 [5952]P22(f312(f133(x59521),x59522))+P22(f312(f312(f228(a853),f582(x59522,x59521)),f312(f190(f854(x59521)),x59522)))
% 155.90/155.61 [5953]P22(f312(f133(x59531),x59532))+P22(f312(f312(f228(a853),f599(x59532,x59531)),f312(f190(f854(x59531)),x59532)))
% 155.90/155.61 [5968]~E(x59681,f127(x59682))+~P22(f312(f312(f228(a853),f2(a853)),f312(f190(f854(x59682)),x59681)))
% 155.90/155.61 [5981]E(f140(a853,f135(a853,f312(f282(a853,x59811),x59812))),f312(f312(f21(a853),x59812),f87(a853)))+~P22(f312(f312(f228(a853),x59811),x59812))
% 155.90/155.61 [5984]E(f312(f312(f89(a1),x59841),f312(f114(a1),f312(a126,f813(x59842,x59841)))),x59842)+~P22(f312(f312(f228(a1),x59841),x59842))
% 155.90/155.61 [5991]E(x59911,f2(a853))+E(f312(f312(f90(a853),x59912),f312(f312(f240(a853),x59912),f312(f312(f21(a853),x59911),f87(a853)))),f312(f312(f240(a853),x59912),x59911))
% 155.90/155.61 [6014]E(f312(f312(f90(a853),f312(a118,x60141)),f312(a118,x60142)),f312(a118,f312(f312(f90(a1),x60141),x60142)))+~P22(f312(f312(f227(a1),f2(a1)),x60141))
% 155.90/155.61 [6028]~P107(x60281)+E(f312(f312(f89(x60281),x60282),x60282),f312(f312(f90(x60281),f312(f312(f89(x60281),f87(x60281)),f87(x60281))),x60282))
% 155.90/155.61 [6042]E(f312(f312(f21(a1),f312(f114(a1),x60421)),f312(f114(a1),x60422)),f312(f114(a1),f312(f312(f21(a853),x60421),x60422)))+~P22(f312(f312(f227(a853),x60422),x60421))
% 155.90/155.61 [6047]E(f312(f312(f239(a1,a1),f312(f117(a1),a111)),f312(f312(f89(a1),x60471),x60472)),f58(x60471,x60472))+~P22(f312(f312(f227(a1),x60472),f2(a1)))
% 155.90/155.61 [6083]E(f175(x60831,x60832),f127(f854(x60831)))+P22(f312(f312(f314(f854(x60831)),f611(x60832,x60831)),f312(f168(f854(x60831)),x60832)))
% 155.90/155.61 [6169]E(f312(f312(f147(a1),x61691),f174(f312(f312(f89(a1),x61691),f87(a1)),x61692)),f174(x61691,x61692))+~P22(f312(f312(f227(a1),x61691),x61692))
% 155.90/155.61 [6207]~P22(f312(f312(f228(a853),x62072),x62071))+P22(f312(f312(f228(a853),f2(a853)),f312(f312(f21(a853),x62071),x62072)))
% 155.90/155.61 [6233]~P22(f312(f312(f228(a853),x62331),f312(a118,x62332)))+P22(f312(f312(f228(a1),f312(f114(a1),x62331)),x62332))
% 155.90/155.61 [6265]~P103(x62651)+E(f312(f312(f124(f861(x62651,a846)),f312(f279(x62651),x62652)),f312(f312(f289(x62651),x62652),f189(f861(x62651,a846)))),f312(f281(x62651),x62652))
% 155.90/155.61 [6268]~P22(f312(f312(f228(a853),f2(a853)),x62681))+P22(f312(f312(f228(a853),f2(a853)),f312(f312(f240(a853),x62681),x62682)))
% 155.90/155.61 [6269]~P22(f312(f312(f227(a1),f2(a1)),x62691))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f240(a1),x62691),x62692)))
% 155.90/155.61 [6297]~E(f312(x62971,f2(a853)),f2(a853))+E(f312(f312(f6(a853,a853),x62971),f283(a853,f312(a126,f2(a853)),x62972)),f312(f312(f6(a853,a853),x62971),f283(a853,f2(a853),x62972)))
% 155.90/155.61 [6357]~P90(x63571)+E(f312(f312(f90(x63571),f312(f312(f89(x63571),f87(x63571)),f87(x63571))),f312(f117(x63571),x63572)),f312(f117(x63571),f312(f312(f89(a1),x63572),x63572)))
% 155.90/155.61 [6373]E(f312(f312(f289(a1),x63731),f283(a1,f312(f312(f89(a1),x63731),f87(a1)),x63732)),f283(a1,x63731,x63732))+P22(f312(f312(f228(a1),x63732),x63731))
% 155.90/155.61 [6374]P22(f312(f312(f228(a853),x63741),f312(a118,x63742)))+~P22(f312(f312(f228(a1),f312(f114(a1),x63741)),x63742))
% 155.90/155.61 [6404]E(f312(a118,f312(f47(a1,f312(f117(a1),x64041)),f312(f117(a1),x64042))),f312(f47(a853,f312(f117(a853),x64041)),f312(f117(a853),x64042)))+P22(f312(a194,f312(f117(a1),x64041)))
% 155.90/155.61 [6529]P22(f312(f312(f228(a853),x65291),x65292))+~P22(f312(f312(f228(a853),f2(a853)),f312(f312(f21(a853),x65292),x65291)))
% 155.90/155.61 [6572]P22(f312(f312(f228(a853),f2(a853)),x65721))+~P22(f312(f312(f228(a853),f2(a853)),f312(f312(f90(a853),x65722),x65721)))
% 155.90/155.61 [6573]P22(f312(f312(f228(a853),f2(a853)),x65731))+~P22(f312(f312(f228(a853),f2(a853)),f312(f312(f90(a853),x65731),x65732)))
% 155.90/155.61 [6595]~P22(f312(f312(f227(a1),x65951),f2(a1)))+E(f312(f312(f90(a853),f312(a118,f312(f88(a1),x65951))),f312(a118,f312(f88(a1),x65952))),f312(a118,f312(f312(f90(a1),x65951),x65952)))
% 155.90/155.61 [6650]~E(x66502,f189(f861(x66501,a846)))+P22(f312(f312(f227(f861(x66501,a846)),x66502),f312(f88(f861(x66501,a846)),x66502)))
% 155.90/155.61 [6708]~P90(x67081)+E(f312(f312(f89(x67081),f312(f312(f89(x67081),f2(x67081)),f312(f117(x67081),x67082))),f312(f117(x67081),x67082)),f312(f117(x67081),f312(f312(f89(a1),x67082),x67082)))
% 155.90/155.61 [6762]~P22(f312(f312(f228(a1),x67621),x67622))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x67621),f87(a1))),x67622))
% 155.90/155.61 [6827]E(x68271,f2(a853))+~P22(f312(f312(f227(a1),f312(f114(a1),x68272)),f312(f88(a1),f312(f114(a1),x68271))))
% 155.90/155.61 [6828]E(x68281,f2(a853))+~P22(f312(f312(f227(a1),f312(f114(a1),x68281)),f312(f88(a1),f312(f114(a1),x68282))))
% 155.90/155.61 [6938]E(f312(f312(f239(a1,a1),f312(f117(a1),a111)),f312(f312(f89(a1),x69381),x69382)),f58(x69381,x69382))+~P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),x69381),x69382)))
% 155.90/155.61 [6978]~P20(x69781,x69782)+P41(x69781,f312(f246(f861(f860(x69781,x69781),a846),f861(f860(x69781,x69781),a846)),x69782))
% 155.90/155.61 [7000]~P22(f312(f312(f227(a853),f312(a126,f2(a853))),x70001))+P22(f312(f312(f227(a853),f312(a126,f2(a853))),f312(f312(f240(a853),x70001),x70002)))
% 155.90/155.61 [7161]~P22(f312(f312(f228(a1),x71611),x71612))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x71611),x71611)),f312(f312(f89(a1),x71612),x71612)))
% 155.90/155.61 [7172]~P22(f312(f312(f227(a1),x71721),x71722))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x71721),x71721)),f312(f312(f89(a1),x71722),x71722)))
% 155.90/155.61 [7220]~P22(f312(f312(f228(a853),f2(a853)),x72201))+P22(f312(f312(f228(a853),f312(f312(f21(a853),x72201),f312(a126,x72202))),x72201))
% 155.90/155.61 [7258]P22(f312(f312(f227(a853),f312(a126,f2(a853))),x72581))+~P22(f312(f312(f227(a853),f312(a126,f2(a853))),f312(f312(f90(a853),x72582),x72581)))
% 155.90/155.61 [7259]P22(f312(f312(f227(a853),f312(a126,f2(a853))),x72591))+~P22(f312(f312(f227(a853),f312(a126,f2(a853))),f312(f312(f90(a853),x72591),x72592)))
% 155.90/155.61 [7262]P22(f312(f312(f227(a853),f312(f312(f161(a853),x72621),x72622)),f312(f162(a853),x72621)))+~P22(f312(f312(f228(a853),x72622),f312(f190(f854(a853)),x72621)))
% 155.90/155.61 [7304]P22(f312(f312(f228(a1),x73041),x73042))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x73041),f87(a1))),x73042))
% 155.90/155.61 [7346]P22(f312(f70(x73461),f235(f861(x73461,a846))))+~P22(f312(f70(f861(x73462,x73461)),f235(f861(f861(x73462,x73461),a846))))
% 155.90/155.61 [7347]P22(f312(f70(x73471),f235(f861(x73471,a846))))+~P22(f312(f70(f859(x73472,x73471)),f235(f861(f859(x73472,x73471),a846))))
% 155.90/155.61 [7348]P22(f312(f70(x73481),f235(f861(x73481,a846))))+~P22(f312(f70(f859(x73481,x73482)),f235(f861(f859(x73481,x73482),a846))))
% 155.90/155.61 [7389]E(x73891,f189(f861(x73892,a846)))+~P22(f312(f312(f227(f861(x73892,a846)),x73891),f312(f88(f861(x73892,a846)),x73891)))
% 155.90/155.61 [7525]E(f312(f138(f854(x75251),f854(x75251),f129(x75251),f127(x75251)),x75252),f127(x75251))+P22(f312(f312(f314(f854(x75251)),f658(x75252,x75251)),f312(f168(f854(x75251)),x75252)))
% 155.90/155.61 [7526]E(f312(f138(f854(x75261),f854(x75261),f129(x75261),f127(x75261)),x75262),f127(x75261))+P22(f312(f312(f314(f854(x75261)),f659(x75262,x75261)),f312(f168(f854(x75261)),x75262)))
% 155.90/155.61 [7765]P22(f312(f312(f228(a1),x77651),x77652))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x77651),x77651)),f312(f312(f89(a1),x77652),x77652)))
% 155.90/155.61 [7768]P22(f312(f312(f227(a1),x77681),x77682))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x77681),x77681)),f312(f312(f89(a1),x77682),x77682)))
% 155.90/155.61 [7855]~P107(x78551)+E(f312(f312(f90(x78551),f312(f312(f89(x78551),f87(x78551)),f87(x78551))),f312(f312(f6(a853,x78551),f114(x78551)),f283(a853,f87(a853),x78552))),f312(f312(f90(x78551),f312(f114(x78551),x78552)),f312(f312(f89(x78551),f312(f114(x78551),x78552)),f87(x78551))))
% 155.90/155.61 [7908]P22(f312(f312(f314(a853),x79081),x79082))+~P22(f312(f312(f314(a1),f312(f114(a1),x79081)),f312(f290(a853,a1,f114(a1)),x79082)))
% 155.90/155.61 [8072]~P22(f312(f70(x80721),x80722))+E(f312(f290(a853,x80721,f556(x80722,x80721)),f312(f233(a853),f312(f312(f7(a853,a853,a846),f228(a853)),f557(x80722,x80721)))),x80722)
% 155.90/155.61 [8366]P51(x83661,x83662)+P22(f312(f312(f314(f860(x83661,x83661)),f312(f312(f239(x83661,x83661),f360(x83662,x83661)),f360(x83662,x83661))),x83662))
% 155.90/155.61 [8512]~P90(x85121)+E(f312(f312(f21(x85121),f87(x85121)),f312(f117(x85121),x85122)),f312(f117(x85121),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f88(a1),x85122))))
% 155.90/155.61 [8619]~P22(f312(f312(f228(f861(a853,a846)),x86191),x86192))+P22(f312(f312(f228(f861(a1,a846)),f312(f290(a853,a1,f114(a1)),x86191)),f312(f290(a853,a1,f114(a1)),x86192)))
% 155.90/155.61 [8650]~P22(f312(f312(f228(a1),x86501),x86502))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x86501),x86501)),a111)),f312(f312(f89(a1),x86502),x86502)))
% 155.90/155.61 [8652]~P22(f312(f312(f228(a1),x86521),x86522))+P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x86521),x86521)),a111)),f312(f312(f89(a1),x86522),x86522)))
% 155.90/155.61 [8720]~P22(f312(f312(f314(a853),x87201),f312(f168(a853),x87202)))+P22(f312(f312(f227(a853),x87201),f312(f138(a853,a853,f89(a853),f2(a853)),x87202)))
% 155.90/155.61 [8809]P48(x88091,x88092)+~P22(f312(f312(f314(f860(x88091,x88091)),f312(f312(f239(x88091,x88091),f342(x88092,x88091)),f342(x88092,x88091))),x88092))
% 155.90/155.61 [8959]~P22(f312(f312(f228(f861(a1,a846)),f312(f290(a853,a1,f114(a1)),x89591)),f312(f290(a853,a1,f114(a1)),x89592)))+P22(f312(f312(f228(f861(a853,a846)),x89591),x89592))
% 155.90/155.61 [8960]~P22(f312(f312(f227(f861(a1,a846)),f312(f290(a853,a1,f114(a1)),x89601)),f312(f290(a853,a1,f114(a1)),x89602)))+P22(f312(f312(f227(f861(a853,a846)),x89601),x89602))
% 155.90/155.61 [9039]P22(f312(f312(f228(a1),x90391),x90392))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x90391),x90391)),a111)),f312(f312(f89(a1),x90392),x90392)))
% 155.90/155.61 [9041]P22(f312(f312(f228(a1),x90411),x90412))+~P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x90411),x90411)),a111)),f312(f312(f89(a1),x90412),x90412)))
% 155.90/155.61 [9943]~P22(f312(f70(x99431),x99432))+E(f312(f190(f854(x99431)),f99(f854(x99431),f312(f312(f18(f854(x99431),a846,a846),f312(f312(f8(a846,f861(a846,a846),f854(x99431)),a310),f312(f312(f7(f854(x99431),f861(x99431,a846),a846),f312(f312(f8(f861(x99431,a846),f861(f861(x99431,a846),a846),f854(x99431)),a309),f168(x99431))),x99432))),f133(x99431)))),f207(x99431,x99432))
% 155.90/155.61 [10083]~P18(a848,x100831,f312(f312(f289(f852(a848)),f312(f312(f312(f100(a848),a309),x100832),f195(x100832))),f189(f861(f852(a848),a846))))+P18(a848,x100831,f312(f312(f289(f852(a848)),f312(f312(f312(f100(a848),f312(f312(f8(f861(a848,f861(a848,a846)),f861(a848,a846),a848),f312(f8(f861(a848,a846),a846,a848),f97(a848))),f312(f312(f8(f861(a848,a846),f861(a848,f861(a848,a846)),a848),f312(f7(a848,f861(a848,a846),f861(a848,a846)),f312(f312(f8(f861(a848,f861(a846,a846)),f861(f861(a848,a846),f861(a848,a846)),a848),f18(a848,a846,a846)),f312(f312(f8(f861(a848,a846),f861(a848,f861(a846,a846)),a848),f312(f8(a846,f861(a846,a846),a848),a315)),f195(x100832))))),a309))),x100832),a309)),f189(f861(f852(a848),a846))))
% 155.90/155.61 [5980]E(f312(f312(f89(a853),f312(f312(f21(a853),x59801),x59802)),x59802),x59801)+~P22(f312(f312(f227(a853),x59802),x59801))
% 155.90/155.61 [6017]E(f312(f47(a853,f312(f312(f90(a853),x60171),x60172)),x60172),x60171)+~P22(f312(f312(f228(a853),f2(a853)),x60172))
% 155.90/155.61 [6018]E(f312(f47(a853,f312(f312(f90(a853),x60181),x60182)),x60181),x60182)+~P22(f312(f312(f228(a853),f2(a853)),x60181))
% 155.90/155.61 [6043]~P26(x60431)+E(f312(f312(f6(a853,x60431),f312(f161(x60431),x60432)),f312(f282(a853,f2(a853)),f312(f190(f854(x60431)),x60432))),f312(f162(x60431),x60432))
% 155.90/155.61 [6161]E(f54(a853,f312(a126,f312(f312(f90(a853),x61611),x61612)),x61611),f87(a853))+~P22(f312(f312(f228(a853),f87(a853)),x61611))
% 155.90/155.61 [6167]E(f312(a126,f312(f312(f89(a853),f312(f117(a853),x61671)),x61672)),f312(f312(f89(a853),f87(a853)),x61672))+~P22(f312(a194,f312(f117(a1),x61671)))
% 155.90/155.61 [6195]E(f312(a118,f312(f312(f240(a1),f312(f117(a1),x61951)),x61952)),f312(f312(f240(a853),f312(f117(a853),x61951)),x61952))+P22(f312(a194,f312(f117(a1),x61951)))
% 155.90/155.61 [6427]E(f312(f312(f21(a853),x64271),f312(f117(a853),f312(f312(f89(a1),x64272),a111))),f312(f312(f21(a853),f312(a126,x64271)),f312(f117(a853),x64272)))+~P22(f312(f312(f228(a1),a92),x64272))
% 155.90/155.61 [6502]E(x65021,f2(a853))+E(f312(a126,f312(f312(f89(a853),f312(f312(f21(a853),x65021),f87(a853))),x65022)),f312(f312(f89(a853),x65021),x65022))
% 155.90/155.61 [6542]E(x65421,f2(a1))+P22(f312(f312(f228(a1),f2(a1)),f312(f312(f240(a1),f312(f84(a1),x65421)),x65422)))
% 155.90/155.61 [6558]~E(x65582,f2(a853))+P22(f312(f312(f228(a1),f2(a1)),f312(f312(f240(a1),f312(f84(a1),x65581)),x65582)))
% 155.90/155.61 [6599]E(x65991,f2(a853))+E(f312(f312(f89(a853),x65992),f312(f312(f90(a853),f312(f312(f21(a853),x65991),f87(a853))),x65992)),f312(f312(f90(a853),x65991),x65992))
% 155.90/155.61 [6644]~P22(f312(f312(f227(a1),x66441),x66442))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x66441),a111)),x66442))
% 155.90/155.61 [6765]E(f312(f312(f147(a853),x67651),f135(a853,f312(f282(a853,f312(a126,x67651)),x67652))),f135(a853,f312(f282(a853,x67651),x67652)))+~P22(f312(f312(f228(a853),x67651),x67652))
% 155.90/155.61 [6970]E(x69701,x69702)+~E(f312(f312(f21(a1),f312(f312(f89(a1),x69701),x69701)),a111),f312(f312(f21(a1),f312(f312(f89(a1),x69702),x69702)),a111))
% 155.90/155.61 [6973]E(x69731,f127(x69732))+E(f254(x69732,f312(f312(f150(x69732,f860(a113,x69732)),f312(f239(a113,x69732),f87(a113))),x69731)),f261(x69732,x69731))
% 155.90/155.61 [7190]P22(f312(f312(f227(a1),x71901),x71902))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x71901),a111)),x71902))
% 155.90/155.61 [7666]~P22(f312(f312(f228(a853),x76661),x76662))+P22(f312(f312(f314(f860(a853,a853)),f312(f312(f239(a853,a853),x76661),x76662)),a232))
% 155.90/155.61 [7882]~P22(f312(f312(f228(a113),f2(a113)),x78821))+P22(f312(f312(f228(a113),f312(f246(a113,f860(a113,a113)),f312(f255(x78821),x78822))),x78821))
% 155.90/155.61 [8201]~P83(x82011)+P22(f312(f312(f227(x82011),f312(f84(x82011),f312(f162(x82011),x82012))),f312(f162(x82011),f312(f312(f150(x82011,x82011),f84(x82011)),x82012))))
% 155.90/155.61 [8224]P22(f312(f312(f228(a853),x82241),x82242))+~P22(f312(f312(f314(f860(a853,a853)),f312(f312(f239(a853,a853),x82241),x82242)),a232))
% 155.90/155.61 [8392]E(f312(f312(f239(x83921,x83921),f774(x83922,x83921)),f774(x83922,x83921)),x83922)+~P22(f312(f312(f314(f860(x83921,x83921)),x83922),f287(x83921,f189(f861(f860(x83921,x83921),a846)))))
% 155.90/155.61 [8432]E(f312(f282(a853,x84321),f312(f312(f89(a853),x84321),f312(f53(a853),x84322))),x84322)+~P22(f312(f312(f227(f861(a853,a846)),x84322),f312(f282(a853,x84321),f312(f312(f89(a853),x84321),f312(f53(a853),x84322)))))
% 155.90/155.61 [8750]E(f312(f47(a1,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x87501),x87501)),a111))),f312(f117(a1),f312(f312(f89(a1),x87502),x87502))),f312(f47(a1,f312(f117(a1),x87501)),f312(f117(a1),x87502)))+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x87502)))
% 155.90/155.61 [8874]E(f312(f47(a1,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x88741),x88741)),a111))),f312(f117(a1),f312(f312(f89(a1),x88742),x88742))),f312(f47(a1,f312(f312(f89(a1),f312(f117(a1),x88741)),f87(a1))),f312(f117(a1),x88742)))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x88742)))
% 155.90/155.61 [8886]E(f172(f854(x88861),f312(f312(f8(a846,a846,f854(x88861)),a307),f312(f312(f7(f854(x88861),f854(x88861),a846),a309),f127(x88861))),x88862),f175(x88861,f175(x88861,x88862)))+~P33(a853,f312(f165(a853),f312(f312(f150(f854(x88861),a853),f190(f854(x88861))),x88862)))
% 155.90/155.61 [9708]P22(f312(a194,x97082))+E(f312(f312(f95(a1,a853),f312(f312(f21(a1),x97081),x97082)),f312(f312(f18(a1,a853,a853),f312(f312(f7(a1,a853,f861(a853,a853)),f312(f312(f8(a846,f861(a853,f861(a853,a853)),a1),f108(a853)),a194)),f2(a853))),a118)),f312(f312(f21(a853),f312(a118,x97081)),f312(a118,x97082)))
% 155.90/155.61 [9716]E(f312(f312(f95(a1,a853),f312(f117(a1),f312(f312(f89(a1),x97161),f312(f88(a1),x97162)))),f312(f312(f18(a1,a853,a853),f312(f312(f7(a1,a853,f861(a853,a853)),f312(f312(f8(a846,f861(a853,f861(a853,a853)),a1),f108(a853)),a194)),f2(a853))),a118)),f312(f312(f21(a853),f312(f117(a853),x97161)),f312(f117(a853),x97162)))+P22(f312(f312(f228(a1),x97162),a92))
% 155.90/155.61 [9717]~P20(x97171,x97172)+P22(f312(f312(f227(f861(f860(x97171,x97171),a846)),f312(f312(f267(x97171,x97171,x97171),f312(f246(f861(f860(x97171,x97171),a846),f861(f860(x97171,x97171),a846)),x97172)),f312(f248(f861(f860(x97171,x97171),a846),f861(f860(x97171,x97171),a846)),x97172))),f312(f246(f861(f860(x97171,x97171),a846),f861(f860(x97171,x97171),a846)),x97172)))
% 155.90/155.61 [9784]~E(f312(f53(a853),f312(f233(a853),f312(f312(f18(a853,a846,a846),f312(f312(f8(a846,f861(a846,a846),a853),a310),f312(f312(f7(a853,f861(a853,a846),a846),f314(a853)),x97841))),f312(f312(f7(a853,a853,a846),f228(a853)),f312(a126,x97842))))),f2(a853))+~P22(f312(f312(f314(a853),f2(a853)),x97841))
% 155.90/155.61 [9845]E(f54(a1,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x98451),x98451)),a111)),f312(f117(a1),f312(f312(f89(a1),x98452),x98452))),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),x98451),f312(f117(a1),x98452)))),f87(a1)))+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x98452)))
% 155.90/155.61 [9854]E(f54(a1,f312(f117(a1),f312(f312(f21(a1),f312(f312(f89(a1),x98541),x98541)),a111)),f312(f117(a1),f312(f312(f89(a1),x98542),x98542))),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),x98541)),f87(a1)),f312(f117(a1),x98542)))),f87(a1)))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x98542)))
% 155.90/155.61 [9910]~P31(x99101)+E(f48(x99101,f312(f233(x99101),f312(f312(f8(f861(x99101,a846),a846,x99101),f97(x99101)),f312(f312(f8(f861(x99101,a846),f861(x99101,a846),x99101),f312(f18(x99101,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99101),a315),f312(f312(f7(x99101,f861(x99101,a846),a846),f314(x99101)),x99102)))),f227(x99101))))),f49(x99101,x99102))
% 155.90/155.61 [9936]~P41(x99361,x99362)+P59(x99361,f312(f312(f7(x99361,f861(f860(x99361,x99361),a846),f861(x99361,a846)),f312(f312(f8(f861(x99361,f861(f861(f860(x99361,x99361),a846),a846)),f861(f861(f860(x99361,x99361),a846),f861(x99361,a846)),x99361),f7(x99361,f861(f860(x99361,x99361),a846),a846)),f312(f312(f8(f861(x99361,f860(x99361,x99361)),f861(x99361,f861(f861(f860(x99361,x99361),a846),a846)),x99361),f312(f8(f860(x99361,x99361),f861(f861(f860(x99361,x99361),a846),a846),x99361),f314(f860(x99361,x99361)))),f239(x99361,x99361)))),x99362))
% 155.90/155.61 [9937]~P3(x99371,f235(f861(x99371,a846)),x99372)+P2(x99371,f312(f312(f7(x99371,f861(f860(x99371,x99371),a846),f861(x99371,a846)),f312(f312(f8(f861(x99371,f861(f861(f860(x99371,x99371),a846),a846)),f861(f861(f860(x99371,x99371),a846),f861(x99371,a846)),x99371),f7(x99371,f861(f860(x99371,x99371),a846),a846)),f312(f312(f8(f861(x99371,f860(x99371,x99371)),f861(x99371,f861(f861(f860(x99371,x99371),a846),a846)),x99371),f312(f8(f860(x99371,x99371),f861(f861(f860(x99371,x99371),a846),a846),x99371),f314(f860(x99371,x99371)))),f239(x99371,x99371)))),x99372))
% 155.90/155.61 [9973]P41(x99731,x99732)+~P59(x99731,f312(f312(f7(x99731,f861(f860(x99731,x99731),a846),f861(x99731,a846)),f312(f312(f8(f861(x99731,f861(f861(f860(x99731,x99731),a846),a846)),f861(f861(f860(x99731,x99731),a846),f861(x99731,a846)),x99731),f7(x99731,f861(f860(x99731,x99731),a846),a846)),f312(f312(f8(f861(x99731,f860(x99731,x99731)),f861(x99731,f861(f861(f860(x99731,x99731),a846),a846)),x99731),f312(f8(f860(x99731,x99731),f861(f861(f860(x99731,x99731),a846),a846),x99731),f314(f860(x99731,x99731)))),f239(x99731,x99731)))),x99732))
% 155.90/155.61 [9974]P3(x99741,f235(f861(x99741,a846)),x99742)+~P2(x99741,f312(f312(f7(x99741,f861(f860(x99741,x99741),a846),f861(x99741,a846)),f312(f312(f8(f861(x99741,f861(f861(f860(x99741,x99741),a846),a846)),f861(f861(f860(x99741,x99741),a846),f861(x99741,a846)),x99741),f7(x99741,f861(f860(x99741,x99741),a846),a846)),f312(f312(f8(f861(x99741,f860(x99741,x99741)),f861(x99741,f861(f861(f860(x99741,x99741),a846),a846)),x99741),f312(f8(f860(x99741,x99741),f861(f861(f860(x99741,x99741),a846),a846),x99741),f314(f860(x99741,x99741)))),f239(x99741,x99741)))),x99742))
% 155.90/155.61 [7150]E(f312(f312(f89(a853),f312(f117(a853),f312(f312(f21(a1),x71501),a111))),x71502),f312(a126,f312(f312(f89(a853),f312(f117(a853),x71501)),x71502)))+P22(f312(a194,f312(f117(a1),x71501)))
% 155.90/155.61 [7583]~P90(x75831)+E(f312(f312(f89(x75831),f312(f312(f89(x75831),f87(x75831)),f312(f117(x75831),x75832))),f312(f117(x75831),x75832)),f312(f117(x75831),f312(f312(f21(a1),f312(f312(f89(a1),x75832),x75832)),a111)))
% 155.90/155.61 [8228]~P22(f312(f312(f227(a1),x82281),x82282))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x82281),x82281)),f312(f312(f21(a1),f312(f312(f89(a1),x82282),x82282)),a111)))
% 155.90/155.61 [8230]~P22(f312(f312(f227(a1),x82301),x82302))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x82301),x82301)),f312(f312(f21(a1),f312(f312(f89(a1),x82302),x82302)),a111)))
% 155.90/155.61 [8654]P22(f312(f312(f227(a1),x86541),x86542))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),x86541),x86541)),f312(f312(f21(a1),f312(f312(f89(a1),x86542),x86542)),a111)))
% 155.90/155.61 [8656]P22(f312(f312(f227(a1),x86561),x86562))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x86561),x86561)),f312(f312(f21(a1),f312(f312(f89(a1),x86562),x86562)),a111)))
% 155.90/155.61 [8948]~P22(f312(f312(f228(a1),x89481),x89482))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89481),x89481)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x89482),x89482)),a111)))
% 155.90/155.61 [8950]~P22(f312(f312(f227(a1),x89501),x89502))+P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x89501),x89501)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x89502),x89502)),a111)))
% 155.90/155.61 [9212]P22(f312(f312(f228(a1),x92121),x92122))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),x92121),x92121)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x92122),x92122)),a111)))
% 155.90/155.61 [9214]P22(f312(f312(f227(a1),x92141),x92142))+~P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),x92141),x92141)),a111)),f312(f312(f21(a1),f312(f312(f89(a1),x92142),x92142)),a111)))
% 155.90/155.61 [9244]~P22(f312(f70(x92441),x92442))+P22(f312(f70(f861(x92441,a846)),f312(f233(f861(x92441,a846)),f312(f312(f7(f861(x92441,a846),f861(x92441,a846),a846),f227(f861(x92441,a846))),x92442))))
% 155.90/155.61 [9291]~E(f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),x92911),f189(f861(f860(a853,a853),a846)))),f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),x92912),f189(f861(f860(a853,a853),a846)))))+P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),x92911),x92912)),a122))
% 155.90/155.61 [9374]E(f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),x93741),f189(f861(f860(a853,a853),a846)))),f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),x93742),f189(f861(f860(a853,a853),a846)))))+~P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),x93741),x93742)),a122))
% 155.90/155.61 [9921]~P31(x99211)+E(f49(x99211,f312(f233(x99211),f312(f312(f8(f861(x99211,a846),a846,x99211),f97(x99211)),f312(f312(f8(f861(x99211,a846),f861(x99211,a846),x99211),f312(f18(x99211,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99211),a315),f312(f312(f7(x99211,f861(x99211,a846),a846),f314(x99211)),x99212)))),f312(f7(x99211,x99211,a846),f227(x99211)))))),f48(x99211,x99212))
% 155.90/155.61 [9942]P22(f312(f312(f314(a853),f2(a853)),x99421))+E(f312(f53(a853),f312(f233(a853),f312(f312(f18(a853,a846,a846),f312(f312(f8(a846,f861(a846,a846),a853),a310),f312(f312(f7(a853,f861(a853,a846),a846),f312(f312(f8(a853,f861(f861(a853,a846),a846),a853),f314(a853)),a126)),x99421))),f312(f312(f7(a853,a853,a846),f228(a853)),x99422)))),f312(f53(a853),f312(f233(a853),f312(f312(f18(a853,a846,a846),f312(f312(f8(a846,f861(a846,a846),a853),a310),f312(f312(f7(a853,f861(a853,a846),a846),f314(a853)),x99421))),f312(f312(f7(a853,a853,a846),f228(a853)),f312(a126,x99422))))))
% 155.90/155.61 [7452]~P90(x74521)+E(f312(f312(f90(x74521),x74522),f312(f117(x74521),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),x74522)
% 155.90/155.61 [7716]~P90(x77161)+E(f312(f312(f89(x77161),f312(f117(x77161),x77162)),f87(x77161)),f312(f117(x77161),f312(f312(f89(a1),x77162),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))))
% 155.90/155.61 [7853]P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x78532)))+E(f312(f312(f240(a1),x78531),f312(f117(a853),f312(f312(f21(a1),f312(f312(f89(a1),x78532),x78532)),a111))),f87(a1))
% 155.90/155.61 [9268]~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x92682)))+E(f312(f312(f240(a1),x92681),f312(f117(a853),f312(f312(f21(a1),f312(f312(f89(a1),x92682),x92682)),a111))),f312(f312(f95(a1,a1),f312(f312(f240(a1),x92681),f312(f117(a853),x92682))),f312(f312(f18(a1,a1,a1),f312(f312(f8(a1,f861(a1,a1),a1),f90(a1)),f312(f90(a1),x92681))),f5(a1))))
% 155.90/155.61 [9774]~P22(f312(f312(f228(a853),f312(f117(a853),x97741)),f312(a126,x97742)))+P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x97741),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f7(a1,a853,a846),f312(f312(f8(a853,f861(a853,a846),a1),f228(a853)),a118)),x97742))))
% 155.90/155.61 [9775]~P22(f312(f312(f227(a853),f312(f117(a853),x97751)),f312(a126,x97752)))+P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x97751),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f7(a1,a853,a846),f312(f312(f8(a853,f861(a853,a846),a1),f227(a853)),a118)),x97752))))
% 155.90/155.61 [9829]P22(f312(f312(f228(a853),f312(f117(a853),x98291)),f312(a126,x98292)))+~P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x98291),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f7(a1,a853,a846),f312(f312(f8(a853,f861(a853,a846),a1),f228(a853)),a118)),x98292))))
% 155.90/155.61 [9830]P22(f312(f312(f227(a853),f312(f117(a853),x98301)),f312(a126,x98302)))+~P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x98301),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f7(a1,a853,a846),f312(f312(f8(a853,f861(a853,a846),a1),f227(a853)),a118)),x98302))))
% 155.90/155.61 [9860]~P22(f312(f312(f228(a853),f312(a126,x98602)),f312(f117(a853),x98601)))+P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x98601),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f8(a853,a846,a1),f312(f228(a853),x98602)),a118)))))
% 155.90/155.61 [9861]~P22(f312(f312(f227(a853),f312(a126,x98612)),f312(f117(a853),x98611)))+P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x98611),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f8(a853,a846,a1),f312(f227(a853),x98612)),a118)))))
% 155.90/155.61 [9908]P22(f312(f312(f228(a853),f312(a126,x99081)),f312(f117(a853),x99082)))+~P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x99082),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f8(a853,a846,a1),f312(f228(a853),x99081)),a118)))))
% 155.90/155.61 [9909]P22(f312(f312(f227(a853),f312(a126,x99091)),f312(f117(a853),x99092)))+~P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x99092),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f8(a853,a846,a1),f312(f227(a853),x99091)),a118)))))
% 155.90/155.61 [9981]~P22(f312(f312(f314(a853),f2(a853)),x99811))+E(f312(a126,f312(f53(a853),f312(f233(a853),f312(f312(f18(a853,a846,a846),f312(f312(f8(a846,f861(a846,a846),a853),a310),f312(f312(f7(a853,f861(a853,a846),a846),f312(f312(f8(a853,f861(f861(a853,a846),a846),a853),f314(a853)),a126)),x99811))),f312(f312(f7(a853,a853,a846),f228(a853)),x99812))))),f312(f53(a853),f312(f233(a853),f312(f312(f18(a853,a846,a846),f312(f312(f8(a846,f861(a846,a846),a853),a310),f312(f312(f7(a853,f861(a853,a846),a846),f314(a853)),x99811))),f312(f312(f7(a853,a853,a846),f228(a853)),f312(a126,x99812))))))
% 155.90/155.61 [8416]~P90(x84161)+E(f312(f312(f90(x84161),f312(f117(x84161),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),x84162),x84162)
% 155.90/155.61 [8479]~P90(x84791)+E(f312(f312(f89(x84791),f87(x84791)),f312(f117(x84791),x84792)),f312(f117(x84791),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),x84792)))
% 155.90/155.61 [8534]~P90(x85341)+E(f312(f312(f21(x85341),f312(f117(x85341),x85342)),f87(x85341)),f312(f117(x85341),f312(f312(f89(a1),x85342),f312(f88(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 155.90/155.61 [8672]~P22(f312(f312(f228(a853),f312(f117(a853),a92)),x86722))+E(f312(f312(f21(a853),x86721),f312(f312(f21(a853),x86722),f312(f117(a853),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))),f312(f312(f21(a853),f312(a126,x86721)),x86722))
% 155.90/155.61 [9307]~P107(x93071)+E(f312(f312(f90(x93071),x93072),x93072),f312(f312(f240(x93071),x93072),f312(f117(a853),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)))))
% 155.90/155.61 [9308]~P78(x93081)+E(f312(f312(f240(x93081),x93082),f312(f117(a853),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(x93081),x93082),x93082))
% 155.90/155.61 [9310]~P90(x93101)+E(f312(f312(f90(x93101),x93102),f312(f117(x93101),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(x93101),x93102),x93102))
% 155.90/155.61 [9546]~P111(x95461)+E(f312(f312(f240(x95461),f312(f88(x95461),x95462)),f312(f117(a853),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(x95461),x95462),f312(f117(a853),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)))))
% 155.90/155.61 [9547]~P112(x95471)+E(f312(f312(f240(x95471),f312(f84(x95471),x95472)),f312(f117(a853),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(x95471),x95472),f312(f117(a853),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)))))
% 155.90/155.61 [9543]~P90(x95431)+E(f312(f312(f90(x95431),f312(f117(x95431),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)))),x95432),f312(f312(f89(x95431),x95432),x95432))
% 155.90/155.61 [9666]~P112(x96661)+E(f312(f84(x96661),f312(f312(f240(x96661),x96662),f312(f117(a853),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(x96661),x96662),f312(f117(a853),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)))))
% 155.90/155.61 [9726]~P112(x97261)+P22(f312(f312(f227(x97261),f2(x97261)),f312(f312(f240(x97261),x97262),f312(f117(a853),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))))))
% 155.90/155.61 [9901]~E(f312(a126,x99012),f312(f117(a853),x99011))+P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x99011),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f7(a1,a853,a846),f312(f312(f8(a853,f861(a853,a846),a1),a309),a118)),x99012)))))
% 155.90/155.61 [9902]~E(f312(f117(a853),x99021),f312(a126,x99022))+P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x99021),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f7(a1,a853,a846),f312(f312(f8(a853,f861(a853,a846),a1),a309),a118)),x99022)))))
% 155.90/155.61 [9945]E(f312(a126,x99451),f312(f117(a853),x99452))+~P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x99452),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f7(a1,a853,a846),f312(f312(f8(a853,f861(a853,a846),a1),a309),a118)),x99451)))))
% 155.90/155.61 [9946]E(f312(f117(a853),x99461),f312(a126,x99462))+~P22(f312(f312(f95(a1,a846),f312(f117(a1),f312(f312(f89(a1),x99461),a111))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a310),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f18(a1,a846,a846),f312(f312(f8(a846,f861(a846,a846),a1),a315),f312(f312(f8(a846,a846,a1),a307),a194))),f312(f312(f7(a1,a853,a846),f312(f312(f8(a853,f861(a853,a846),a1),a309),a118)),x99462)))))
% 155.90/155.61 [9722]~P90(x97221)+E(f312(f312(f240(x97221),f312(f117(x97221),a111)),f312(f312(f90(a853),f312(f117(a853),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)))),x97222)),f87(x97221))
% 155.90/155.61 [9723]~P111(x97231)+E(f312(f312(f240(x97231),f312(f88(x97231),f87(x97231))),f312(f312(f90(a853),f312(f117(a853),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)))),x97232)),f87(x97231))
% 155.90/155.61 [9728]~P78(x97281)+E(f312(f312(f240(x97281),x97282),f312(f117(a853),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(x97281),f312(f312(f90(x97281),x97282),x97282)),x97282))
% 155.90/155.61 [9924]~P22(f312(f312(f227(a1),f2(a1)),x99242))+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)))),x99241)),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)))),x99242)),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,x99241,x99242))))
% 155.90/155.61 [9948]~P22(f312(f312(f227(a1),f2(a1)),x99482))+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)))),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(f47(a1,x99481),x99482))
% 155.90/155.61 [9950]~P22(f312(f312(f227(a1),x99502),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)))),x99501))),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)))),x99502)),f312(f47(a1,f312(f312(f89(a1),x99501),f87(a1))),x99502))
% 155.90/155.61 [9951]~P22(f312(f312(f227(a1),x99512),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)))),x99511)),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)))),x99512)),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),x99511),f87(a1)),x99512))),f87(a1)))
% 155.90/155.61 [9820]~P90(x98201)+E(f312(f312(f240(x98201),f312(f117(x98201),a111)),f312(a126,f312(f312(f90(a853),f312(f117(a853),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)))),x98202))),f312(f117(x98201),a111))
% 155.90/155.61 [9822]~P111(x98221)+E(f312(f312(f240(x98221),f312(f88(x98221),f87(x98221))),f312(a126,f312(f312(f90(a853),f312(f117(a853),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)))),x98222))),f312(f88(x98221),f87(x98221)))
% 155.90/155.61 [5042]~P18(x50421,x50422,x50423)+P21(x50421,x50422,x50423)
% 155.90/155.61 [7923]~E(x79232,x79233)+P39(x79231,x79231,a309,x79232,x79233)
% 155.90/155.61 [8494]E(x84941,x84942)+~P39(x84943,x84943,a309,x84941,x84942)
% 155.90/155.61 [5047]~P41(x50471,x50473)+P41(x50471,f306(x50471,x50472,x50473))
% 155.90/155.61 [5220]P34(x52201,x52202,x52203)+~P34(x52201,f312(a126,x52202),x52203)
% 155.90/155.61 [5300]~P3(x53001,x53002,x53003)+P3(f854(x53001),f157(x53001,x53002),f154(x53001,x53003))
% 155.90/155.61 [5301]~P50(x53011,x53012,x53013)+P50(f854(x53011),f157(x53011,x53012),f154(x53011,x53013))
% 155.90/155.61 [5412]P54(x54121,x54122,x54123)+~E(f723(x54123,x54122,x54121),f724(x54123,x54122,x54121))
% 155.90/155.61 [5413]P55(x54131,x54132,x54133)+~E(f756(x54133,x54132,x54131),f757(x54133,x54132,x54131))
% 155.90/155.61 [6334]P21(x63341,x63342,x63343)+~P34(x63341,f645(x63343,x63342,x63341),f663(x63343,x63342,x63341))
% 155.90/155.61 [4597]~E(x45971,f192(x45972))+~E(x45971,f312(f219(x45972),x45973))
% 155.90/155.61 [4650]~E(f312(f165(x46502),x46501),x46503)+E(x46501,f312(f165(x46502),x46503))
% 155.90/155.61 [4651]~E(x46512,f312(f165(x46511),x46513))+E(f312(f165(x46511),x46512),x46513)
% 155.90/155.61 [4701]E(x47011,x47012)+~E(f312(f219(x47013),x47011),f312(f219(x47013),x47012))
% 155.90/155.61 [4702]E(x47021,x47022)+~E(f312(f165(x47023),x47021),f312(f165(x47023),x47022))
% 155.90/155.61 [4905]~P2(x49053,x49051)+P22(f312(f312(x49051,x49052),x49052))
% 155.90/155.61 [4906]~P52(x49063,x49061)+P22(f312(f312(x49061,x49062),x49062))
% 155.90/155.61 [4908]~P59(x49081,x49082)+P22(f312(f300(x49081,x49082),x49083))
% 155.90/155.61 [4963]~P41(x49631,x49632)+P41(f854(x49631),f312(f139(x49631,x49632),x49633))
% 155.90/155.61 [4968]~P22(f312(x49682,x49683))+~E(f312(f233(x49681),x49682),f189(f861(x49681,a846)))
% 155.90/155.61 [4969]~P22(f312(x49692,x49693))+~E(f189(f861(x49691,a846)),f312(f233(x49691),x49692))
% 155.90/155.61 [5000]~P22(f312(x50001,x50003))+P22(f312(x50001,f99(x50002,x50001)))
% 155.90/155.61 [5130]~E(x51302,x51303)+P22(f312(f312(f314(x51301),x51302),f312(a309,x51303)))
% 155.90/155.61 [5142]P22(f312(x51421,x51422))+~P22(f312(x51421,f785(x51421,x51423)))
% 155.90/155.61 [5186]E(f312(f165(x51861),x51862),f312(f312(f147(x51861),x51863),f127(x51861)))+~E(x51862,f312(f312(f147(x51861),x51863),f127(x51861)))
% 155.90/155.61 [5187]~E(x51873,f312(f312(f147(x51871),x51872),f127(x51871)))+E(f312(f312(f147(x51871),x51872),f127(x51871)),f312(f165(x51871),x51873))
% 155.90/155.61 [5213]~E(x52133,f312(f16(f857(x52132),x52131),f192(x52132)))+E(f179(x52131,x52132,x52133),f189(f861(x52131,a846)))
% 155.90/155.61 [5233]~P38(x52331,x52332,x52333)+P38(x52331,x52332,f312(f165(x52331),x52333))
% 155.90/155.61 [5236]E(f312(f53(x52361),f365(x52362,x52363,x52361)),x52362)+~E(f312(f53(x52361),x52363),f312(a126,x52362))
% 155.90/155.61 [5242]~P41(x52421,x52423)+P22(f312(f312(f314(x52421),x52422),f301(x52421,x52423)))
% 155.90/155.61 [5245]~E(f312(f165(x52452),x52451),f312(f312(f147(x52452),x52453),f127(x52452)))+E(x52451,f312(f312(f147(x52452),x52453),f127(x52452)))
% 155.90/155.61 [5246]~E(f312(f312(f147(x52462),x52463),f127(x52462)),f312(f165(x52462),x52461))+E(x52461,f312(f312(f147(x52462),x52463),f127(x52462)))
% 155.90/155.61 [5259]E(x52591,f312(f16(f857(x52592),x52593),f192(x52592)))+~E(f179(x52593,x52592,x52591),f189(f861(x52593,a846)))
% 155.90/155.61 [5266]E(f94(f860(a853,a853),f56(x52661,x52662)),x52663)+~P22(f312(f56(x52661,x52662),x52663))
% 155.90/155.61 [5274]~E(x52743,f312(f219(x52741),x52742))+P22(f312(f312(f314(x52741),x52742),f218(x52741,x52743)))
% 155.90/155.61 [5304]P38(x53041,x53042,x53043)+~P38(x53041,x53042,f312(f165(x53041),x53043))
% 155.90/155.61 [5365]~E(x53652,f127(x53651))+P22(f312(f312(f314(f854(x53651)),x53652),f157(x53651,x53653)))
% 155.90/155.61 [5373]~P50(x53731,x53732,x53733)+P50(x53731,x53732,f312(f265(x53731,x53731),x53733))
% 155.90/155.61 [5374]~P55(x53741,x53742,x53743)+P55(x53741,x53742,f312(f265(x53741,x53741),x53743))
% 155.90/155.61 [5393]~P60(x53931)+E(f54(x53931,f54(x53931,x53932,x53933),x53933),f54(x53931,x53932,x53933))
% 155.90/155.61 [5489]E(x54891,x54892)+~P22(f312(f312(f314(x54893),x54891),f312(a309,x54892)))
% 155.90/155.61 [5538]~P23(x55381)+E(f191(x55381,x55382,f2(a853),x55383),x55383)
% 155.90/155.61 [5560]P50(x55601,x55602,x55603)+~P50(x55601,x55602,f312(f265(x55601,x55601),x55603))
% 155.90/155.61 [5561]P55(x55611,x55612,x55613)+~P55(x55611,x55612,f312(f265(x55611,x55611),x55613))
% 155.90/155.61 [5565]~P103(x55652)+E(f144(x55651,x55652,x55653,f127(x55651)),f127(x55651))
% 155.90/155.61 [5581]E(f166(x55811,x55812,f148(x55811,x55813)),f148(x55811,f166(x55811,x55812,x55813)))+~P22(f312(f133(x55811),x55813))
% 155.90/155.61 [5584]E(x55841,f312(f219(x55842),x55843))+~P22(f312(f312(f314(x55842),x55843),f218(x55842,x55841)))
% 155.90/155.61 [5665]~P22(f312(a24,x56653))+P22(f312(a24,f32(x56651,x56652,x56653)))
% 155.90/155.61 [5674]E(f312(f132(x56741,x56742),x56743),f127(x56741))+P22(f312(x56742,f614(x56743,x56742,x56741)))
% 155.90/155.61 [5810]~P22(f312(f133(x58101),x58103))+P22(f312(f133(x58101),f166(x58101,x58102,x58103)))
% 155.90/155.61 [5811]~P22(f312(f133(x58111),x58112))+P22(f312(f133(x58111),f170(x58111,x58112,x58113)))
% 155.90/155.61 [5812]~P22(f312(f133(x58121),x58123))+P22(f312(f133(x58121),f172(x58121,x58122,x58123)))
% 155.90/155.61 [5813]~P22(f312(f133(x58131),x58133))+P22(f312(f133(x58131),f136(x58131,x58132,x58133)))
% 155.90/155.61 [5814]~P139(x58141,x58143,x58142)+P22(f312(x58141,f54(a1,x58142,x58143)))
% 155.90/155.61 [5832]~P38(x58323,x58321,x58322)+P22(f312(x58321,f737(x58322,x58321,x58323)))
% 155.90/155.61 [5853]E(f312(f132(x58531,x58532),x58533),f172(x58531,x58532,x58533))+P22(f312(x58532,f671(x58533,x58532,x58531)))
% 155.90/155.61 [5900]~P22(f312(f133(x59001),x59003))+P22(f312(f133(f854(x59001)),f63(x59001,x59002,x59003)))
% 155.90/155.61 [5920]P22(f312(a24,f31(x59201,x59202,x59203)))+~P22(f312(a24,f312(a27,x59202)))
% 155.90/155.61 [5935]~P105(x59351)+E(f312(f312(f115(f861(x59351,a846)),f312(f281(x59351),x59352)),f285(x59351,x59352,x59353)),f189(f861(x59351,a846)))
% 155.90/155.61 [5936]~P105(x59361)+E(f312(f312(f115(f861(x59361,a846)),f312(f281(x59361),x59362)),f284(x59361,x59362,x59363)),f189(f861(x59361,a846)))
% 155.90/155.61 [5937]~P105(x59371)+E(f312(f312(f115(f861(x59371,a846)),f312(f279(x59371),x59372)),f283(x59371,x59372,x59373)),f189(f861(x59371,a846)))
% 155.90/155.61 [6072]P22(f312(a24,x60721))+~P22(f312(a24,f32(x60722,x60723,x60721)))
% 155.90/155.61 [6074]P22(f312(a24,x60741))+~P22(f312(a24,f33(x60742,x60743,x60741)))
% 155.90/155.61 [6076]P22(f312(a24,x60761))+~P22(f312(a24,f33(x60762,x60761,x60763)))
% 155.90/155.61 [6157]E(f312(f132(x61571,x61572),x61573),x61573)+~P22(f312(x61572,f643(x61573,x61572,x61571)))
% 155.90/155.61 [6159]E(f312(f312(f289(x61591),f387(x61592,x61593,x61591)),f365(x61592,x61593,x61591)),x61593)+~E(f312(f53(x61591),x61593),f312(a126,x61592))
% 155.90/155.61 [6175]P139(x61751,x61752,x61753)+~P22(f312(x61751,f54(a1,x61753,x61752)))
% 155.90/155.61 [6223]E(f172(x62231,x62232,x62233),x62233)+~P22(f312(x62232,f657(x62233,x62232,x62231)))
% 155.90/155.61 [6261]~P22(f312(a24,f31(x62612,x62611,x62613)))+P22(f312(a24,f312(a27,x62611)))
% 155.90/155.61 [6304]~P22(f312(x63042,f795(x63043,x63042,x63041)))+P22(f312(f243(x63041,x63042),x63043))
% 155.90/155.61 [6305]~P22(f312(x63052,f644(x63053,x63052,x63051)))+P22(f312(f156(x63051,x63052),x63053))
% 155.90/155.61 [6543]~P22(f312(f300(x65431,x65432),f339(x65433,x65432,x65431)))+P22(f312(f300(x65431,x65432),x65433))
% 155.90/155.61 [6544]~P22(f312(f300(x65441,x65442),f345(x65443,x65442,x65441)))+P22(f312(f300(x65441,x65442),x65443))
% 155.90/155.61 [6900]~P60(x69001)+E(f312(f312(f89(x69001),f312(f312(f90(x69001),x69002),f312(f47(x69001,x69003),x69002))),f54(x69001,x69003,x69002)),x69003)
% 155.90/155.61 [7606]E(f312(f312(f239(x76061,x76061),f418(x76062,x76063,x76061)),f418(x76062,x76063,x76061)),x76063)+~P22(f312(f312(f314(f860(x76061,x76061)),x76063),f237(x76061,x76062)))
% 155.90/155.61 [7619]~P60(x76191)+E(f312(f312(f89(x76191),f312(f312(f90(x76191),f312(f47(x76191,x76192),x76193)),x76193)),f54(x76191,x76192,x76193)),x76192)
% 155.90/155.61 [7724]~P22(f312(f312(f314(x77241),f346(x77243,x77242,x77241)),f301(x77241,x77243)))+P22(f312(f312(f314(x77241),x77242),f301(x77241,x77243)))
% 155.90/155.61 [7725]~P22(f312(f312(f314(x77251),f726(x77253,x77252,x77251)),f301(x77251,x77253)))+P22(f312(f312(f314(x77251),x77252),f301(x77251,x77253)))
% 155.90/155.61 [7726]~P22(f312(f312(f314(x77261),f735(x77263,x77262,x77261)),f301(x77261,x77263)))+P22(f312(f312(f314(x77261),x77262),f301(x77261,x77263)))
% 155.90/155.61 [7949]~E(f312(f53(x79491),x79492),f312(a126,x79493))+~P22(f312(f312(f314(x79491),f387(x79493,x79492,x79491)),f365(x79493,x79492,x79491)))
% 155.90/155.61 [8582]P22(f312(f312(f227(f861(f860(x85821,x85821),a846)),f287(x85821,x85822)),f287(x85821,x85823)))+~P22(f312(f312(f227(f861(f860(x85821,x85821),a846)),x85822),f287(x85821,x85823)))
% 155.90/155.61 [8853]E(x88531,f127(x88532))+~P22(f312(f312(f314(f860(f854(x88532),f854(x88532))),f312(f312(f239(f854(x88532),f854(x88532)),x88531),f127(x88532))),f154(x88532,x88533)))
% 155.90/155.61 [8880]E(x88801,f127(x88802))+~P22(f312(f312(f314(f860(f854(x88802),f854(x88802))),f312(f312(f239(f854(x88802),f854(x88802)),f127(x88802)),x88801)),f154(x88802,x88803)))
% 155.90/155.61 [9002]E(f312(f312(f147(x90021),f631(x90022,x90023,x90021)),f632(x90022,x90023,x90021)),x90023)+~P22(f312(f312(f314(f860(f854(x90021),f854(x90021))),f312(f312(f239(f854(x90021),f854(x90021)),f127(x90021)),x90023)),f143(x90021,x90022)))
% 155.90/155.61 [9237]~P119(x92371)+~P22(f312(f312(f228(x92371),f312(f312(f89(x92371),f312(f312(f90(x92371),x92372),x92372)),f312(f312(f90(x92371),x92373),x92373))),f2(x92371)))
% 155.90/155.61 [9286]P22(f312(f70(x92861),x92862))+~P22(f312(f312(f314(f860(f861(x92861,a846),f861(x92861,a846))),f312(f312(f239(f861(x92861,a846),f861(x92861,a846)),x92863),x92862)),f286(x92861)))
% 155.90/155.61 [10027]~P112(x100271)+~P22(f312(f312(f228(x100271),f312(f312(f89(x100271),f312(f312(f240(x100271),x100272),f312(f117(a853),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(x100271),x100273),f312(f117(a853),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(x100271)))
% 155.90/155.61 [4683]~E(x46833,f127(x46831))+E(f312(f312(f129(x46831),x46832),x46833),x46832)
% 155.90/155.61 [4684]~E(x46842,f127(x46841))+E(f312(f312(f129(x46841),x46842),x46843),x46843)
% 155.90/155.61 [4691]~E(x46912,f2(a853))+E(f312(f312(f169(x46911),x46912),x46913),f127(x46911))
% 155.90/155.61 [4696]~E(x46963,f127(x46961))+E(f312(f312(f169(x46961),x46962),x46963),f127(x46961))
% 155.90/155.61 [4733]~E(x47331,x47333)+E(x47331,f312(f312(f129(x47332),f127(x47332)),x47333))
% 155.90/155.61 [4819]~P24(x48192)+E(f312(f189(f861(x48191,x48192)),x48193),f189(x48192))
% 155.90/155.61 [4820]~P106(x48202)+E(f312(f235(f861(x48201,x48202)),x48203),f235(x48202))
% 155.90/155.61 [4839]E(x48391,f127(x48392))+~E(f312(f312(f129(x48392),x48393),x48391),x48393)
% 155.90/155.61 [4840]E(x48401,f127(x48402))+~E(f312(f312(f129(x48402),x48401),x48403),x48403)
% 155.90/155.61 [4849]E(x48491,f127(x48492))+~E(f312(f312(f129(x48492),x48493),x48491),f127(x48492))
% 155.90/155.61 [4850]E(x48501,f127(x48502))+~E(f312(f312(f129(x48502),x48501),x48503),f127(x48502))
% 155.90/155.61 [4873]~E(x48732,f2(a853))+E(f312(f312(f90(a853),x48731),x48732),f312(f312(f90(a853),x48733),x48732))
% 155.90/155.61 [4875]~E(x48751,f2(a853))+E(f312(f312(f90(a853),x48751),x48752),f312(f312(f90(a853),x48751),x48753))
% 155.90/155.61 [4925]~P107(x49251)+E(f312(f312(f89(x49251),x49252),x49253),f312(f312(f89(x49251),x49253),x49252))
% 155.90/155.61 [4926]~P87(x49261)+E(f312(f312(f124(x49261),x49262),x49263),f312(f312(f124(x49261),x49263),x49262))
% 155.90/155.61 [4928]~P98(x49281)+E(f312(f312(f124(x49281),x49282),x49283),f312(f312(f124(x49281),x49283),x49282))
% 155.90/155.61 [4929]~P87(x49291)+E(f312(f312(f115(x49291),x49292),x49293),f312(f312(f115(x49291),x49293),x49292))
% 155.90/155.61 [4931]~P99(x49311)+E(f312(f312(f115(x49311),x49312),x49313),f312(f312(f115(x49311),x49313),x49312))
% 155.90/155.61 [4932]~P107(x49321)+E(f312(f312(f90(x49321),x49322),x49323),f312(f312(f90(x49321),x49323),x49322))
% 155.90/155.61 [4934]~P103(x49341)+E(f312(f312(f225(x49341),x49342),x49343),f312(f312(f225(x49341),x49343),x49342))
% 155.90/155.61 [4936]~P103(x49361)+E(f312(f312(f226(x49361),x49362),x49363),f312(f312(f226(x49361),x49363),x49362))
% 155.90/155.61 [4995]E(f54(a853,x49951,x49952),f2(a853))+~E(x49951,f312(f312(f90(a853),x49952),x49953))
% 155.90/155.61 [4996]E(f54(a1,x49961,x49962),f2(a1))+~E(x49961,f312(f312(f90(a1),x49962),x49963))
% 155.90/155.61 [5059]E(x50591,x50592)+~E(f312(f312(f89(a853),x50593),x50591),f312(f312(f89(a853),x50593),x50592))
% 155.90/155.61 [5060]E(x50601,x50602)+~E(f312(f312(f89(a853),x50601),x50603),f312(f312(f89(a853),x50602),x50603))
% 155.90/155.61 [5072]~P30(x50721)+E(f312(f312(f89(x50721),x50722),f312(f88(x50721),x50723)),f312(f312(f21(x50721),x50722),x50723))
% 155.90/155.61 [5073]~P71(x50731)+E(f312(f312(f89(x50731),x50732),f312(f88(x50731),x50733)),f312(f312(f21(x50731),x50732),x50733))
% 155.90/155.61 [5074]~P108(x50741)+E(f312(f312(f89(x50741),x50742),f312(f88(x50741),x50743)),f312(f312(f21(x50741),x50742),x50743))
% 155.90/155.61 [5075]~P88(x50751)+E(f312(f312(f115(x50751),x50752),f312(f88(x50751),x50753)),f312(f312(f21(x50751),x50752),x50753))
% 155.90/155.61 [5076]~P71(x50761)+E(f312(f312(f21(x50761),x50762),f312(f88(x50761),x50763)),f312(f312(f89(x50761),x50762),x50763))
% 155.90/155.61 [5123]~P22(f312(x51233,x51232))+P22(f312(f312(f314(x51231),x51232),x51233))
% 155.90/155.61 [5125]~P72(x51252)+E(f312(f312(f9(x51251,x51252),x51253),f189(f861(x51251,a846))),f87(x51252))
% 155.90/155.61 [5127]~P26(x51272)+E(f312(f312(f6(x51271,x51272),x51273),f189(f861(x51271,a846))),f2(x51272))
% 155.90/155.61 [5175]~E(x51752,f312(f312(f89(a853),x51751),x51753))+P22(f312(f312(f227(a853),x51751),x51752))
% 155.90/155.61 [5178]~E(x51782,f189(f861(x51781,a846)))+E(f312(f312(f69(x51781),x51782),x51783),f189(f861(f861(x51781,a846),a846)))
% 155.90/155.61 [5179]~E(x51792,f189(f861(x51791,a846)))+E(f189(f861(f861(x51791,a846),a846)),f312(f312(f69(x51791),x51792),x51793))
% 155.90/155.61 [5249]~E(f312(f236(x52492,x52493),x52491),f189(f861(x52493,a846)))+E(x52491,f189(f861(f860(x52492,x52493),a846)))
% 155.90/155.61 [5250]~E(f312(f238(x52502,x52503),x52501),f189(f861(x52502,a846)))+E(x52501,f189(f861(f860(x52502,x52503),a846)))
% 155.90/155.61 [5280]E(f312(f236(x52801,x52802),x52803),f189(f861(x52802,a846)))+~E(x52803,f189(f861(f860(x52801,x52802),a846)))
% 155.90/155.61 [5281]E(f312(f238(x52811,x52812),x52813),f189(f861(x52811,a846)))+~E(x52813,f189(f861(f860(x52811,x52812),a846)))
% 155.90/155.61 [5284]E(f260(x52841,x52842,x52843),f312(f312(f21(a113),x52842),x52843))+P22(f312(f312(f228(a113),x52842),x52843))
% 155.90/155.61 [5298]P22(f312(x52981,x52982))+~P22(f312(f312(f314(x52983),x52982),x52981))
% 155.90/155.61 [5335]E(x53351,x53352)+~E(f312(f88(f861(x53353,a846)),x53351),f312(f88(f861(x53353,a846)),x53352))
% 155.90/155.61 [5340]E(f293(x53401,x53402,x53403),f192(f854(a308)))+~P22(f312(f312(f228(a1),x53402),x53403))
% 155.90/155.61 [5345]~E(x53451,f189(f861(x53452,a846)))+~P22(f312(f312(f314(x53452),x53453),x53451))
% 155.90/155.61 [5375]~E(x53752,f312(f312(f89(a1),x53751),f312(f114(a1),x53753)))+P22(f312(f312(f227(a1),x53751),x53752))
% 155.90/155.61 [5391]E(f312(f312(f289(x53911),x53912),x53913),x53913)+~P22(f312(f312(f314(x53911),x53912),x53913))
% 155.90/155.61 [5402]E(x54021,f189(f861(x54022,a846)))+~E(f312(f312(f69(x54022),x54021),x54023),f189(f861(f861(x54022,a846),a846)))
% 155.90/155.61 [5403]E(x54031,f189(f861(x54032,a846)))+~E(f189(f861(f861(x54032,a846),a846)),f312(f312(f69(x54032),x54031),x54033))
% 155.90/155.61 [5409]~P120(x54091)+E(f312(f312(f90(x54091),f312(f88(x54091),x54092)),f312(f88(x54091),x54093)),f312(f312(f90(x54091),x54092),x54093))
% 155.90/155.61 [5411]~P64(x54111)+E(f312(f312(f268(x54111),f312(f88(x54111),x54112)),f312(f88(x54111),x54113)),f312(f312(f268(x54111),x54112),x54113))
% 155.90/155.61 [5442]~P22(f312(x54423,x54422))+P22(f312(f312(f314(x54421),x54422),f312(f233(x54421),x54423)))
% 155.90/155.61 [5482]E(f166(x54821,x54822,x54823),x54823)+P22(f312(f312(f314(x54821),x54822),f312(f168(x54821),x54823)))
% 155.90/155.61 [5544]~P140(x55441,x55443,x55442)+P22(f312(x55441,f312(f47(a1,x55442),x55443)))
% 155.90/155.61 [5566]~P60(x55661)+E(f312(f47(x55661,f54(x55661,x55662,x55663)),x55663),f2(x55661))
% 155.90/155.61 [5570]~P22(f312(f133(x55701),x55703))+P22(f312(f133(x55701),f312(f132(x55701,x55702),x55703)))
% 155.90/155.61 [5629]E(f170(x56291,f312(f312(f147(x56291),x56292),f127(x56291)),x56293),f127(x56291))+P22(f312(f312(f314(a853),f2(a853)),x56293))
% 155.90/155.61 [5683]E(f312(f312(f147(x56831),x56832),x56833),f136(x56831,x56832,x56833))+P22(f312(f312(f314(x56831),x56832),f312(f168(x56831),x56833)))
% 155.90/155.61 [5692]E(x56921,x56922)+~E(f312(f312(f90(a853),f312(a126,x56923)),x56921),f312(f312(f90(a853),f312(a126,x56923)),x56922))
% 155.90/155.61 [5693]~E(x56932,f312(f312(f89(a1),x56931),f312(f114(a1),f312(a126,x56933))))+P22(f312(f312(f228(a1),x56931),x56932))
% 155.90/155.61 [5793]~E(x57933,f127(x57931))+E(f312(f312(f312(f184(f854(x57931),f854(x57931)),x57932),f164(x57931)),x57933),f127(x57931))
% 155.90/155.61 [5797]P22(f312(x57971,x57972))+~P22(f312(f312(f314(x57973),x57972),f312(f233(x57973),x57971)))
% 155.90/155.61 [5821]P140(x58211,x58212,x58213)+~P22(f312(x58211,f312(f47(a1,x58213),x58212)))
% 155.90/155.61 [5828]E(x58281,x58282)+~E(f312(f312(f289(x58283),x58281),f189(f861(x58283,a846))),f312(f312(f289(x58283),x58282),f189(f861(x58283,a846))))
% 155.90/155.61 [5837]~P105(x58371)+E(f312(f312(f115(f861(x58371,a846)),f312(f279(x58371),x58372)),f312(f282(x58371,x58372),x58373)),f189(f861(x58371,a846)))
% 155.90/155.61 [5879]E(f136(x58791,x58792,x58793),x58793)+~P22(f312(f312(f314(x58791),x58792),f312(f168(x58791),x58793)))
% 155.90/155.61 [5908]~P76(x59081)+E(f312(f290(x59081,x59081,f88(x59081)),f312(f282(x59081,x59082),x59083)),f284(x59081,f312(f88(x59081),x59083),f312(f88(x59081),x59082)))
% 155.90/155.61 [5916]E(f312(f190(f854(x59161)),f166(x59161,x59162,x59163)),f312(f190(f854(x59161)),x59163))+P22(f312(f312(f314(x59161),x59162),f312(f168(x59161),x59163)))
% 155.90/155.61 [5967]~P105(x59671)+E(f312(f312(f115(f861(x59671,a846)),f312(f282(x59671,x59672),x59673)),f312(f234(x59671),x59673)),f189(f861(x59671,a846)))
% 155.90/155.61 [5989]~P76(x59891)+E(f312(f290(x59891,x59891,f88(x59891)),f285(x59891,x59892,x59893)),f285(x59891,f312(f88(x59891),x59893),f312(f88(x59891),x59892)))
% 155.90/155.61 [5990]~P76(x59901)+E(f312(f290(x59901,x59901,f88(x59901)),f283(x59901,x59902,x59903)),f283(x59901,f312(f88(x59901),x59903),f312(f88(x59901),x59902)))
% 155.90/155.61 [6040]E(f170(x60401,f312(f312(f147(x60401),x60402),f127(x60401)),x60403),f312(f312(f147(x60401),x60402),f127(x60401)))+~P22(f312(f312(f314(a853),f2(a853)),x60403))
% 155.90/155.61 [6050]~P76(x60501)+E(f312(f290(x60501,x60501,f88(x60501)),f284(x60501,x60502,x60503)),f312(f282(x60501,f312(f88(x60501),x60503)),f312(f88(x60501),x60502)))
% 155.90/155.61 [6067]~P61(x60671)+E(f54(x60671,f312(f88(x60671),f54(x60671,x60672,x60673)),x60673),f54(x60671,f312(f88(x60671),x60672),x60673))
% 155.90/155.61 [6172]~P22(f312(f70(f860(x61722,x61721)),x61723))+P22(f312(f70(x61721),f312(f236(x61722,x61721),x61723)))
% 155.90/155.61 [6173]~P22(f312(f70(f860(x61731,x61732)),x61733))+P22(f312(f70(x61731),f312(f238(x61731,x61732),x61733)))
% 155.90/155.61 [6179]~P105(x61791)+E(f312(f312(f115(f861(x61791,a846)),f285(x61791,x61792,x61793)),f312(f234(x61791),x61793)),f189(f861(x61791,a846)))
% 155.90/155.61 [6180]~P105(x61801)+E(f312(f312(f115(f861(x61801,a846)),f284(x61801,x61802,x61803)),f312(f280(x61801),x61803)),f189(f861(x61801,a846)))
% 155.90/155.61 [6181]~P105(x61811)+E(f312(f312(f115(f861(x61811,a846)),f283(x61811,x61812,x61813)),f312(f280(x61811),x61813)),f189(f861(x61811,a846)))
% 155.90/155.61 [6244]E(f312(f312(f161(x62441),x62442),f600(x62442,x62443,x62441)),x62443)+~P22(f312(f312(f314(x62441),x62443),f312(f168(x62441),x62442)))
% 155.90/155.61 [6383]E(x63831,f127(x63832))+~E(f312(f312(f312(f184(f854(x63832),f854(x63832)),x63833),f164(x63832)),x63831),f127(x63832))
% 155.90/155.61 [6481]~P22(f312(f70(f860(x64812,x64811)),x64813))+P22(f312(f70(f860(x64811,x64812)),f312(f265(x64812,x64811),x64813)))
% 155.90/155.61 [6633]P55(x66331,x66332,x66333)+P22(f312(f312(f314(x66331),f757(x66333,x66332,x66331)),x66332))
% 155.90/155.61 [6634]P55(x66341,x66342,x66343)+P22(f312(f312(f314(x66341),f756(x66343,x66342,x66341)),x66342))
% 155.90/155.61 [6646]P22(f312(f300(x66461,x66462),x66463))+P22(f312(f312(x66462,f339(x66463,x66462,x66461)),x66463))
% 155.90/155.61 [6647]P22(f312(f300(x66471,x66472),x66473))+P22(f312(f312(x66472,f345(x66473,x66472,x66471)),x66473))
% 155.90/155.61 [6677]E(f312(f190(f854(x66771)),f166(x66771,x66772,x66773)),f312(f312(f21(a853),f312(f190(f854(x66771)),x66773)),f87(a853)))+~P22(f312(f312(f314(x66771),x66772),f312(f168(x66771),x66773)))
% 155.90/155.61 [6714]P22(f312(f243(x67141,x67142),x67143))+P22(f312(f312(f314(x67141),f795(x67143,x67142,x67141)),x67143))
% 155.90/155.61 [6724]~P22(f312(f70(f860(x67242,x67241)),f312(f265(x67241,x67242),x67243)))+P22(f312(f70(f860(x67241,x67242)),x67243))
% 155.90/155.61 [6776]~P22(f312(f312(f314(x67761),x67762),f312(f168(x67761),f128(x67761,x67763))))+P22(f312(f312(f314(x67761),x67762),f312(f168(x67761),x67763)))
% 155.90/155.61 [6781]P21(x67811,x67812,x67813)+P22(f312(f312(f314(f852(x67811)),f663(x67813,x67812,x67811)),x67813))
% 155.90/155.61 [6808]E(f312(f132(x68081,x68082),x68083),x68083)+P22(f312(f312(f314(x68081),f643(x68083,x68082,x68081)),f312(f168(x68081),x68083)))
% 155.90/155.61 [6823]E(f312(f132(x68231,x68232),x68233),f127(x68231))+P22(f312(f312(f314(x68231),f614(x68233,x68232,x68231)),f312(f168(x68231),x68233)))
% 155.90/155.61 [6852]E(f172(x68521,x68522,x68523),x68523)+P22(f312(f312(f314(x68521),f657(x68523,x68522,x68521)),f312(f168(x68521),x68523)))
% 155.90/155.61 [6862]~P22(f312(f312(f227(a853),x68621),x68623))+P22(f312(f312(f227(a853),f312(f47(a853,x68621),x68622)),f312(f47(a853,x68623),x68622)))
% 155.90/155.61 [6939]P22(f312(f156(x69391,x69392),x69393))+P22(f312(f312(f314(x69391),f644(x69393,x69392,x69391)),f312(f168(x69391),x69393)))
% 155.90/155.61 [6949]~P38(x69491,x69493,x69492)+P22(f312(f312(f314(x69491),f737(x69492,x69493,x69491)),f312(f168(x69491),x69492)))
% 155.90/155.61 [6984]~P26(x69841)+E(f312(f312(f89(x69841),f312(f312(f6(a853,x69841),x69842),f312(f279(a853),x69843))),f312(x69842,x69843)),f312(f312(f6(a853,x69841),x69842),f312(f279(a853),f312(a126,x69843))))
% 155.90/155.61 [7075]~P38(x70752,x70751,x70753)+P22(f312(x70751,f312(f312(f161(x70752),x70753),f744(x70753,x70751,x70752))))
% 155.90/155.61 [7089]~P22(f312(f312(f314(x70891),x70892),f745(x70892,x70893,x70891)))+P22(f312(f312(f314(x70891),x70892),f49(f861(x70891,a846),x70893)))
% 155.90/155.61 [7118]~P26(x71181)+E(f312(f312(f89(x71181),f312(f312(f6(a853,x71181),x71182),f312(f281(a853),x71183))),f312(x71182,f312(a126,x71183))),f312(f312(f6(a853,x71181),x71182),f312(f281(a853),f312(a126,x71183))))
% 155.90/155.61 [7245]P22(f312(f312(f314(f854(x72451)),x72452),f157(x72451,x72453)))+P22(f312(f312(f314(x72451),f601(x72453,x72452,x72451)),f312(f168(x72451),x72452)))
% 155.90/155.61 [7261]~P22(f312(f312(f314(f854(x72611)),x72612),f157(x72611,f301(x72611,x72613))))+P22(f312(f312(f314(f854(x72611)),x72612),f301(f854(x72611),f153(x72611,x72613))))
% 155.90/155.61 [7284]~P22(f312(f312(f314(f854(x72841)),x72842),f301(f854(x72841),f153(x72841,x72843))))+P22(f312(f312(f314(f854(x72841)),x72842),f157(x72841,f301(x72841,x72843))))
% 155.90/155.61 [7320]E(f312(f312(f312(f184(f854(x73201),f854(x73201)),x73202),f164(x73201)),x73203),x73203)+~P22(f312(f312(f227(a853),f312(f190(f854(x73201)),x73203)),f87(a853)))
% 155.90/155.61 [7355]E(f312(f312(f129(x73551),f762(x73552,x73553,x73551)),f312(f312(f147(x73551),x73553),f780(x73552,x73553,x73551))),x73552)+~P22(f312(f312(f314(x73551),x73553),f312(f168(x73551),x73552)))
% 155.90/155.61 [7356]E(f312(f312(f129(x73561),f781(x73562,x73563,x73561)),f312(f312(f147(x73561),x73563),f782(x73562,x73563,x73561))),x73562)+~P22(f312(f312(f314(x73561),x73563),f312(f168(x73561),x73562)))
% 155.90/155.61 [7357]E(f312(f312(f129(x73571),f783(x73572,x73573,x73571)),f312(f312(f147(x73571),x73573),f784(x73572,x73573,x73571))),x73572)+~P22(f312(f312(f314(x73571),x73573),f312(f168(x73571),x73572)))
% 155.90/155.61 [7380]~P19(x73801,x73802,x73803,f235(f861(x73801,a846)))+P19(f854(x73801),f854(x73802),f312(f150(x73801,x73802),x73803),f235(f861(f854(x73801),a846)))
% 155.90/155.61 [7529]E(x75291,f312(f312(f89(a853),f312(f312(f90(a853),f312(f246(a853,a853),x75292)),x75293)),f312(f248(a853,a853),x75292)))+~P22(f312(f56(x75291,x75293),x75292))
% 155.90/155.61 [7537]P19(x75371,x75372,x75373,f235(f861(x75371,a846)))+~P19(f854(x75371),f854(x75372),f312(f150(x75371,x75372),x75373),f235(f861(f854(x75371),a846)))
% 155.90/155.61 [7573]~P22(f312(f312(f195(x75731),x75732),x75733))+P22(f312(f312(f312(f312(a198,x75731),x75732),f329(x75733,x75732,x75731)),x75733))
% 155.90/155.61 [7574]~P22(f312(f312(f195(x75741),x75742),x75743))+P22(f312(f312(f312(f312(a198,x75741),x75742),f397(x75743,x75742,x75741)),x75743))
% 155.90/155.61 [7578]P22(f312(f312(f314(f861(x75781,a846)),f745(x75782,x75783,x75781)),x75783))+P22(f312(f312(f314(x75781),x75782),f49(f861(x75781,a846),x75783)))
% 155.90/155.61 [7671]P22(f312(f312(f314(f854(x76711)),x76712),f157(x76711,x76713)))+~P22(f312(f312(f314(x76711),f601(x76713,x76712,x76711)),x76713))
% 155.90/155.61 [7796]E(x77961,x77962)+~E(f312(f312(f7(x77963,f861(x77963,a846),a846),f314(x77963)),x77961),f312(f312(f7(x77963,f861(x77963,a846),a846),f314(x77963)),x77962))
% 155.93/155.61 [7801]~P22(f312(f312(f314(f860(x78011,x78011)),x78013),f237(x78011,x78012)))+P22(f312(f312(f314(x78011),f418(x78012,x78013,x78011)),x78012))
% 155.93/155.61 [7977]~P22(f312(f312(f314(x79771),x79772),f312(f168(x79771),f782(x79773,x79772,x79771))))+~P22(f312(f312(f314(x79771),x79772),f312(f168(x79771),x79773)))
% 155.93/155.61 [7978]~P22(f312(f312(f314(x79781),x79782),f312(f168(x79781),f783(x79783,x79782,x79781))))+~P22(f312(f312(f314(x79781),x79782),f312(f168(x79781),x79783)))
% 155.93/155.61 [8071]E(f312(f221(f857(f854(a308)),f854(a308),f293(x80711,x80712,f312(f312(f89(a1),x80713),f87(a1))),f219(f854(a308))),f312(x80711,x80713)),f293(x80711,x80712,x80713))+P22(f312(f312(f228(a1),x80712),x80713))
% 155.93/155.61 [8173]E(x81731,f127(x81732))+P22(f312(f312(f314(x81732),f312(f246(x81732,f860(a113,a113)),f312(f261(x81732,x81731),x81733))),f312(f168(x81732),x81731)))
% 155.93/155.61 [8271]~P29(x82711)+E(f312(f138(x82711,x82711,f312(f7(x82711,x82711,x82711),f89(x82711)),x82712),f312(f165(x82711),x82713)),f312(f138(x82711,x82711,f89(x82711),x82712),x82713))
% 155.93/155.61 [8764]~P103(x87641)+E(f312(f168(x87641),f146(x87641,x87641,f5(x87641),x87642,x87643)),f312(f312(f289(x87641),x87642),f312(f168(x87641),x87643)))
% 155.93/155.61 [8775]P22(f312(f312(f228(a853),f2(a853)),f765(x87751,x87752,x87753)))+~P22(f312(f312(f314(f860(x87753,x87753)),x87752),f312(f312(f267(x87753,x87753,x87753),x87751),f287(x87753,x87751))))
% 155.93/155.61 [9062]~P57(x90621,x90622)+~P22(f312(f312(f314(f860(x90621,x90621)),f312(f312(f239(x90621,x90621),x90623),x90623)),f312(f312(f267(x90621,x90621,x90621),x90622),f287(x90621,x90622))))
% 155.93/155.61 [9195]~E(f312(f312(f115(f861(f860(x91951,x91951),a846)),f312(f265(x91951,x91951),x91952)),f287(x91951,x91952)),f189(f861(f860(x91951,x91951),a846)))+~P22(f312(f312(f314(f860(x91951,x91951)),f312(f312(f239(x91951,x91951),x91953),x91953)),f312(f312(f267(x91951,x91951,x91951),x91952),f287(x91951,x91952))))
% 155.93/155.61 [9370]~P22(f312(f70(x93701),x93702))+P22(f312(f312(f227(a853),f312(f53(x93701),f312(f312(f21(f861(x93701,a846)),x93702),f312(f312(f289(x93701),x93703),f189(f861(x93701,a846)))))),f312(f53(x93701),x93702)))
% 155.93/155.61 [4984]~E(x49843,f127(x49841))+E(f140(x49841,f312(f312(f147(x49841),x49842),x49843)),x49842)
% 155.93/155.61 [4992]~E(x49923,f127(x49921))+E(f128(x49921,f312(f312(f147(x49921),x49922),x49923)),f127(x49921))
% 155.93/155.61 [5022]E(x50221,f127(x50222))+E(f140(x50222,f312(f312(f147(x50222),x50223),x50221)),f140(x50222,x50221))
% 155.93/155.61 [5024]E(x50241,f127(x50242))+E(f140(x50242,f312(f312(f129(x50242),x50243),x50241)),f140(x50242,x50241))
% 155.93/155.61 [5030]~E(x50303,f127(x50301))+E(f128(x50301,f312(f312(f129(x50301),x50302),x50303)),f128(x50301,x50302))
% 155.93/155.61 [5032]~E(x50323,f127(x50321))+E(f140(x50321,f312(f312(f129(x50321),x50322),x50323)),f140(x50321,x50322))
% 155.93/155.61 [5066]E(x50661,f127(x50662))+E(f312(f137(x50662),f312(f312(f129(x50662),x50661),x50663)),f312(f137(x50662),x50661))
% 155.93/155.61 [5097]~E(x50972,f127(x50971))+E(f312(f137(x50971),f312(f312(f129(x50971),x50972),x50973)),f312(f137(x50971),x50973))
% 155.93/155.61 [5152]~P87(x51521)+E(f312(f312(f124(x51521),x51522),f312(f312(f115(x51521),x51522),x51523)),x51522)
% 155.93/155.61 [5153]~P87(x51531)+E(f312(f312(f115(x51531),x51532),f312(f312(f124(x51531),x51532),x51533)),x51532)
% 155.93/155.61 [5154]~P103(x51541)+E(f312(f312(f225(x51541),x51542),f312(f312(f226(x51541),x51542),x51543)),x51542)
% 155.93/155.61 [5155]~P103(x51551)+E(f312(f312(f226(x51551),x51552),f312(f312(f225(x51551),x51552),x51553)),x51552)
% 155.93/155.61 [5173]~P60(x51731)+E(f54(x51731,f312(f312(f90(x51731),x51732),x51733),x51733),f2(x51731))
% 155.93/155.61 [5174]~P60(x51741)+E(f54(x51741,f312(f312(f90(x51741),x51742),x51743),x51742),f2(x51741))
% 155.93/155.61 [5244]~P30(x52441)+E(f312(f88(x52441),f312(f312(f21(x52441),x52442),x52443)),f312(f312(f21(x52441),x52443),x52442))
% 155.93/155.61 [5302]E(x53021,f127(x53022))+E(f128(x53022,f312(f312(f147(x53022),x53023),x53021)),f312(f312(f147(x53022),x53023),f128(x53022,x53021)))
% 155.93/155.61 [5303]E(x53031,f127(x53032))+E(f128(x53032,f312(f312(f129(x53032),x53033),x53031)),f312(f312(f129(x53032),x53033),f128(x53032,x53031)))
% 155.93/155.61 [5305]~P31(x53051)+E(f48(x53051,f312(f312(f289(x53051),x53052),x53053)),f312(f312(f124(x53051),x53052),f48(x53051,x53053)))
% 155.93/155.61 [5306]~P31(x53061)+E(f49(x53061,f312(f312(f289(x53061),x53062),x53063)),f312(f312(f115(x53061),x53062),f49(x53061,x53063)))
% 155.93/155.61 [5350]~P87(x53501)+E(f312(f312(f124(x53501),x53502),f312(f312(f124(x53501),x53502),x53503)),f312(f312(f124(x53501),x53502),x53503))
% 155.93/155.61 [5352]~P98(x53521)+E(f312(f312(f124(x53521),x53522),f312(f312(f124(x53521),x53522),x53523)),f312(f312(f124(x53521),x53522),x53523))
% 155.93/155.61 [5353]~P87(x53531)+E(f312(f312(f115(x53531),x53532),f312(f312(f115(x53531),x53532),x53533)),f312(f312(f115(x53531),x53532),x53533))
% 155.93/155.61 [5355]~P99(x53551)+E(f312(f312(f115(x53551),x53552),f312(f312(f115(x53551),x53552),x53553)),f312(f312(f115(x53551),x53552),x53553))
% 155.93/155.61 [5356]~P93(x53561)+E(f312(f312(f90(x53561),x53562),f312(f312(f90(x53561),x53562),x53563)),f312(f312(f90(x53561),x53562),x53563))
% 155.93/155.61 [5358]~P103(x53581)+E(f312(f312(f225(x53581),x53582),f312(f312(f225(x53581),x53582),x53583)),f312(f312(f225(x53581),x53582),x53583))
% 155.93/155.61 [5360]~P103(x53601)+E(f312(f312(f226(x53601),x53602),f312(f312(f226(x53601),x53602),x53603)),f312(f312(f226(x53601),x53602),x53603))
% 155.93/155.61 [5368]~P60(x53681)+E(f54(x53681,f312(f312(f89(x53681),x53682),x53683),x53683),f54(x53681,x53682,x53683))
% 155.93/155.61 [5369]~P60(x53691)+E(f54(x53691,f312(f312(f89(x53691),x53692),x53693),x53692),f54(x53691,x53693,x53692))
% 155.93/155.61 [5376]~P120(x53761)+E(f312(f312(f90(x53761),x53762),f312(f88(x53761),x53763)),f312(f88(x53761),f312(f312(f90(x53761),x53762),x53763)))
% 155.93/155.61 [5377]~P64(x53771)+E(f312(f312(f268(x53771),x53772),f312(f88(x53771),x53773)),f312(f88(x53771),f312(f312(f268(x53771),x53772),x53773)))
% 155.93/155.61 [5378]~P25(x53781)+E(f312(f312(f89(x53781),x53782),f312(f162(x53781),x53783)),f312(f162(x53781),f312(f312(f147(x53781),x53782),x53783)))
% 155.93/155.61 [5408]~P120(x54081)+E(f312(f312(f90(x54081),f312(f88(x54081),x54082)),x54083),f312(f312(f90(x54081),x54082),f312(f88(x54081),x54083)))
% 155.93/155.61 [5414]~P3(x54141,x54142,x54143)+E(f48(f861(x54141,a846),f312(f312(f69(x54141),x54142),x54143)),x54142)
% 155.93/155.61 [5472]~P109(x54721)+E(f312(f312(f90(x54721),x54722),f312(f312(f240(x54721),x54722),x54723)),f312(f312(f240(x54721),x54722),f312(a126,x54723)))
% 155.93/155.61 [5473]~P107(x54731)+E(f312(f312(f90(x54731),x54732),f312(f312(f240(x54731),x54732),x54733)),f312(f312(f240(x54731),x54732),f312(a126,x54733)))
% 155.93/155.61 [5485]~P71(x54851)+E(f312(f312(f89(x54851),f312(f88(x54851),x54852)),f312(f312(f89(x54851),x54852),x54853)),x54853)
% 155.93/155.61 [5508]~P23(x55081)+E(f312(f312(f240(x55081),f312(f114(x55081),x55082)),x55083),f312(f114(x55081),f312(f312(f240(a853),x55082),x55083)))
% 155.93/155.61 [5509]~P111(x55091)+E(f312(f312(f240(x55091),f312(f116(x55091),x55092)),x55093),f312(f116(x55091),f312(f312(f240(a1),x55092),x55093)))
% 155.93/155.61 [5515]~P83(x55151)+E(f312(f84(x55151),f312(f312(f21(x55151),x55152),x55153)),f312(f84(x55151),f312(f312(f21(x55151),x55153),x55152)))
% 155.93/155.61 [5517]~P112(x55171)+E(f312(f312(f90(x55171),f91(x55171,x55172)),f91(x55171,x55173)),f91(x55171,f312(f312(f90(x55171),x55172),x55173)))
% 155.93/155.61 [5522]E(x55221,f127(x55222))+E(f312(f312(f129(x55222),f312(f167(x55222),x55221)),x55223),f312(f167(x55222),f312(f312(f129(x55222),x55221),x55223)))
% 155.93/155.61 [5527]~E(x55272,f312(a126,f312(f312(f89(a853),x55271),x55273)))+P22(f312(f312(f228(a853),x55271),x55272))
% 155.93/155.61 [5528]~P120(x55281)+E(f312(f312(f90(x55281),f312(f88(x55281),x55282)),x55283),f312(f88(x55281),f312(f312(f90(x55281),x55282),x55283)))
% 155.93/155.61 [5529]~P114(x55291)+E(f312(f312(f268(x55291),f312(f88(x55291),x55292)),x55293),f312(f88(x55291),f312(f312(f268(x55291),x55292),x55293)))
% 155.93/155.61 [5530]~P112(x55301)+E(f312(f312(f240(x55301),f312(f84(x55301),x55302)),x55303),f312(f84(x55301),f312(f312(f240(x55301),x55302),x55303)))
% 155.93/155.61 [5628]E(f794(x56281,x56282,x56283),f812(x56281,x56282,x56283))+E(f312(f312(f115(f861(x56283,a846)),x56282),x56281),f189(f861(x56283,a846)))
% 155.93/155.61 [5642]~P72(x56422)+E(f312(f312(f9(x56421,x56422),f312(f16(x56422,x56421),f87(x56422))),x56423),f87(x56422))
% 155.93/155.61 [5643]~P26(x56432)+E(f312(f312(f6(x56431,x56432),f312(f16(x56432,x56431),f2(x56432))),x56433),f2(x56432))
% 155.93/155.61 [5645]~P23(x56451)+E(f312(f312(f89(x56451),f312(f114(x56451),x56452)),f312(f114(x56451),x56453)),f312(f114(x56451),f312(f312(f89(a853),x56452),x56453)))
% 155.93/155.61 [5646]~P23(x56461)+E(f312(f312(f90(x56461),f312(f114(x56461),x56462)),f312(f114(x56461),x56463)),f312(f114(x56461),f312(f312(f90(a853),x56462),x56463)))
% 155.93/155.61 [5648]~P90(x56481)+E(f312(f312(f21(x56481),f312(f117(x56481),x56482)),f312(f117(x56481),x56483)),f312(f117(x56481),f312(f312(f21(a1),x56482),x56483)))
% 155.93/155.61 [5650]~P111(x56501)+E(f312(f312(f89(x56501),f312(f116(x56501),x56502)),f312(f116(x56501),x56503)),f312(f116(x56501),f312(f312(f89(a1),x56502),x56503)))
% 155.93/155.61 [5651]~P111(x56511)+E(f312(f312(f21(x56511),f312(f116(x56511),x56512)),f312(f116(x56511),x56513)),f312(f116(x56511),f312(f312(f21(a1),x56512),x56513)))
% 155.93/155.61 [5652]~P111(x56521)+E(f312(f312(f90(x56521),f312(f116(x56521),x56522)),f312(f116(x56521),x56523)),f312(f116(x56521),f312(f312(f90(a1),x56522),x56523)))
% 155.93/155.61 [5653]~P90(x56531)+E(f312(f312(f89(x56531),f312(f117(x56531),x56532)),f312(f117(x56531),x56533)),f312(f117(x56531),f312(f312(f89(a1),x56532),x56533)))
% 155.93/155.61 [5654]~P90(x56541)+E(f312(f312(f90(x56541),f312(f117(x56541),x56542)),f312(f117(x56541),x56543)),f312(f117(x56541),f312(f312(f90(a1),x56542),x56543)))
% 155.93/155.61 [5698]~E(x56983,x56982)+P22(f312(f312(f227(f861(x56981,a846)),x56982),x56983))
% 155.93/155.61 [5704]~E(x57042,x57043)+P22(f312(f312(f227(f861(x57041,a846)),x57042),x57043))
% 155.93/155.61 [5709]~P71(x57091)+E(f312(f312(f89(x57091),f312(f88(x57091),x57092)),f312(f88(x57091),x57093)),f312(f88(x57091),f312(f312(f89(x57091),x57093),x57092)))
% 155.93/155.61 [5710]~P30(x57101)+E(f312(f312(f89(x57101),f312(f88(x57101),x57102)),f312(f88(x57101),x57103)),f312(f88(x57101),f312(f312(f89(x57101),x57102),x57103)))
% 155.93/155.61 [5711]~P88(x57111)+E(f312(f312(f115(x57111),f312(f88(x57111),x57112)),f312(f88(x57111),x57113)),f312(f88(x57111),f312(f312(f124(x57111),x57112),x57113)))
% 155.93/155.61 [5712]~P88(x57121)+E(f312(f312(f124(x57121),f312(f88(x57121),x57122)),f312(f88(x57121),x57123)),f312(f88(x57121),f312(f312(f115(x57121),x57122),x57123)))
% 155.93/155.61 [5713]~P70(x57131)+E(f312(f312(f226(x57131),f312(f88(x57131),x57132)),f312(f88(x57131),x57133)),f312(f88(x57131),f312(f312(f225(x57131),x57132),x57133)))
% 155.93/155.61 [5714]~P70(x57141)+E(f312(f312(f225(x57141),f312(f88(x57141),x57142)),f312(f88(x57141),x57143)),f312(f88(x57141),f312(f312(f226(x57141),x57142),x57143)))
% 155.93/155.61 [5715]~P112(x57151)+E(f312(f312(f90(x57151),f312(f84(x57151),x57152)),f312(f84(x57151),x57153)),f312(f84(x57151),f312(f312(f90(x57151),x57152),x57153)))
% 155.93/155.61 [5716]~P66(x57161)+E(f312(f312(f268(x57161),f312(f84(x57161),x57162)),f312(f84(x57161),x57163)),f312(f84(x57161),f312(f312(f268(x57161),x57162),x57163)))
% 155.93/155.61 [5717]~P25(x57171)+E(f312(f312(f89(x57171),f312(f162(x57171),x57172)),f312(f162(x57171),x57173)),f312(f162(x57171),f312(f312(f129(x57171),x57172),x57173)))
% 155.93/155.61 [5718]E(x57181,f189(f861(x57182,a846)))+~E(f312(f312(f124(f861(x57182,a846)),x57183),x57181),f189(f861(x57182,a846)))
% 155.93/155.61 [5719]E(x57191,f189(f861(x57192,a846)))+~E(f312(f312(f124(f861(x57192,a846)),x57191),x57193),f189(f861(x57192,a846)))
% 155.93/155.61 [5765]~P22(f312(f70(x57651),x57653))+P22(f312(f70(x57651),f312(f312(f289(x57651),x57652),x57653)))
% 155.93/155.61 [5766]~P22(f312(f133(x57661),x57663))+P22(f312(f133(x57661),f312(f312(f169(x57661),x57662),x57663)))
% 155.93/155.61 [5767]~P22(f312(f133(x57671),x57673))+P22(f312(f133(x57671),f312(f312(f134(x57671),x57672),x57673)))
% 155.93/155.61 [5774]~E(x57741,f2(a853))+E(f312(f47(a853,f312(f312(f90(a853),x57741),x57742)),f312(f312(f90(a853),x57741),x57743)),f2(a853))
% 155.93/155.61 [5798]~P87(x57981)+P22(f312(f312(f227(x57981),x57982),f312(f312(f124(x57981),x57983),x57982)))
% 155.93/155.61 [5799]~P98(x57991)+P22(f312(f312(f227(x57991),x57992),f312(f312(f124(x57991),x57993),x57992)))
% 155.93/155.61 [5800]~P87(x58001)+P22(f312(f312(f227(x58001),x58002),f312(f312(f124(x58001),x58002),x58003)))
% 155.93/155.61 [5801]~P98(x58011)+P22(f312(f312(f227(x58011),x58012),f312(f312(f124(x58011),x58012),x58013)))
% 155.93/155.61 [5802]~P103(x58021)+P22(f312(f312(f227(x58021),x58022),f312(f312(f226(x58021),x58023),x58022)))
% 155.93/155.61 [5803]~P103(x58031)+P22(f312(f312(f227(x58031),x58032),f312(f312(f226(x58031),x58032),x58033)))
% 155.93/155.61 [5882]P22(f312(x58821,x58822))+P22(f312(f312(f195(f35(x58821,x58823)),x58822),x58822))
% 155.93/155.61 [5899]E(x58991,f2(a853))+E(f312(f47(a853,f312(f312(f90(a853),x58991),x58992)),f312(f312(f90(a853),x58991),x58993)),f312(f47(a853,x58992),x58993))
% 155.93/155.61 [5902]~P90(x59021)+E(f312(f312(f21(x59021),f312(f117(x59021),x59022)),f312(f117(x59021),x59023)),f312(f117(x59021),f312(f312(f89(a1),x59022),f312(f88(a1),x59023))))
% 155.93/155.61 [5987]E(f148(x59871,f312(f312(f147(x59871),x59872),x59873)),f312(f312(f147(x59871),x59872),f148(x59871,x59873)))+P22(f312(f312(f314(x59871),x59872),f312(f168(x59871),x59873)))
% 155.93/155.61 [6088]E(x60881,f127(x60882))+E(f312(f312(f147(x60882),f312(f137(x60882),x60881)),f312(f312(f169(x60882),x60883),f312(f167(x60882),x60881))),f312(f312(f169(x60882),f312(a126,x60883)),x60881))
% 155.93/155.61 [6094]E(f312(f312(f21(f861(x60941,a846)),x60942),x60943),x60942)+~E(f312(f312(f115(f861(x60941,a846)),x60942),x60943),f189(f861(x60941,a846)))
% 155.93/155.61 [6108]E(f148(x61081,f312(f312(f147(x61081),x61082),x61083)),f148(x61081,x61083))+~P22(f312(f312(f314(x61081),x61082),f312(f168(x61081),x61083)))
% 155.93/155.61 [6145]~P22(f312(f312(f228(a853),x61451),x61453))+P22(f312(f312(f228(a853),x61451),f312(f312(f89(a853),x61452),x61453)))
% 155.93/155.61 [6147]~P22(f312(f312(f228(a853),x61471),x61472))+P22(f312(f312(f228(a853),x61471),f312(f312(f89(a853),x61472),x61473)))
% 155.93/155.61 [6149]~P22(f312(f312(f227(a853),x61491),x61493))+P22(f312(f312(f227(a853),x61491),f312(f312(f89(a853),x61492),x61493)))
% 155.93/155.61 [6151]~P22(f312(f312(f227(a853),x61511),x61512))+P22(f312(f312(f227(a853),x61511),f312(f312(f89(a853),x61512),x61513)))
% 155.93/155.61 [6188]P22(f312(f70(x61881),x61882))+~P22(f312(f70(x61881),f312(f312(f289(x61881),x61883),x61882)))
% 155.93/155.61 [6189]P22(f312(f133(x61891),x61892))+~P22(f312(f133(x61891),f312(f312(f147(x61891),x61893),x61892)))
% 155.93/155.61 [6190]P22(f312(f133(x61901),x61902))+~P22(f312(f133(x61901),f312(f312(f129(x61901),x61903),x61902)))
% 155.93/155.61 [6191]P22(f312(f133(x61911),x61912))+~P22(f312(f133(x61911),f312(f312(f129(x61911),x61912),x61913)))
% 155.93/155.61 [6232]~P107(x62321)+E(f312(f312(f89(x62321),x62322),f312(f312(f90(x62321),x62323),x62322)),f312(f312(f90(x62321),f312(f312(f89(x62321),x62323),f87(x62321))),x62322))
% 155.93/155.61 [6281]~E(x62811,x62812)+~P22(f312(f312(f228(f861(x62813,a846)),x62811),x62812))
% 155.93/155.61 [6323]P22(f312(f312(f314(x63231),x63232),x63233))+P22(f312(f312(f314(x63231),x63232),f312(f88(f861(x63231,a846)),x63233)))
% 155.93/155.61 [6330]E(f312(f47(a1,x63301),f312(f312(f90(a1),x63302),x63303)),f312(f47(a1,f312(f47(a1,x63301),x63302)),x63303))+~P22(f312(f312(f228(a1),f2(a1)),x63303))
% 155.93/155.61 [6331]E(f140(x63311,f312(f312(f134(x63311),x63312),x63313)),f140(x63311,x63313))+~P22(f312(f312(f228(a853),x63312),f312(f190(f854(x63311)),x63313)))
% 155.93/155.61 [6332]E(f312(f312(f169(x63321),x63322),f128(x63321,x63323)),f312(f312(f169(x63321),x63322),x63323))+~P22(f312(f312(f228(a853),x63322),f312(f190(f854(x63321)),x63323)))
% 155.93/155.61 [6385]E(f312(f312(f312(f184(f854(x63851),f854(x63851)),x63852),f164(x63851)),x63853),x63853)+~E(f54(a853,x63852,f312(f190(f854(x63851)),x63853)),f2(a853))
% 155.93/155.61 [6392]~P3(x63921,x63923,x63922)+E(f312(f312(f267(x63921,x63921,x63921),f312(f265(x63921,x63921),x63922)),x63922),x63922)
% 155.93/155.61 [6423]E(f312(f47(a853,f312(f312(f90(a853),x64231),x64232)),f312(f312(f90(a853),x64231),x64233)),f312(f47(a853,x64232),x64233))+~P22(f312(f312(f228(a853),f2(a853)),x64231))
% 155.93/155.61 [6430]~E(f312(f312(f124(f861(x64301,a846)),x64302),x64303),x64303)+P22(f312(f312(f227(f861(x64301,a846)),x64302),x64303))
% 155.93/155.61 [6435]~P54(x64351,x64351,x64353)+P54(x64351,x64351,f312(f312(f184(f860(x64351,x64351),a846),x64352),x64353))
% 155.93/155.61 [6437]~P22(f312(f312(f314(x64371),x64373),f312(f168(x64371),x64372)))+P22(f312(f312(f228(a853),f2(a853)),f312(f190(f854(x64371)),x64372)))
% 155.93/155.61 [6464]~P83(x64641)+E(f312(f84(x64641),f312(f312(f89(x64641),f312(f84(x64641),x64642)),f312(f84(x64641),x64643))),f312(f312(f89(x64641),f312(f84(x64641),x64642)),f312(f84(x64641),x64643)))
% 155.93/155.61 [6522]E(x65221,x65222)+~P22(f312(f312(f312(f312(a198,a23),x65221),x65223),x65222))
% 155.93/155.61 [6610]~P22(f312(f70(x66101),x66103))+E(f312(f312(f73(x66101,f861(x66101,a846),f289(x66101)),x66102),x66103),f312(f312(f124(f861(x66101,a846)),x66103),x66102))
% 155.93/155.61 [6670]E(f312(f312(f124(f861(x66701,a846)),x66702),x66703),x66702)+~P22(f312(f312(f227(f861(x66701,a846)),x66703),x66702))
% 155.93/155.61 [6672]E(f312(f312(f124(f861(x66721,a846)),x66722),x66723),x66723)+~P22(f312(f312(f227(f861(x66721,a846)),x66722),x66723))
% 155.93/155.61 [6673]E(f312(f312(f115(f861(x66731,a846)),x66732),x66733),x66733)+~P22(f312(f312(f227(f861(x66731,a846)),x66733),x66732))
% 155.93/155.61 [6674]E(f312(f312(f115(f861(x66741,a846)),x66742),x66743),x66742)+~P22(f312(f312(f227(f861(x66741,a846)),x66742),x66743))
% 155.93/155.61 [6722]~P22(f312(f133(x67221),x67222))+E(f312(f312(f21(f861(x67221,a846)),f312(f168(x67221),x67222)),f312(f312(f289(x67221),x67223),f189(f861(x67221,a846)))),f312(f168(x67221),f166(x67221,x67223,x67222)))
% 155.93/155.61 [6772]P41(x67721,x67722)+~P41(x67721,f312(f312(f184(f860(x67721,x67721),a846),x67723),x67722))
% 155.93/155.61 [6836]P22(f312(f57(x68361,x68362),f312(a59,x68363)))+~P22(f312(f57(f312(f88(a1),x68361),f312(f88(a1),x68362)),x68363))
% 155.93/155.61 [6842]E(f312(f312(f21(f861(x68421,a846)),f312(f312(f289(x68421),x68422),x68423)),f312(f312(f289(x68421),x68422),f189(f861(x68421,a846)))),x68423)+P22(f312(f312(f314(x68421),x68422),x68423))
% 155.93/155.61 [6863]E(f312(f312(f115(f861(x68631,a846)),f312(f168(x68631),x68632)),f312(f168(x68631),x68633)),f189(f861(x68631,a846)))+~P22(f312(f133(x68631),f312(f312(f129(x68631),x68632),x68633)))
% 155.93/155.61 [6878]~P22(f312(f312(f314(x68781),x68782),f312(f168(x68781),x68783)))+~P22(f312(f133(x68781),f312(f312(f147(x68781),x68782),x68783)))
% 155.93/155.61 [6963]E(f312(f312(f115(f861(x69631,a846)),x69632),x69633),f189(f861(x69631,a846)))+P22(f312(f312(f314(x69631),f794(x69633,x69632,x69631)),x69632))
% 155.93/155.61 [6964]E(f312(f312(f115(f861(x69641,a846)),x69642),x69643),f189(f861(x69641,a846)))+P22(f312(f312(f314(x69641),f812(x69643,x69642,x69641)),x69643))
% 155.93/155.61 [6968]E(f128(x69681,f312(f312(f169(x69681),x69682),x69683)),f312(f312(f169(x69681),f312(f312(f21(a853),x69682),f87(a853))),x69683))+~P22(f312(f312(f227(a853),x69682),f312(f190(f854(x69681)),x69683)))
% 155.93/155.61 [7028]~P38(x70283,x70282,x70281)+P22(f312(f312(f228(a853),f744(x70281,x70282,x70283)),f312(f190(f854(x70283)),x70281)))
% 155.93/155.61 [7045]P22(f312(f312(f228(a853),f2(a853)),x70451))+P22(f312(f312(f227(a853),f312(f312(f90(a853),x70452),x70451)),f312(f312(f90(a853),x70453),x70451)))
% 155.93/155.61 [7046]P22(f312(f312(f228(a853),f2(a853)),x70461))+P22(f312(f312(f227(a853),f312(f312(f90(a853),x70461),x70462)),f312(f312(f90(a853),x70461),x70463)))
% 155.93/155.61 [7049]~P22(f312(f312(f314(x70491),x70492),x70493))+~P22(f312(f312(f314(x70491),x70492),f312(f88(f861(x70491,a846)),x70493)))
% 155.93/155.61 [7058]~P22(f312(f312(f228(f861(x70581,a846)),x70582),x70583))+P22(f312(f312(f227(f861(x70581,a846)),x70582),x70583))
% 155.93/155.61 [7157]~P22(f312(f312(f228(a853),x71572),x71573))+P22(f312(f312(f228(a853),f312(f312(f89(a853),x71571),x71572)),f312(f312(f89(a853),x71571),x71573)))
% 155.93/155.61 [7158]~P22(f312(f312(f228(a853),x71581),x71583))+P22(f312(f312(f228(a853),f312(f312(f89(a853),x71581),x71582)),f312(f312(f89(a853),x71583),x71582)))
% 155.93/155.61 [7159]~P22(f312(f312(f228(a1),x71591),x71593))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x71591),x71592)),f312(f312(f89(a1),x71593),x71592)))
% 155.93/155.61 [7162]~P22(f312(f312(f227(a853),x71622),x71623))+P22(f312(f312(f227(a853),f312(f312(f89(a853),x71621),x71622)),f312(f312(f89(a853),x71621),x71623)))
% 155.93/155.61 [7163]~P22(f312(f312(f227(a853),x71631),x71633))+P22(f312(f312(f227(a853),f312(f312(f89(a853),x71631),x71632)),f312(f312(f89(a853),x71633),x71632)))
% 155.93/155.61 [7164]~P22(f312(f312(f227(a853),x71643),x71642))+P22(f312(f312(f227(a853),f312(f312(f21(a853),x71641),x71642)),f312(f312(f21(a853),x71641),x71643)))
% 155.93/155.61 [7165]~P22(f312(f312(f227(a853),x71651),x71653))+P22(f312(f312(f227(a853),f312(f312(f21(a853),x71651),x71652)),f312(f312(f21(a853),x71653),x71652)))
% 155.93/155.61 [7167]~P22(f312(f312(f227(a853),x71672),x71673))+P22(f312(f312(f227(a853),f312(f312(f90(a853),x71671),x71672)),f312(f312(f90(a853),x71671),x71673)))
% 155.93/155.61 [7169]~P22(f312(f312(f227(a853),x71691),x71693))+P22(f312(f312(f227(a853),f312(f312(f90(a853),x71691),x71692)),f312(f312(f90(a853),x71693),x71692)))
% 155.93/155.61 [7170]~P22(f312(f312(f227(a1),x71702),x71703))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x71701),x71702)),f312(f312(f89(a1),x71701),x71703)))
% 155.93/155.61 [7244]E(x72441,x72442)+~P22(f312(f312(f314(x72443),x72441),f312(f312(f289(x72443),x72442),f189(f861(x72443,a846)))))
% 155.93/155.61 [7246]~E(f312(f312(f115(f861(x72461,a846)),x72462),x72463),f189(f861(x72461,a846)))+P22(f312(f312(f227(f861(x72461,a846)),x72462),f312(f88(f861(x72461,a846)),x72463)))
% 155.93/155.61 [7254]P22(f312(f312(f314(f861(x72541,a846)),x72542),f312(f288(x72541),x72543)))+~P22(f312(f312(f227(f861(x72541,a846)),x72542),x72543))
% 155.93/155.61 [7306]E(f312(f312(f147(x73061),f312(f312(f161(x73061),x73062),x73063)),f312(f312(f134(x73061),f312(a126,x73063)),x73062)),f312(f312(f134(x73061),x73063),x73062))+~P22(f312(f312(f228(a853),x73063),f312(f190(f854(x73061)),x73062)))
% 155.93/155.61 [7331]P22(f312(f312(f314(f860(x73311,x73311)),x73312),f287(x73311,x73313)))+~P22(f312(f312(f314(f860(x73311,x73311)),x73312),x73313))
% 155.93/155.61 [7341]~P22(f312(f312(f314(f861(x73411,a846)),x73412),f312(f288(x73411),x73413)))+P22(f312(f312(f227(f861(x73411,a846)),x73412),x73413))
% 155.93/155.61 [7386]P22(f312(f312(f227(f861(x73861,a846)),x73862),f48(f861(x73861,a846),x73863)))+~P22(f312(f312(f314(f861(x73861,a846)),x73862),x73863))
% 155.93/155.61 [7410]~P111(x74101)+E(f312(f312(f90(x74101),f312(f312(f240(x74101),f312(f88(x74101),f87(x74101))),x74102)),f312(f312(f240(x74101),x74103),x74102)),f312(f312(f240(x74101),f312(f88(x74101),x74103)),x74102))
% 155.93/155.61 [7431]E(f312(f312(f161(x74311),x74312),f312(f312(f21(a853),f312(f190(f854(x74311)),x74312)),f312(a126,x74313))),f312(f312(f161(x74311),f312(f165(x74311),x74312)),x74313))+~P22(f312(f312(f228(a853),x74313),f312(f190(f854(x74311)),x74312)))
% 155.93/155.61 [7448]~E(f312(f312(f115(f861(x74481,a846)),f678(x74483,x74482,x74481)),x74483),f189(f861(x74481,a846)))+E(f312(f312(f115(f861(x74481,a846)),f48(f861(x74481,a846),x74482)),x74483),f189(f861(x74481,a846)))
% 155.93/155.61 [7510]~P22(f312(f312(f314(x75103),x75102),f312(f168(x75103),x75101)))+P22(f312(f312(f228(a853),f600(x75101,x75102,x75103)),f312(f190(f854(x75103)),x75101)))
% 155.93/155.61 [7518]P22(f312(f312(f314(x75181),f312(f312(f161(x75181),x75182),x75183)),f312(f168(x75181),x75182)))+~P22(f312(f312(f228(a853),x75183),f312(f190(f854(x75181)),x75182)))
% 155.93/155.61 [7616]~P22(f312(x76162,f664(x76163,x76162,x76161)))+E(f312(f312(f134(x76161),f312(f190(f854(x76161)),f172(x76161,x76162,x76163))),x76163),f127(x76161))
% 155.93/155.61 [7627]P22(f312(f312(f227(f861(f854(x76271),a846)),f157(x76271,x76272)),f157(x76271,x76273)))+~P22(f312(f312(f227(f861(x76271,a846)),x76272),x76273))
% 155.93/155.61 [7628]P22(f312(f312(f227(f861(f854(x76281),a846)),f156(x76281,x76282)),f156(x76281,x76283)))+~P22(f312(f312(f227(f861(x76281,a846)),x76282),x76283))
% 155.93/155.61 [7658]E(f312(f312(f115(f861(x76581,a846)),f48(f861(x76581,a846),x76582)),x76583),f189(f861(x76581,a846)))+P22(f312(f312(f314(f861(x76581,a846)),f678(x76583,x76582,x76581)),x76582))
% 155.93/155.61 [7660]~P22(f312(f312(f314(f861(x76601,a846)),x76603),x76602))+P22(f312(f312(f227(f861(x76601,a846)),f49(f861(x76601,a846),x76602)),x76603))
% 155.93/155.61 [7662]E(f312(f312(f115(f861(x76621,a846)),x76622),x76623),f189(f861(x76621,a846)))+~P22(f312(f312(f227(f861(x76621,a846)),x76622),f312(f88(f861(x76621,a846)),x76623)))
% 155.93/155.61 [7712]E(f312(f312(f21(a853),f312(f312(f89(a853),f312(f162(a853),x77121)),x77122)),f312(f312(f161(a853),x77121),x77123)),f312(f162(a853),f312(f312(f155(a853,x77121),x77123),x77122)))+~P22(f312(f312(f228(a853),x77123),f312(f190(f854(a853)),x77121)))
% 155.93/155.61 [7761]P22(f312(f312(f228(a853),x77611),x77612))+~P22(f312(f312(f228(a853),f312(f312(f89(a853),x77613),x77611)),f312(f312(f89(a853),x77613),x77612)))
% 155.93/155.61 [7762]P22(f312(f312(f228(a853),x77621),x77622))+~P22(f312(f312(f228(a853),f312(f312(f90(a853),x77623),x77621)),f312(f312(f90(a853),x77623),x77622)))
% 155.93/155.61 [7763]P22(f312(f312(f228(a853),x77631),x77632))+~P22(f312(f312(f228(a853),f312(f312(f90(a853),x77631),x77633)),f312(f312(f90(a853),x77632),x77633)))
% 155.93/155.61 [7766]P22(f312(f312(f227(a853),x77661),x77662))+~P22(f312(f312(f227(a853),f312(f312(f89(a853),x77663),x77661)),f312(f312(f89(a853),x77663),x77662)))
% 155.93/155.61 [7794]P22(f312(f312(f228(a853),f2(a853)),x77941))+~P22(f312(f312(f228(a853),f312(f312(f90(a853),x77942),x77941)),f312(f312(f90(a853),x77943),x77941)))
% 155.93/155.61 [7795]P22(f312(f312(f228(a853),f2(a853)),x77951))+~P22(f312(f312(f228(a853),f312(f312(f90(a853),x77951),x77952)),f312(f312(f90(a853),x77951),x77953)))
% 155.93/155.61 [7862]E(f242(x78621,x78622,x78623),x78622)+~P22(f312(f312(f227(f861(x78621,a846)),x78623),f312(f312(f289(x78621),x78622),f189(f861(x78621,a846)))))
% 155.93/155.61 [7917]~P22(f312(f133(x79171),x79173))+E(f312(f132(x79171,f312(f312(f8(a846,a846,x79171),a307),f312(a309,x79172))),x79173),f166(x79171,x79172,x79173))
% 155.93/155.61 [7940]E(f312(f312(f134(x79401),f312(f190(f854(x79401)),f172(x79401,x79402,x79403))),x79403),f127(x79401))+P22(f312(f312(f314(x79401),f664(x79403,x79402,x79401)),f312(f168(x79401),x79403)))
% 155.93/155.61 [7944]E(f312(f312(f129(x79441),f312(f312(f169(x79441),x79442),x79443)),f312(f312(f147(x79441),f312(f312(f161(x79441),x79443),x79442)),f127(x79441))),f312(f312(f169(x79441),f312(a126,x79442)),x79443))+~P22(f312(f312(f228(a853),x79442),f312(f190(f854(x79441)),x79443)))
% 155.93/155.61 [8006]E(f312(f132(x80061,f312(f312(f8(a846,a846,x80061),a307),f312(a309,x80062))),x80063),x80063)+P22(f312(f312(f314(x80061),x80062),f312(f168(x80061),x80063)))
% 155.93/155.61 [8016]P22(f312(f312(f227(f861(f861(x80161,a846),a846)),f243(x80161,x80162)),f243(x80161,x80163)))+~P22(f312(f312(f227(f861(x80161,a846)),x80162),x80163))
% 155.93/155.61 [8062]~P22(f312(f133(x80621),x80623))+P22(f312(f133(x80621),f312(f312(f312(f184(f854(x80621),f854(x80621)),x80622),f164(x80621)),x80623)))
% 155.93/155.61 [8067]~P22(f312(f312(f228(a853),x80672),x80673))+P22(f312(f312(f228(a853),f312(f312(f90(a853),f312(a126,x80671)),x80672)),f312(f312(f90(a853),f312(a126,x80671)),x80673)))
% 155.93/155.61 [8088]P22(f312(f312(f227(f861(f861(x80881,a846),a846)),f312(f288(x80881),x80882)),f312(f288(x80881),x80883)))+~P22(f312(f312(f227(f861(x80881,a846)),x80882),x80883))
% 155.93/155.61 [8257]~P22(f312(f312(f227(f861(x82571,a846)),x82573),x82572))+P22(f312(f312(f227(f861(x82571,a846)),f312(f88(f861(x82571,a846)),x82572)),f312(f88(f861(x82571,a846)),x82573)))
% 155.93/155.61 [8287]E(f312(f290(a853,a853,f312(f312(f7(a853,a853,a853),f21(a853)),x82871)),f312(f282(a853,x82872),x82873)),f312(f282(a853,f312(f312(f21(a853),x82872),x82871)),f312(f312(f21(a853),x82873),x82871)))+~P22(f312(f312(f228(a853),x82871),x82873))
% 155.93/155.61 [8306]E(f312(f312(f89(a1),f312(f312(f90(a1),x83061),f54(a1,f312(f47(a1,x83062),x83061),x83063))),f54(a1,x83062,x83061)),f54(a1,x83062,f312(f312(f90(a1),x83061),x83063)))+~P22(f312(f312(f228(a1),f2(a1)),x83063))
% 155.93/155.61 [8316]~P25(x83161)+E(f312(f312(f89(x83161),x83162),f312(f138(x83161,x83161,f89(x83161),f2(x83161)),x83163)),f312(f138(x83161,x83161,f89(x83161),x83162),x83163))
% 155.93/155.61 [8404]~P83(x84041)+P22(f312(f312(f227(x84041),f312(f84(x84041),f312(f312(f89(x84041),x84042),x84043))),f312(f312(f89(x84041),f312(f84(x84041),x84042)),f312(f84(x84041),x84043))))
% 155.93/155.61 [8405]~P83(x84051)+P22(f312(f312(f227(x84051),f312(f84(x84051),f312(f312(f21(x84051),x84052),x84053))),f312(f312(f89(x84051),f312(f84(x84051),x84052)),f312(f84(x84051),x84053))))
% 155.93/155.61 [8420]E(f312(f312(f129(x84201),f312(f312(f169(x84201),x84202),x84203)),f312(f312(f147(x84201),f312(f137(x84201),f312(f312(f134(x84201),x84202),x84203))),f127(x84201))),f312(f312(f169(x84201),f312(a126,x84202)),x84203))+~P22(f312(f312(f228(a853),x84202),f312(f190(f854(x84201)),x84203)))
% 155.93/155.61 [8440]E(f312(f256(x84401,f312(f312(f150(x84401,f860(a113,x84401)),f312(f239(a113,x84401),f87(a113))),x84402)),f312(a3,x84403)),f312(f312(f161(x84401),x84402),x84403))+~P22(f312(f312(f228(a853),x84403),f312(f190(f854(x84401)),x84402)))
% 155.93/155.61 [8509]P22(f312(f312(f314(f860(x85091,x85091)),x85092),f312(f312(f267(x85091,x85091,x85091),x85093),f287(x85091,x85093))))+~P22(f312(f312(f314(f860(x85091,x85091)),x85092),x85093))
% 155.93/155.61 [8525]P22(f312(f312(f227(a853),x85251),x85252))+~P22(f312(f312(f227(a853),f312(f312(f90(a853),f312(a126,x85253)),x85251)),f312(f312(f90(a853),f312(a126,x85253)),x85252)))
% 155.93/155.61 [8539]P22(f312(f312(f227(f861(x85391,a846)),x85392),x85393))+~P22(f312(f312(f227(f861(x85391,a846)),f312(f88(f861(x85391,a846)),x85393)),f312(f88(f861(x85391,a846)),x85392)))
% 155.93/155.61 [8557]P22(f312(f133(x85571),x85572))+~P22(f312(f133(x85571),f312(f312(f312(f184(f854(x85571),f854(x85571)),x85573),f164(x85571)),x85572)))
% 155.93/155.61 [8615]E(f312(f290(f860(x86151,x86152),x86152,f248(x86151,x86152)),f312(f168(f860(x86151,x86152)),x86153)),f181(x86151,x86152,f312(f173(x86151,x86152),x86153)))+~P22(f312(f133(x86151),f312(f312(f150(f860(x86151,x86152),x86151),f246(x86151,x86152)),x86153)))
% 155.93/155.61 [8624]E(f312(f264(x86241,x86241,f287(x86241,x86242)),x86243),x86243)+~P22(f312(f312(f227(f861(x86241,a846)),f312(f264(x86241,x86241,x86242),x86243)),x86243))
% 155.93/155.61 [8668]~P103(x86681)+P33(x86681,f312(f132(x86681,f312(f312(f7(x86681,x86681,a846),a309),f312(x86682,x86683))),x86683))
% 155.93/155.61 [8674]~P22(f312(f312(f227(a853),x86741),x86742))+P22(f312(f312(f227(a853),x86741),f312(f138(a853,a853,f89(a853),x86742),x86743)))
% 155.93/155.61 [8749]~P22(f312(f312(f314(f860(x87491,x87491)),x87492),f287(x87491,x87493)))+P22(f312(f312(f314(f860(x87491,x87491)),x87492),f312(f312(f184(f860(x87491,x87491),a846),f764(x87493,x87492,x87491)),x87493)))
% 155.93/155.61 [8838]~P25(x88381)+E(f312(f312(f89(x88381),x88382),f312(f138(x88381,x88381,f312(f7(x88381,x88381,x88381),f89(x88381)),f2(x88381)),f312(f165(x88381),x88383))),f312(f138(x88381,x88381,f89(x88381),x88382),x88383))
% 155.93/155.61 [9106]P54(x91061,x91062,x91063)+P22(f312(f312(f314(f860(x91061,x91062)),f312(f312(f239(x91061,x91062),f754(x91063,x91062,x91061)),f724(x91063,x91062,x91061))),x91063))
% 155.93/155.61 [9107]P54(x91071,x91072,x91073)+P22(f312(f312(f314(f860(x91071,x91072)),f312(f312(f239(x91071,x91072),f754(x91073,x91072,x91071)),f723(x91073,x91072,x91071))),x91073))
% 155.93/155.61 [9180]~P22(f312(f312(f314(f860(x91801,x91801)),x91802),f312(f312(f267(x91801,x91801,x91801),x91803),f287(x91801,x91803))))+P22(f312(f312(f314(f860(x91801,x91801)),x91802),f312(f312(f184(f860(x91801,x91801),a846),f765(x91803,x91802,x91801)),x91803)))
% 155.93/155.61 [9181]~P22(f312(x91811,f312(f312(f161(x91812),x91813),f312(f190(f854(x91812)),f172(x91812,x91811,x91813)))))+~P22(f312(f312(f228(a853),f312(f190(f854(x91812)),f172(x91812,x91811,x91813))),f312(f190(f854(x91812)),x91813)))
% 155.93/155.61 [9266]~P22(f312(f312(f227(f861(x92661,a846)),x92662),x92663))+P22(f312(f312(f227(f861(x92661,a846)),f312(f312(f7(x92661,f861(x92661,a846),a846),f314(x92661)),x92662)),f312(f312(f7(x92661,f861(x92661,a846),a846),f314(x92661)),x92663)))
% 155.93/155.61 [9320]~P22(f312(f312(f314(f860(f861(x93201,a846),f861(x93201,a846))),f312(f312(f239(f861(x93201,a846),f861(x93201,a846)),x93202),x93203)),f286(x93201)))+P22(f312(f312(f228(f861(x93201,a846)),x93202),x93203))
% 155.93/155.61 [9346]P55(x93461,x93462,x93463)+~P22(f312(f312(f314(f860(x93461,x93461)),f312(f312(f239(x93461,x93461),f757(x93463,x93462,x93461)),f756(x93463,x93462,x93461))),x93463))
% 155.93/155.61 [9347]P55(x93471,x93472,x93473)+~P22(f312(f312(f314(f860(x93471,x93471)),f312(f312(f239(x93471,x93471),f756(x93473,x93472,x93471)),f757(x93473,x93472,x93471))),x93473))
% 155.93/155.61 [9380]~P22(f312(f312(f314(f860(f854(x93801),f854(x93801))),f312(f312(f239(f854(x93801),f854(x93801)),x93802),x93802)),f143(x93801,x93803)))+P22(f312(f312(f314(f860(x93801,x93801)),f312(f312(f239(x93801,x93801),f608(x93802,x93803,x93801)),f608(x93802,x93803,x93801))),x93803))
% 155.93/155.61 [9433]P22(f312(f312(f227(f861(x94331,a846)),x94332),x94333))+~P22(f312(f312(f227(f861(x94331,a846)),f312(f312(f7(x94331,f861(x94331,a846),a846),f314(x94331)),x94332)),f312(f312(f7(x94331,f861(x94331,a846),a846),f314(x94331)),x94333)))
% 155.93/155.61 [9515]E(f312(f312(f21(a853),f312(f312(f6(a853,a853),x95151),f312(f279(a853),x95152))),f312(f312(f6(a853,a853),x95153),f312(f279(a853),x95152))),f312(f312(f6(a853,a853),f312(f312(f18(a853,a853,a853),f312(f312(f8(a853,f861(a853,a853),a853),f21(a853)),x95151)),x95153)),f312(f279(a853),x95152)))+~P22(f312(f312(f227(a853),f312(x95153,f499(x95152,x95151,x95153))),f312(x95151,f499(x95152,x95151,x95153))))
% 155.93/155.61 [9815]E(f312(f233(f860(x98151,x98152)),f312(f249(x98151,x98152,a846),f312(f312(f7(x98151,f861(x98152,f857(x98152)),f861(x98152,a846)),f312(f312(f8(f861(f857(x98152),a846),f861(f861(x98152,f857(x98152)),f861(x98152,a846)),x98151),f8(f857(x98152),a846,x98152)),f312(f312(f8(f857(x98152),f861(f857(x98152),a846),x98151),a309),f312(f173(x98151,x98152),x98153)))),f219(x98152)))),f312(f168(f860(x98151,x98152)),x98153))+~P22(f312(f133(x98151),f312(f312(f150(f860(x98151,x98152),x98151),f246(x98151,x98152)),x98153)))
% 155.93/155.61 [5567]~P71(x55671)+E(f312(f312(f89(x55671),f312(f312(f21(x55671),x55672),x55673)),x55673),x55672)
% 155.93/155.61 [5568]~P71(x55681)+E(f312(f312(f21(x55681),f312(f312(f89(x55681),x55682),x55683)),x55683),x55682)
% 155.93/155.61 [5773]~P71(x57731)+E(f312(f312(f89(x57731),x57732),f312(f312(f89(x57731),f312(f88(x57731),x57732)),x57733)),x57733)
% 155.93/155.61 [5856]~P78(x58561)+E(f312(f312(f90(x58561),f312(f312(f240(x58561),x58562),x58563)),x58562),f312(f312(f240(x58561),x58562),f312(a126,x58563)))
% 155.93/155.61 [5857]~P107(x58571)+E(f312(f312(f90(x58571),f312(f312(f240(x58571),x58572),x58573)),x58572),f312(f312(f240(x58571),x58572),f312(a126,x58573)))
% 155.93/155.61 [6064]~P112(x60641)+E(f312(f84(x60641),f312(f312(f240(x60641),f312(f88(x60641),x60642)),x60643)),f312(f84(x60641),f312(f312(f240(x60641),x60642),x60643)))
% 155.93/155.61 [6122]~P78(x61221)+E(f312(f312(f90(x61221),f312(f312(f240(x61221),x61222),x61223)),x61222),f312(f312(f90(x61221),x61222),f312(f312(f240(x61221),x61222),x61223)))
% 155.93/155.61 [6178]E(f312(f312(f21(a113),f312(f312(f89(a113),x61781),x61782)),x61783),f260(x61781,x61782,x61783))+~P22(f312(f312(f228(a113),x61782),x61783))
% 155.93/155.61 [6200]~E(f312(f312(f134(x62001),x62003),x62002),f127(x62001))+P22(f312(f312(f227(a853),f312(f190(f854(x62001)),x62002)),x62003))
% 155.93/155.61 [6329]E(f312(f312(f90(a853),f312(f117(a853),x63291)),f312(f312(f90(a853),f312(f117(a853),x63292)),x63293)),f2(a853))+~P22(f312(f312(f228(a1),x63291),a92))
% 155.93/155.61 [6345]~P64(x63451)+E(f312(f312(f240(x63451),f312(f312(f268(x63451),f87(x63451)),x63452)),x63453),f312(f312(f268(x63451),f87(x63451)),f312(f312(f240(x63451),x63452),x63453)))
% 155.93/155.61 [6421]E(f312(f312(f21(a853),f312(f312(f89(a853),x64211),x64212)),x64213),f312(f312(f21(a853),x64211),f312(f312(f21(a853),x64213),x64212)))+~P22(f312(f312(f227(a853),x64212),x64213))
% 155.93/155.61 [6422]E(f312(f312(f21(a853),f312(f312(f89(a853),x64221),x64222)),x64223),f312(f312(f89(a853),x64221),f312(f312(f21(a853),x64222),x64223)))+~P22(f312(f312(f227(a853),x64223),x64222))
% 155.93/155.61 [6455]~P87(x64551)+P22(f312(f312(f227(x64551),f312(f312(f115(x64551),x64552),x64553)),x64553))
% 155.93/155.61 [6456]~P99(x64561)+P22(f312(f312(f227(x64561),f312(f312(f115(x64561),x64562),x64563)),x64563))
% 155.93/155.61 [6457]~P87(x64571)+P22(f312(f312(f227(x64571),f312(f312(f115(x64571),x64572),x64573)),x64572))
% 155.93/155.61 [6458]~P99(x64581)+P22(f312(f312(f227(x64581),f312(f312(f115(x64581),x64582),x64583)),x64582))
% 155.93/155.61 [6459]~P103(x64591)+P22(f312(f312(f227(x64591),f312(f312(f225(x64591),x64592),x64593)),x64593))
% 155.93/155.61 [6460]~P103(x64601)+P22(f312(f312(f227(x64601),f312(f312(f225(x64601),x64602),x64603)),x64602))
% 155.93/155.61 [6525]~P107(x65251)+E(f312(f312(f89(x65251),f312(f312(f90(x65251),x65252),x65253)),x65253),f312(f312(f90(x65251),f312(f312(f89(x65251),x65252),f87(x65251))),x65253))
% 155.93/155.61 [6526]~P90(x65261)+E(f312(f312(f90(x65261),f312(f88(x65261),f312(f117(x65261),x65262))),x65263),f312(f312(f90(x65261),f312(f117(x65261),f312(f88(a1),x65262))),x65263))
% 155.93/155.61 [6602]~P25(x66021)+E(f312(f162(x66021),f312(f312(f150(x66022,x66021),f312(f16(x66021,x66022),f2(x66021))),x66023)),f2(x66021))
% 155.93/155.61 [6613]E(f312(f312(f89(a853),f312(f117(a853),x66131)),f312(f312(f89(a853),f312(f117(a853),x66132)),x66133)),f312(f312(f89(a853),f312(f117(a853),x66132)),x66133))+~P22(f312(a194,f312(f117(a1),x66131)))
% 155.93/155.61 [6629]~P31(x66291)+E(f48(x66291,f312(f312(f289(x66291),x66292),f312(f312(f289(x66291),x66293),f189(f861(x66291,a846))))),f312(f312(f124(x66291),x66292),x66293))
% 155.93/155.61 [6630]~P31(x66301)+E(f49(x66301,f312(f312(f289(x66301),x66302),f312(f312(f289(x66301),x66303),f189(f861(x66301,a846))))),f312(f312(f115(x66301),x66302),x66303))
% 155.93/155.61 [6654]E(f312(f312(f169(x66541),x66542),x66543),x66543)+~P22(f312(f312(f227(a853),f312(f190(f854(x66541)),x66543)),x66542))
% 155.93/155.61 [6665]E(f312(f312(f134(x66651),x66652),x66653),f127(x66651))+~P22(f312(f312(f227(a853),f312(f190(f854(x66651)),x66653)),x66652))
% 155.93/155.61 [6676]E(f312(f312(f21(a853),f312(f312(f89(a853),x66761),x66762)),x66763),f312(f312(f89(a853),f312(f312(f21(a853),x66761),x66763)),x66762))+~P22(f312(f312(f227(a853),x66763),x66761))
% 155.93/155.61 [6690]~P22(f312(f312(f228(a853),x66901),x66903))+P22(f312(f312(f228(a853),f312(f312(f21(a853),x66901),x66902)),x66903))
% 155.93/155.61 [6715]~P103(x67151)+E(f166(x67151,x67152,f312(f312(f145(x67151,x67151,f5(x67151)),x67152),x67153)),x67153)
% 155.93/155.61 [6796]E(f312(f312(f21(a853),f312(f312(f89(a853),x67961),x67962)),f312(a126,x67963)),f312(f312(f21(a853),x67961),f312(a126,f312(f312(f21(a853),x67963),x67962))))+~P22(f312(f312(f227(a853),x67962),x67963))
% 155.93/155.61 [6797]~P112(x67971)+P22(f312(f312(f227(x67971),f2(x67971)),f312(f312(f240(x67971),f312(f84(x67971),x67972)),x67973)))
% 155.93/155.61 [6847]P18(x68471,x68472,x68473)+~P22(f312(f312(f227(f861(f852(x68471),a846)),x68473),x68472))
% 155.93/155.61 [6891]~P22(f312(f70(x68911),x68912))+P22(f312(f70(x68911),f312(f312(f21(f861(x68911,a846)),x68912),x68913)))
% 155.93/155.61 [6892]~P22(f312(f70(x68921),x68923))+P22(f312(f70(x68921),f312(f312(f115(f861(x68921,a846)),x68922),x68923)))
% 155.93/155.61 [6893]~P22(f312(f70(x68931),x68932))+P22(f312(f70(x68931),f312(f312(f115(f861(x68931,a846)),x68932),x68933)))
% 155.93/155.61 [6910]~P60(x69101)+E(f312(f312(f89(x69101),f54(x69101,x69102,x69103)),f312(f312(f90(x69101),f312(f47(x69101,x69102),x69103)),x69103)),x69102)
% 155.93/155.61 [7035]~P41(x70351,x70353)+P41(x70351,f312(f312(f115(f861(f860(x70351,x70351),a846)),x70352),x70353))
% 155.93/155.61 [7036]~P41(x70361,x70362)+P41(x70361,f312(f312(f115(f861(f860(x70361,x70361),a846)),x70362),x70363))
% 155.93/155.61 [7153]~P87(x71531)+E(f11(x71531,f312(f168(x71531),f312(f312(f147(x71531),x71532),x71533))),f312(f138(x71531,x71531,f115(x71531),x71532),x71533))
% 155.93/155.61 [7154]~P87(x71541)+E(f10(x71541,f312(f168(x71541),f312(f312(f147(x71541),x71542),x71543))),f312(f138(x71541,x71541,f124(x71541),x71542),x71543))
% 155.93/155.61 [7155]~P103(x71551)+E(f14(x71551,f312(f168(x71551),f312(f312(f147(x71551),x71552),x71553))),f312(f138(x71551,x71551,f226(x71551),x71552),x71553))
% 155.93/155.61 [7156]~P103(x71561)+E(f15(x71561,f312(f168(x71561),f312(f312(f147(x71561),x71562),x71563))),f312(f138(x71561,x71561,f225(x71561),x71562),x71563))
% 155.93/155.61 [7208]~P22(f312(f70(x72081),x72082))+P22(f312(f312(f227(a853),f312(f53(x72081),x72082)),f312(f53(x72081),f312(f312(f289(x72081),x72083),x72082))))
% 155.93/155.61 [7215]E(f312(f312(f124(f861(a853,a846)),f312(f282(a853,x72151),x72152)),f312(f282(a853,x72152),f312(f312(f89(a853),x72152),x72153))),f312(f282(a853,x72151),f312(f312(f89(a853),x72152),x72153)))+~P22(f312(f312(f227(a853),x72151),x72152))
% 155.93/155.61 [7223]P22(f312(f312(f228(a853),x72231),x72232))+~P22(f312(f312(f228(a853),f312(f312(f89(a853),x72231),x72233)),x72232))
% 155.93/155.61 [7226]P22(f312(f312(f227(a853),x72261),x72262))+~P22(f312(f312(f227(a853),f312(f312(f89(a853),x72263),x72261)),x72262))
% 155.93/155.61 [7227]P22(f312(f312(f227(a853),x72271),x72272))+~P22(f312(f312(f227(a853),f312(f312(f89(a853),x72271),x72273)),x72272))
% 155.93/155.61 [7269]~P103(x72691)+E(f12(x72691,f226(x72691),f312(f168(x72691),f312(f312(f147(x72691),x72692),x72693))),f312(f138(x72691,x72691,f226(x72691),x72692),x72693))
% 155.93/155.61 [7270]~P103(x72701)+E(f13(x72701,f225(x72701),f312(f168(x72701),f312(f312(f147(x72701),x72702),x72703))),f312(f138(x72701,x72701,f225(x72701),x72702),x72703))
% 155.93/155.61 [7274]~E(x72742,f189(f861(f860(x72741,x72741),a846)))+P22(f312(f312(f227(f861(f860(x72741,x72741),a846)),x72742),x72743))
% 155.93/155.61 [7381]E(f312(f312(f124(f861(x73811,a846)),x73812),f312(f312(f21(f861(x73811,a846)),x73813),x73812)),x73813)+~P22(f312(f312(f227(f861(x73811,a846)),x73812),x73813))
% 155.93/155.61 [7382]~P22(f312(f312(f228(a853),x73821),f312(f312(f21(a853),x73823),x73822)))+P22(f312(f312(f228(a853),f312(f312(f89(a853),x73821),x73822)),x73823))
% 155.93/155.61 [7383]~P22(f312(f312(f227(a853),x73831),f312(f312(f89(a853),x73833),x73832)))+P22(f312(f312(f227(a853),f312(f312(f21(a853),x73831),x73832)),x73833))
% 155.93/155.61 [7438]E(x74381,f127(x74382))+E(f312(f137(x74382),f312(f312(f312(f184(f854(x74382),f854(x74382)),x74383),f164(x74382)),x74381)),f312(f312(f161(x74382),x74381),f54(a853,x74383,f312(f190(f854(x74382)),x74381))))
% 155.93/155.61 [7447]E(f312(f312(f289(x74471),x74472),f312(f312(f21(f861(x74471,a846)),x74473),f312(f312(f289(x74471),x74472),f189(f861(x74471,a846))))),x74473)+~P22(f312(f312(f314(x74471),x74472),x74473))
% 155.93/155.61 [7608]P22(f312(f312(f228(a853),x76081),f312(f312(f21(a853),x76082),x76083)))+~P22(f312(f312(f228(a853),f312(f312(f89(a853),x76081),x76083)),x76082))
% 155.93/155.61 [7609]P22(f312(f312(f227(a853),x76091),f312(f312(f89(a853),x76092),x76093)))+~P22(f312(f312(f227(a853),f312(f312(f21(a853),x76091),x76093)),x76092))
% 155.93/155.61 [7632]P22(f312(f70(x76321),x76322))+~P22(f312(f70(x76321),f312(f312(f124(f861(x76321,a846)),x76323),x76322)))
% 155.93/155.61 [7633]P22(f312(f70(x76331),x76332))+~P22(f312(f70(x76331),f312(f312(f124(f861(x76331,a846)),x76332),x76333)))
% 155.93/155.61 [7709]~P48(x77091,x77093)+P22(f312(f312(f314(f860(x77091,x77091)),f312(f312(f239(x77091,x77091),x77092),x77092)),x77093))
% 155.93/155.61 [7836]E(f312(f312(f161(a853),f135(a853,f312(f282(a853,x78361),x78362))),x78363),f312(f312(f89(a853),x78361),x78363))+~P22(f312(f312(f228(a853),f312(f312(f89(a853),x78361),x78363)),x78362))
% 155.93/155.61 [7903]~P22(f312(f312(f195(f312(a27,x79031)),x79032),x79033))+P22(f312(f312(f195(f312(f223(a847),f312(a30,x79031))),x79032),x79033))
% 155.93/155.61 [7906]E(f312(f312(f169(a853),x79061),f135(a853,f312(f282(a853,x79062),x79063))),f135(a853,f312(f282(a853,x79062),f312(f312(f89(a853),x79062),x79061))))+~P22(f312(f312(f227(a853),f312(f312(f89(a853),x79062),x79061)),x79063))
% 155.93/155.61 [7959]~P90(x79591)+E(f312(f312(f240(x79591),x79592),f312(f117(a853),f312(f312(f89(a1),x79593),x79593))),f312(f312(f95(x79591,x79591),f312(f312(f240(x79591),x79592),f312(f117(a853),x79593))),f312(f312(f18(x79591,x79591,x79591),f90(x79591)),f5(x79591))))
% 155.93/155.61 [8172]P22(f312(f312(f195(f312(a27,x81721)),x81722),x81723))+~P22(f312(f312(f195(f312(f223(a847),f312(a30,x81721))),x81722),x81723))
% 155.93/155.61 [8235]E(f312(f312(f129(x82351),f312(f312(f169(x82351),x82352),x82353)),f312(f312(f147(x82351),f312(f312(f161(x82351),x82353),x82352)),f312(f312(f134(x82351),f312(a126,x82352)),x82353))),x82353)+~P22(f312(f312(f228(a853),x82352),f312(f190(f854(x82351)),x82353)))
% 155.93/155.61 [8243]P22(f312(f312(f227(f861(x82431,a846)),f300(x82431,x82432)),f300(x82431,x82433)))+~P22(f312(f312(f227(f861(x82431,f861(x82431,a846))),x82433),x82432))
% 155.93/155.61 [8245]~P55(x82451,x82452,x82453)+P55(x82451,x82452,f312(f312(f21(f861(f860(x82451,x82451),a846)),x82453),f287(x82451,f189(f861(f860(x82451,x82451),a846)))))
% 155.93/155.61 [8262]P22(f312(f312(f227(f861(x82621,a846)),f301(x82621,x82622)),f301(x82621,x82623)))+~P22(f312(f312(f227(f861(f860(x82621,x82621),a846)),x82623),x82622))
% 155.93/155.61 [8268]~P119(x82681)+P22(f312(f312(f227(x82681),f2(x82681)),f312(f312(f89(x82681),f312(f312(f90(x82681),x82682),x82682)),f312(f312(f90(x82681),x82683),x82683))))
% 155.93/155.61 [8303]P22(f312(f312(f227(f861(x83031,a846)),f312(f263(x83031),x83032)),f312(f263(x83031),x83033)))+~P22(f312(f312(f227(f861(f860(x83031,x83031),a846)),x83032),x83033))
% 155.93/155.61 [8338]~P51(x83381,x83382)+~P22(f312(f312(f314(f860(x83381,x83381)),f312(f312(f239(x83381,x83381),x83383),x83383)),x83382))
% 155.93/155.61 [8340]~P41(x83401,x83402)+~P22(f312(f312(f314(f860(x83401,x83401)),f312(f312(f239(x83401,x83401),x83403),x83403)),x83402))
% 155.93/155.61 [8406]P22(f312(f312(f227(f861(x84061,a846)),f48(f861(x84061,a846),x84062)),f48(f861(x84061,a846),x84063)))+~P22(f312(f312(f227(f861(f861(x84061,a846),a846)),x84062),x84063))
% 155.93/155.61 [8407]P22(f312(f312(f227(f861(x84071,a846)),f49(f861(x84071,a846),x84072)),f49(f861(x84071,a846),x84073)))+~P22(f312(f312(f227(f861(f861(x84071,a846),a846)),x84073),x84072))
% 155.93/155.61 [8460]~P3(x84601,x84603,x84602)+P22(f312(f312(f227(f861(f860(x84601,x84601),a846)),x84602),f312(f312(f247(x84601,x84601),x84603),f312(f16(f861(x84601,a846),x84601),x84603))))
% 155.93/155.61 [8461]~P50(x84611,x84613,x84612)+P22(f312(f312(f227(f861(f860(x84611,x84611),a846)),x84612),f312(f312(f247(x84611,x84611),x84613),f312(f16(f861(x84611,a846),x84611),x84613))))
% 155.93/155.61 [8510]~P83(x85101)+P22(f312(f312(f227(x85101),f312(f312(f21(x85101),f312(f84(x85101),x85102)),f312(f84(x85101),x85103))),f312(f84(x85101),f312(f312(f21(x85101),x85103),x85102))))
% 155.93/155.61 [8511]~P83(x85111)+P22(f312(f312(f227(x85111),f312(f312(f21(x85111),f312(f84(x85111),x85112)),f312(f84(x85111),x85113))),f312(f84(x85111),f312(f312(f21(x85111),x85112),x85113))))
% 155.93/155.61 [8537]P22(f312(f312(f227(f861(f860(x85371,x85371),a846)),f287(x85371,x85372)),f287(x85371,x85373)))+~P22(f312(f312(f227(f861(f860(x85371,x85371),a846)),x85372),x85373))
% 155.93/155.61 [8691]P55(x86911,x86912,x86913)+~P55(x86911,x86912,f312(f312(f21(f861(f860(x86911,x86911),a846)),x86913),f287(x86911,f189(f861(f860(x86911,x86911),a846)))))
% 155.93/155.61 [8708]P22(f312(f312(f227(f861(f860(f854(x87081),f854(x87081)),a846)),f154(x87081,x87082)),f154(x87081,x87083)))+~P22(f312(f312(f227(f861(f860(x87081,x87081),a846)),x87082),x87083))
% 155.93/155.61 [8709]P22(f312(f312(f227(f861(f860(f854(x87091),f854(x87091)),a846)),f153(x87091,x87092)),f153(x87091,x87093)))+~P22(f312(f312(f227(f861(f860(x87091,x87091),a846)),x87092),x87093))
% 155.93/155.61 [8728]~P50(x87281,x87283,x87282)+P22(f312(f312(f227(f861(f860(x87281,x87281),a846)),x87282),f312(f312(f267(x87281,x87281,x87281),f312(f265(x87281,x87281),x87282)),x87282)))
% 155.93/155.61 [8776]~P22(f312(f133(x87761),x87762))+E(f312(f132(x87761,f312(f312(f7(x87761,f861(x87761,a846),a846),f314(x87761)),f312(f168(x87761),f170(x87761,x87762,x87763)))),x87762),f170(x87761,x87762,x87763))
% 155.93/155.61 [8836]E(x88361,x88362)+~P22(f312(f312(f314(f860(x88363,x88363)),f312(f312(f239(x88363,x88363),x88361),x88362)),f287(x88363,f189(f861(f860(x88363,x88363),a846)))))
% 155.93/155.61 [8926]P22(f312(f312(f314(x89261),x89262),f301(x89261,x89263)))+P22(f312(f312(f314(f860(x89261,x89261)),f312(f312(f239(x89261,x89261),f346(x89263,x89262,x89261)),x89262)),x89263))
% 155.93/155.61 [8927]P22(f312(f312(f314(x89271),x89272),f301(x89271,x89273)))+P22(f312(f312(f314(f860(x89271,x89271)),f312(f312(f239(x89271,x89271),f726(x89273,x89272,x89271)),x89272)),x89273))
% 155.93/155.61 [8928]P22(f312(f312(f314(x89281),x89282),f301(x89281,x89283)))+P22(f312(f312(f314(f860(x89281,x89281)),f312(f312(f239(x89281,x89281),f735(x89283,x89282,x89281)),x89282)),x89283))
% 155.93/155.61 [9010]~P22(f312(f312(f314(f854(x90101)),x90103),f157(x90101,x90102)))+P22(f312(f156(x90101,f312(f312(f7(x90101,f861(x90101,a846),a846),f314(x90101)),x90102)),x90103))
% 155.93/155.61 [9033]P22(f312(x90333,x90332))+E(f312(f233(x90331),f312(f312(f18(x90331,a846,a846),f312(f312(f8(a846,f861(a846,a846),x90331),a310),f312(a309,x90332))),x90333)),f189(f861(x90331,a846)))
% 155.93/155.61 [9052]~P83(x90521)+P22(f312(f312(f227(x90521),f312(f84(x90521),f312(f312(f21(x90521),f312(f84(x90521),x90522)),f312(f84(x90521),x90523)))),f312(f84(x90521),f312(f312(f21(x90521),x90522),x90523))))
% 155.93/155.61 [9065]~P22(f312(x90653,x90652))+E(f312(f233(x90651),f312(f312(f18(x90651,a846,a846),f312(f312(f8(a846,f861(a846,a846),x90651),a310),f312(a309,x90652))),x90653)),f312(f312(f289(x90651),x90652),f189(f861(x90651,a846))))
% 155.93/155.61 [9072]~P22(f312(f312(f314(f861(x90721,a846)),x90723),f312(f288(x90721),x90722)))+P22(f312(f243(x90721,f312(f312(f7(x90721,f861(x90721,a846),a846),f314(x90721)),x90722)),x90723))
% 155.93/155.61 [9105]P41(x91051,x91052)+P22(f312(f312(f314(f860(x91051,x91051)),f312(f312(f239(x91051,x91051),f312(f573(x91052,x91051),f312(a126,x91053))),f312(f573(x91052,x91051),x91053))),x91052))
% 155.93/155.61 [9246]P22(f312(f312(f314(f854(x92461)),x92462),f157(x92461,x92463)))+~P22(f312(f156(x92461,f312(f312(f7(x92461,f861(x92461,a846),a846),f314(x92461)),x92463)),x92462))
% 155.93/155.61 [9258]P22(f312(f312(f314(f861(x92581,a846)),x92582),f312(f288(x92581),x92583)))+~P22(f312(f243(x92581,f312(f312(f7(x92581,f861(x92581,a846),a846),f314(x92581)),x92583)),x92582))
% 155.93/155.61 [9316]P22(f312(f312(f314(x93161),f312(f256(x93161,x93162),x93163)),f312(f168(x93161),f312(f312(f150(f860(a113,x93161),x93161),f248(a113,x93161)),x93162))))+~P22(f312(f312(f228(a113),x93163),f312(f162(a113),f312(f312(f150(f860(a113,x93161),a113),f246(a113,x93161)),x93162))))
% 155.93/155.61 [9363]P22(f312(f312(f227(f861(f860(f854(x93631),f854(x93631)),a846)),f154(x93631,x93632)),f312(f312(f247(f854(x93631),f854(x93631)),f157(x93631,x93633)),f312(f16(f861(f854(x93631),a846),f854(x93631)),f157(x93631,x93633)))))+~P22(f312(f312(f227(f861(f860(x93631,x93631),a846)),x93632),f312(f312(f247(x93631,x93631),x93633),f312(f16(f861(x93631,a846),x93631),x93633))))
% 155.93/155.61 [9384]P22(f312(f312(f314(x93841),f312(f246(x93841,f860(a113,a113)),f312(f254(x93841,x93842),x93843))),f312(f168(x93841),f312(f312(f150(f860(a113,x93841),x93841),f248(a113,x93841)),x93842))))+~P22(f312(f312(f228(a113),f2(a113)),f312(f162(a113),f312(f312(f150(f860(a113,x93841),a113),f246(a113,x93841)),x93842))))
% 155.93/155.61 [9404]~P22(f312(f312(f227(f861(f860(x94041,x94041),a846)),x94042),f312(f312(f247(x94041,x94041),x94043),f312(f16(f861(x94041,a846),x94041),x94043))))+P22(f312(f312(f227(f861(f860(x94041,x94041),a846)),f312(f312(f267(x94041,x94041,x94041),x94042),f287(x94041,x94042))),f312(f312(f247(x94041,x94041),x94043),f312(f16(f861(x94041,a846),x94041),x94043))))
% 155.93/155.61 [9695]~P41(x96951,x96952)+~P22(f312(f312(f314(f860(x96951,x96951)),f312(f312(f239(x96951,x96951),f312(x96953,f312(a126,f572(x96952,x96951,x96953)))),f312(x96953,f572(x96952,x96951,x96953)))),x96952))
% 155.93/155.61 [9696]~P41(x96961,x96962)+~P22(f312(f312(f314(f860(x96961,x96961)),f312(f312(f239(x96961,x96961),f312(x96963,f312(a126,f749(x96963,x96962,x96961)))),f312(x96963,f749(x96963,x96962,x96961)))),x96962))
% 155.93/155.61 [9960]P22(f312(f312(f227(f861(f860(f861(x99601,a846),f861(x99601,a846)),a846)),f312(f312(f267(f861(x99601,a846),f861(x99601,a846),f861(x99601,a846)),f305(x99601,x99602)),f312(f312(f124(f861(f860(f861(x99601,a846),f861(x99601,a846)),a846)),f305(x99601,x99603)),f312(f312(f289(f860(f861(x99601,a846),f861(x99601,a846))),f312(f312(f239(f861(x99601,a846),f861(x99601,a846)),f189(f861(x99601,a846))),f189(f861(x99601,a846)))),f189(f861(f860(f861(x99601,a846),f861(x99601,a846)),a846)))))),f305(x99601,x99602)))+~P22(f312(f312(f227(f861(f860(x99601,x99601),a846)),f312(f312(f267(x99601,x99601,x99601),x99602),x99603)),x99602))
% 155.93/155.61 [9961]P22(f312(f312(f227(f861(f860(f861(x99611,a846),f861(x99611,a846)),a846)),f312(f312(f267(f861(x99611,a846),f861(x99611,a846),f861(x99611,a846)),f303(x99611,x99612)),f312(f312(f124(f861(f860(f861(x99611,a846),f861(x99611,a846)),a846)),f303(x99611,x99613)),f312(f312(f289(f860(f861(x99611,a846),f861(x99611,a846))),f312(f312(f239(f861(x99611,a846),f861(x99611,a846)),f189(f861(x99611,a846))),f189(f861(x99611,a846)))),f189(f861(f860(f861(x99611,a846),f861(x99611,a846)),a846)))))),f303(x99611,x99612)))+~P22(f312(f312(f227(f861(f860(x99611,x99611),a846)),f312(f312(f267(x99611,x99611,x99611),x99612),x99613)),x99612))
% 155.93/155.61 [7152]~P22(f312(f312(f227(a853),x71522),x71521))+E(f312(f312(f21(a853),f312(a126,f312(f312(f21(a853),x71521),x71522))),x71523),f312(f312(f21(a853),f312(a126,x71521)),f312(f312(f89(a853),x71522),x71523)))
% 155.93/155.61 [7387]E(f312(f312(f90(a853),f312(f117(a853),x73871)),f312(f312(f90(a853),f312(f117(a853),x73872)),x73873)),f312(f312(f90(a853),f312(f117(a853),f312(f312(f90(a1),x73871),x73872))),x73873))+P22(f312(f312(f228(a1),x73871),a92))
% 155.93/155.61 [7845]~P22(f312(f312(f227(a853),x78453),x78452))+P22(f312(f312(f227(a853),x78451),f312(f312(f21(a853),f312(f312(f89(a853),x78452),x78451)),x78453)))
% 155.93/155.61 [8051]~P22(f312(f312(f227(a853),x80511),x80512))+E(f312(f312(f129(a853),f135(a853,f312(f282(a853,x80511),x80512))),f135(a853,f312(f282(a853,x80512),f312(f312(f89(a853),x80512),x80513)))),f135(a853,f312(f282(a853,x80511),f312(f312(f89(a853),x80512),x80513))))
% 155.93/155.61 [8313]~P22(f312(f70(x83131),x83132))+E(f312(a126,f312(f53(x83131),f312(f312(f21(f861(x83131,a846)),x83132),f312(f312(f289(x83131),x83133),f189(f861(x83131,a846)))))),f312(f53(x83131),f312(f312(f289(x83131),x83133),x83132)))
% 155.93/155.61 [8364]~P22(f312(f70(x83641),x83642))+E(f312(f312(f89(a853),f87(a853)),f312(f53(x83641),f312(f312(f21(f861(x83641,a846)),x83642),f312(f312(f289(x83641),x83643),f189(f861(x83641,a846)))))),f312(f53(x83641),f312(f312(f289(x83641),x83643),x83642)))
% 155.93/155.61 [8546]E(f312(f312(f21(a853),f312(f53(x85461),x85462)),f312(f53(x85461),f312(f312(f115(f861(x85461,a846)),x85462),x85463))),f312(f53(x85461),f312(f312(f21(f861(x85461,a846)),x85462),x85463)))+~P22(f312(f70(x85461),f312(f312(f115(f861(x85461,a846)),x85462),x85463)))
% 155.93/155.61 [8772]~P32(f312(x87722,f400(x87722,x87723,x87721)))+E(f312(f114(a1),f312(f312(f9(x87721,a853),f312(f312(f8(a1,a853,x87721),a118),x87722)),x87723)),f312(f312(f9(x87721,a1),x87722),x87723))
% 155.93/155.61 [8773]~P32(f312(x87732,f497(x87732,x87733,x87731)))+E(f312(f114(a1),f312(f312(f6(x87731,a853),f312(f312(f8(a1,a853,x87731),a118),x87732)),x87733)),f312(f312(f6(x87731,a1),x87732),x87733))
% 155.93/155.61 [8818]~P22(f312(f70(x88181),x88183))+P22(f312(f312(f227(a853),f312(f312(f21(a853),f312(f53(x88181),x88182)),f312(f53(x88181),x88183))),f312(f53(x88181),f312(f312(f21(f861(x88181,a846)),x88182),x88183))))
% 155.93/155.61 [8845]P22(f312(f312(f314(x88451),f400(x88452,x88453,x88451)),x88453))+E(f312(f114(a1),f312(f312(f9(x88451,a853),f312(f312(f8(a1,a853,x88451),a118),x88452)),x88453)),f312(f312(f9(x88451,a1),x88452),x88453))
% 155.93/155.61 [8846]P22(f312(f312(f314(x88461),f497(x88462,x88463,x88461)),x88463))+E(f312(f114(a1),f312(f312(f6(x88461,a853),f312(f312(f8(a1,a853,x88461),a118),x88462)),x88463)),f312(f312(f6(x88461,a1),x88462),x88463))
% 155.93/155.61 [8918]E(f94(x89181,f312(f312(f7(x89181,f861(x89181,a846),a846),f314(x89181)),f312(f312(f21(f861(x89181,a846)),x89182),f312(f312(f289(x89181),x89183),f189(f861(x89181,a846)))))),f242(x89181,x89183,x89182))+P22(f312(f312(f227(f861(x89181,a846)),x89182),f312(f312(f289(x89181),x89183),f189(f861(x89181,a846)))))
% 155.93/155.61 [9259]E(f312(f312(f150(f854(x92591),x92591),f312(f312(f7(f854(x92591),a853,x92591),f161(x92591)),x92592)),f312(f132(f854(x92591),f312(f312(f8(a853,a846,f854(x92591)),f312(f228(a853),x92592)),f190(f854(x92591)))),x92593)),f312(f312(f161(f854(x92591)),f175(x92591,x92593)),x92592))+~P22(f312(f312(f228(a853),x92592),f312(f190(f854(f854(x92591))),f175(x92591,x92593))))
% 155.93/155.61 [9334]E(f312(f132(x93341,x93342),x93343),f172(x93341,x93342,x93343))+P22(f312(f312(f314(x93341),f671(x93343,x93342,x93341)),f312(f168(x93341),f312(f312(f134(x93341),f312(f190(f854(x93341)),f172(x93341,x93342,x93343))),x93343))))
% 155.93/155.61 [9472]E(f312(f312(f134(x94721),f312(f190(f854(x94721)),f172(x94721,x94722,x94723))),x94723),f127(x94721))+~P22(f312(x94722,f312(f137(x94721),f312(f312(f134(x94721),f312(f190(f854(x94721)),f172(x94721,x94722,x94723))),x94723))))
% 155.93/155.61 [9561]~P22(f312(f312(f314(f860(x95611,x95611)),x95612),f287(x95611,x95613)))+P22(f312(f312(f314(f860(x95611,x95611)),x95612),f312(f312(f50(a853,f861(f860(x95611,x95611),a846)),f235(f861(a853,a846))),f312(f312(f7(a853,f861(f860(x95611,x95611),a846),f861(f860(x95611,x95611),a846)),f184(f860(x95611,x95611),a846)),x95613))))
% 155.93/155.61 [9617]~P22(f312(f312(f227(f861(x96171,a846)),f312(f312(f50(a853,f861(x96171,a846)),f312(f282(a853,f2(a853)),f489(x96173,x96172,x96171))),x96172)),x96173))+P22(f312(f312(f227(f861(x96171,a846)),f312(f312(f50(a853,f861(x96171,a846)),f235(f861(a853,a846))),x96172)),x96173))
% 155.93/155.61 [9674]~P22(f312(f312(f228(a1),f2(a1)),x96743))+P22(f312(f312(f228(a1),x96741),f312(f312(f89(a1),x96742),f312(f312(f90(a1),f312(f312(f89(a1),f312(f84(a1),f312(f312(f21(a1),x96742),x96741))),f87(a1))),x96743))))
% 155.93/155.61 [9684]~P41(x96841,f312(f312(f124(f861(f860(x96841,x96841),a846)),x96842),x96843))+P41(x96841,f312(f312(f124(f861(f860(x96841,x96841),a846)),f312(f312(f124(f861(f860(x96841,x96841),a846)),f312(f312(f267(x96841,x96841,x96841),x96842),x96842)),f312(f312(f267(x96841,x96841,x96841),x96843),x96842))),x96843))
% 155.93/155.61 [9765]P41(x97651,f312(f312(f124(f861(f860(x97651,x97651),a846)),x97652),x97653))+~P41(x97651,f312(f312(f124(f861(f860(x97651,x97651),a846)),f312(f312(f124(f861(f860(x97651,x97651),a846)),f312(f312(f267(x97651,x97651,x97651),x97652),x97652)),f312(f312(f267(x97651,x97651,x97651),x97653),x97652))),x97653))
% 155.93/155.61 [9339]~P111(x93391)+E(f312(f116(x93391),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x93392),x93393)),f189(f861(f860(a853,a853),a846)))))),f312(f312(f21(x93391),f312(f114(x93391),x93392)),f312(f114(x93391),x93393)))
% 155.93/155.61 [9420]P22(f312(x94203,x94202))+E(f312(f233(x94201),f312(f312(f18(x94201,a846,a846),f312(f312(f8(a846,f861(a846,a846),x94201),a310),f312(f312(f7(x94201,x94201,a846),a309),x94202))),x94203)),f189(f861(x94201,a846)))
% 155.93/155.61 [9422]~P22(f312(x94223,x94222))+E(f312(f233(x94221),f312(f312(f18(x94221,a846,a846),f312(f312(f8(a846,f861(a846,a846),x94221),a310),f312(f312(f7(x94221,x94221,a846),a309),x94222))),x94223)),f312(f312(f289(x94221),x94222),f189(f861(x94221,a846))))
% 155.93/155.61 [9793]~P22(f312(f312(f228(a1),f2(a1)),x97933))+P22(f312(f312(f228(a1),f312(f312(f21(a1),x97931),f312(f312(f90(a1),f312(f312(f89(a1),f312(f84(a1),f312(f312(f21(a1),x97931),x97932))),f87(a1))),x97933))),x97932))
% 155.93/155.61 [10023]~P22(f312(f312(f314(x100231),x100233),f301(x100231,x100232)))+P22(f312(f300(x100231,f312(f312(f7(x100231,f861(f860(x100231,x100231),a846),f861(x100231,a846)),f312(f312(f8(f861(x100231,f861(f861(f860(x100231,x100231),a846),a846)),f861(f861(f860(x100231,x100231),a846),f861(x100231,a846)),x100231),f7(x100231,f861(f860(x100231,x100231),a846),a846)),f312(f312(f8(f861(x100231,f860(x100231,x100231)),f861(x100231,f861(f861(f860(x100231,x100231),a846),a846)),x100231),f312(f8(f860(x100231,x100231),f861(f861(f860(x100231,x100231),a846),a846),x100231),f314(f860(x100231,x100231)))),f239(x100231,x100231)))),x100232)),x100233))
% 155.93/155.61 [10035]P22(f312(f312(f314(x100351),x100352),f301(x100351,x100353)))+~P22(f312(f300(x100351,f312(f312(f7(x100351,f861(f860(x100351,x100351),a846),f861(x100351,a846)),f312(f312(f8(f861(x100351,f861(f861(f860(x100351,x100351),a846),a846)),f861(f861(f860(x100351,x100351),a846),f861(x100351,a846)),x100351),f7(x100351,f861(f860(x100351,x100351),a846),a846)),f312(f312(f8(f861(x100351,f860(x100351,x100351)),f861(x100351,f861(f861(f860(x100351,x100351),a846),a846)),x100351),f312(f8(f860(x100351,x100351),f861(f861(f860(x100351,x100351),a846),a846),x100351),f314(f860(x100351,x100351)))),f239(x100351,x100351)))),x100353)),x100352))
% 155.93/155.61 [9615]~P22(f312(f70(x96151),f312(f233(x96151),x96153)))+P22(f312(f70(x96151),f312(f233(x96151),f312(f312(f18(x96151,a846,a846),f312(f312(f8(a846,f861(a846,a846),x96151),a310),x96152)),x96153))))
% 155.93/155.61 [9616]~P22(f312(f70(x96161),f312(f233(x96161),x96162)))+P22(f312(f70(x96161),f312(f233(x96161),f312(f312(f18(x96161,a846,a846),f312(f312(f8(a846,f861(a846,a846),x96161),a310),x96162)),x96163))))
% 155.93/155.61 [9714]P22(f312(f70(x97141),f312(f233(x97141),x97142)))+~P22(f312(f70(x97141),f312(f233(x97141),f312(f312(f18(x97141,a846,a846),f312(f312(f8(a846,f861(a846,a846),x97141),a311),x97143)),x97142))))
% 155.93/155.61 [9715]P22(f312(f70(x97151),f312(f233(x97151),x97152)))+~P22(f312(f70(x97151),f312(f233(x97151),f312(f312(f18(x97151,a846,a846),f312(f312(f8(a846,f861(a846,a846),x97151),a311),x97152)),x97153))))
% 155.93/155.61 [10010]~P22(f312(f70(x100101),x100102))+P22(f312(f70(f854(x100101)),f312(f233(f854(x100101)),f312(f312(f18(f854(x100101),a846,a846),f312(f312(f8(a846,f861(a846,a846),f854(x100101)),a310),f312(f312(f7(f854(x100101),f861(x100101,a846),a846),f312(f312(f8(f861(x100101,a846),f861(f861(x100101,a846),a846),f854(x100101)),f227(f861(x100101,a846))),f168(x100101))),x100102))),f312(f312(f7(f854(x100101),a853,a846),f312(f312(f8(a853,f861(a853,a846),f854(x100101)),a309),f190(f854(x100101)))),x100103)))))
% 155.93/155.61 [10011]~P22(f312(f70(x100111),x100112))+P22(f312(f70(f854(x100111)),f312(f233(f854(x100111)),f312(f312(f18(f854(x100111),a846,a846),f312(f312(f8(a846,f861(a846,a846),f854(x100111)),a310),f312(f312(f7(f854(x100111),f861(x100111,a846),a846),f312(f312(f8(f861(x100111,a846),f861(f861(x100111,a846),a846),f854(x100111)),f227(f861(x100111,a846))),f168(x100111))),x100112))),f312(f312(f7(f854(x100111),a853,a846),f312(f312(f8(a853,f861(a853,a846),f854(x100111)),f227(a853)),f190(f854(x100111)))),x100113)))))
% 155.93/155.61 [9730]~P107(x97301)+E(f312(f312(f240(x97301),x97302),f312(f312(f90(a853),f312(f117(a853),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)))),x97303)),f312(f312(f90(x97301),f312(f312(f240(x97301),x97302),x97303)),f312(f312(f240(x97301),x97302),x97303)))
% 155.93/155.61 [9770]~P78(x97701)+E(f312(f312(f240(x97701),f312(f312(f240(x97701),x97702),x97703)),f312(f117(a853),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(x97701),x97702),f312(f312(f90(a853),f312(f117(a853),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)))),x97703)))
% 155.93/155.61 [9821]~P111(x98211)+E(f312(f312(f240(x98211),f312(f88(x98211),x98212)),f312(f312(f90(a853),f312(f117(a853),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)))),x98213)),f312(f312(f240(x98211),x98212),f312(f312(f90(a853),f312(f117(a853),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)))),x98213)))
% 155.93/155.61 [9967]~P112(x99671)+P22(f312(f312(f227(x99671),f2(x99671)),f312(f312(f89(x99671),f312(f312(f240(x99671),x99672),f312(f117(a853),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(x99671),x99673),f312(f117(a853),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)))))))
% 155.93/155.61 [9831]~P107(x98311)+E(f312(f312(f240(x98311),x98312),f312(a126,f312(f312(f90(a853),f312(f117(a853),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)))),x98313))),f312(f312(f90(x98311),x98312),f312(f312(f90(x98311),f312(f312(f240(x98311),x98312),x98313)),f312(f312(f240(x98311),x98312),x98313))))
% 155.93/155.61 [9884]~P78(x98841)+E(f312(f312(f90(x98841),x98842),f312(f312(f240(x98841),f312(f312(f240(x98841),x98842),x98843)),f312(f117(a853),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(x98841),x98842),f312(a126,f312(f312(f90(a853),f312(f117(a853),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)))),x98843))))
% 155.93/155.61 [9923]~P112(x99231)+P22(f312(f312(f227(x99231),f2(x99231)),f312(f312(f240(x99231),x99232),f312(f312(f90(a853),f312(f117(a853),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)))),x99233))))
% 155.93/155.61 [9988]~P90(x99881)+E(f312(f312(f89(x99881),f312(f312(f89(x99881),f312(f312(f240(x99881),x99882),f312(f117(a853),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(x99881),x99883),f312(f117(a853),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(x99881),f312(f312(f90(x99881),f312(f117(x99881),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)))),x99882)),x99883)),f312(f312(f240(x99881),f312(f312(f89(x99881),x99882),x99883)),f312(f117(a853),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)))))
% 155.93/155.61 [9989]~P90(x99891)+E(f312(f312(f21(x99891),f312(f312(f89(x99891),f312(f312(f240(x99891),x99892),f312(f117(a853),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(x99891),x99893),f312(f117(a853),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(x99891),f312(f312(f90(x99891),f312(f117(x99891),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)))),x99892)),x99893)),f312(f312(f240(x99891),f312(f312(f21(x99891),x99892),x99893)),f312(f117(a853),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)))))
% 155.93/155.61 [10092]~P34(x100921,x100922,x100923)+P22(f107(x100921,a846,f312(f312(f8(f861(a847,f861(f861(x100921,f861(a848,a846)),f861(x100921,a846))),f861(a847,f861(f861(x100921,f861(a848,a846)),a846)),f861(x100921,f861(a848,a846))),f312(f8(f861(f861(x100921,f861(a848,a846)),f861(x100921,a846)),f861(f861(x100921,f861(a848,a846)),a846),a847),f312(f8(f861(x100921,a846),a846,f861(x100921,f861(a848,a846))),f97(x100921)))),f312(f312(f8(f861(a847,f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846)))),f861(a847,f861(f861(x100921,f861(a848,a846)),f861(x100921,a846))),f861(x100921,f861(a848,a846))),f312(f8(f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846))),f861(f861(x100921,f861(a848,a846)),f861(x100921,a846)),a847),f312(f8(f861(x100921,f861(a848,a846)),f861(x100921,a846),f861(x100921,f861(a848,a846))),f312(f8(f861(a848,a846),a846,x100921),f97(a848))))),f312(f312(f7(f861(x100921,f861(a848,a846)),f861(a847,f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846)))),f861(a847,f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846))))),f312(f312(f8(f861(f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846))),f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846)))),f861(f861(a847,f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846)))),f861(a847,f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846))))),f861(x100921,f861(a848,a846))),f8(f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846))),f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846))),a847)),f312(f312(f8(f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846))),f861(f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846))),f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846)))),f861(x100921,f861(a848,a846))),f8(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846)))),f312(f312(f8(f861(x100921,f861(f861(a848,a846),f861(a848,a846))),f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846))),f861(x100921,f861(a848,a846))),f18(x100921,f861(a848,a846),f861(a848,a846))),f312(f312(f8(f861(x100921,f861(a848,f861(a846,a846))),f861(x100921,f861(f861(a848,a846),f861(a848,a846))),f861(x100921,f861(a848,a846))),f312(f8(f861(a848,f861(a846,a846)),f861(f861(a848,a846),f861(a848,a846)),x100921),f18(a848,a846,a846))),f312(f8(f861(a848,a846),f861(a848,f861(a846,a846)),x100921),f312(f8(a846,f861(a846,a846),a848),a315))))))),f312(f312(f8(f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,f861(a848,a846)))),f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846))),a847),f312(f8(f861(x100921,f861(a848,f861(a848,a846))),f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,a846))),f312(f8(f861(a848,f861(a848,a846)),f861(a848,a846),x100921),f312(f8(f861(a848,a846),a846,a848),f97(a848))))),f312(f312(f8(f861(f861(a848,a846),f861(a848,f861(a848,a846))),f861(f861(x100921,f861(a848,a846)),f861(x100921,f861(a848,f861(a848,a846)))),a847),f8(f861(a848,a846),f861(a848,f861(a848,a846)),x100921)),f312(f312(f8(f861(a848,f861(f861(a848,a846),f861(a848,a846))),f861(f861(a848,a846),f861(a848,f861(a848,a846))),a847),f7(a848,f861(a848,a846),f861(a848,a846))),f312(f312(f8(f861(a848,f861(a848,f861(a846,a846))),f861(a848,f861(f861(a848,a846),f861(a848,a846))),a847),f312(f8(f861(a848,f861(a846,a846)),f861(f861(a848,a846),f861(a848,a846)),a848),f18(a848,a846,a846))),f312(f312(f8(f861(a848,f861(a848,a846)),f861(a848,f861(a848,f861(a846,a846))),a847),f312(f8(f861(a848,a846),f861(a848,f861(a846,a846)),a848),f312(f8(a846,f861(a846,a846),a848),a315))),f312(f312(f7(a847,a853,f861(a848,f861(a848,a846))),f312(f312(f8(f861(a848,f861(a853,f861(a848,a846))),f861(a853,f861(a848,f861(a848,a846))),a847),f7(a848,a853,f861(a848,a846))),a198)),x100922))))))))),x100923))
% 155.93/155.61 [10094]P34(x100941,x100942,x100943)+~P22(f107(x100941,a846,f312(f312(f8(f861(a847,f861(f861(x100941,f861(a848,a846)),f861(x100941,a846))),f861(a847,f861(f861(x100941,f861(a848,a846)),a846)),f861(x100941,f861(a848,a846))),f312(f8(f861(f861(x100941,f861(a848,a846)),f861(x100941,a846)),f861(f861(x100941,f861(a848,a846)),a846),a847),f312(f8(f861(x100941,a846),a846,f861(x100941,f861(a848,a846))),f97(x100941)))),f312(f312(f8(f861(a847,f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846)))),f861(a847,f861(f861(x100941,f861(a848,a846)),f861(x100941,a846))),f861(x100941,f861(a848,a846))),f312(f8(f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846))),f861(f861(x100941,f861(a848,a846)),f861(x100941,a846)),a847),f312(f8(f861(x100941,f861(a848,a846)),f861(x100941,a846),f861(x100941,f861(a848,a846))),f312(f8(f861(a848,a846),a846,x100941),f97(a848))))),f312(f312(f7(f861(x100941,f861(a848,a846)),f861(a847,f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846)))),f861(a847,f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846))))),f312(f312(f8(f861(f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846))),f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846)))),f861(f861(a847,f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846)))),f861(a847,f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846))))),f861(x100941,f861(a848,a846))),f8(f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846))),f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846))),a847)),f312(f312(f8(f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846))),f861(f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846))),f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846)))),f861(x100941,f861(a848,a846))),f8(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846)))),f312(f312(f8(f861(x100941,f861(f861(a848,a846),f861(a848,a846))),f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846))),f861(x100941,f861(a848,a846))),f18(x100941,f861(a848,a846),f861(a848,a846))),f312(f312(f8(f861(x100941,f861(a848,f861(a846,a846))),f861(x100941,f861(f861(a848,a846),f861(a848,a846))),f861(x100941,f861(a848,a846))),f312(f8(f861(a848,f861(a846,a846)),f861(f861(a848,a846),f861(a848,a846)),x100941),f18(a848,a846,a846))),f312(f8(f861(a848,a846),f861(a848,f861(a846,a846)),x100941),f312(f8(a846,f861(a846,a846),a848),a315))))))),f312(f312(f8(f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,f861(a848,a846)))),f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846))),a847),f312(f8(f861(x100941,f861(a848,f861(a848,a846))),f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,a846))),f312(f8(f861(a848,f861(a848,a846)),f861(a848,a846),x100941),f312(f8(f861(a848,a846),a846,a848),f97(a848))))),f312(f312(f8(f861(f861(a848,a846),f861(a848,f861(a848,a846))),f861(f861(x100941,f861(a848,a846)),f861(x100941,f861(a848,f861(a848,a846)))),a847),f8(f861(a848,a846),f861(a848,f861(a848,a846)),x100941)),f312(f312(f8(f861(a848,f861(f861(a848,a846),f861(a848,a846))),f861(f861(a848,a846),f861(a848,f861(a848,a846))),a847),f7(a848,f861(a848,a846),f861(a848,a846))),f312(f312(f8(f861(a848,f861(a848,f861(a846,a846))),f861(a848,f861(f861(a848,a846),f861(a848,a846))),a847),f312(f8(f861(a848,f861(a846,a846)),f861(f861(a848,a846),f861(a848,a846)),a848),f18(a848,a846,a846))),f312(f312(f8(f861(a848,f861(a848,a846)),f861(a848,f861(a848,f861(a846,a846))),a847),f312(f8(f861(a848,a846),f861(a848,f861(a846,a846)),a848),f312(f8(a846,f861(a846,a846),a848),a315))),f312(f312(f7(a847,a853,f861(a848,f861(a848,a846))),f312(f312(f8(f861(a848,f861(a853,f861(a848,a846))),f861(a853,f861(a848,f861(a848,a846))),a847),f7(a848,a853,f861(a848,a846))),a198)),x100942))))))))),x100943))
% 155.93/155.61 [4618]E(x46181,x46182)+~E(f36(x46183,x46181),f36(x46184,x46182))
% 155.93/155.61 [4619]E(x46191,x46192)+~E(f36(x46191,x46193),f36(x46192,x46194))
% 155.93/155.61 [4620]E(x46201,x46202)+~E(f35(x46203,x46201),f35(x46204,x46202))
% 155.93/155.61 [4621]E(x46211,x46212)+~E(f35(x46211,x46213),f35(x46212,x46214))
% 155.93/155.61 [4622]E(x46221,x46222)+~E(f28(x46223,x46221),f28(x46224,x46222))
% 155.93/155.61 [4623]E(x46231,x46232)+~E(f28(x46231,x46233),f28(x46232,x46234))
% 155.93/155.61 [7652]P19(x76521,x76522,x76523,x76524)+~E(f803(x76524,x76523,x76522,x76521),f804(x76524,x76523,x76522,x76521))
% 155.93/155.61 [7938]P39(x79381,x79382,x79383,x79384,f127(x79382))+~E(x79384,f127(x79381))
% 155.93/155.61 [7939]P39(x79391,x79392,x79393,f127(x79391),x79394)+~E(x79394,f127(x79392))
% 155.93/155.61 [8157]~P19(x81571,f857(x81572),x81574,f179(x81571,x81572,x81574))+P19(x81571,f857(x81572),f180(x81571,x81572,x81573,x81574),f179(x81571,x81572,x81574))
% 155.93/155.61 [8246]P36(x82461,x82462,x82463,f180(x82461,x82462,x82463,x82464))+~E(f180(x82461,x82462,x82463,x82464),f180(x82461,x82462,x82464,x82463))
% 155.93/155.61 [8343]~P36(x83431,x83432,x83433,f180(x83431,x83432,x83433,x83434))+E(f180(x83431,x83432,x83433,x83434),f180(x83431,x83432,x83434,x83433))
% 155.93/155.61 [8380]~P19(x83801,f857(x83802),f180(x83801,x83802,x83804,x83803),f179(x83801,x83802,x83803))+P19(x83801,f857(x83802),x83803,f179(x83801,x83802,x83803))
% 155.93/155.61 [8501]~P39(x85012,x85013,x85014,x85011,f127(x85013))+E(x85011,f127(x85012))
% 155.93/155.61 [8502]~P39(x85023,x85022,x85024,f127(x85023),x85021)+E(x85021,f127(x85022))
% 155.93/155.61 [4988]~P12(x49883,x49881,x49884)+E(f312(f312(x49881,x49882),x49882),x49882)
% 155.93/155.61 [5277]~E(x52774,f189(f861(x52771,a846)))+E(f312(f290(x52771,x52772,x52773),x52774),f189(f861(x52772,a846)))
% 155.93/155.61 [5546]~E(f312(f290(x55462,x55463,x55464),x55461),f189(f861(x55463,a846)))+E(x55461,f189(f861(x55462,a846)))
% 155.93/155.61 [5816]~P103(x58162)+E(f312(f312(f145(x58161,x58162,x58163),x58164),f127(x58161)),f312(f312(f147(x58161),x58164),f127(x58161)))
% 155.93/155.61 [5852]E(f312(x58521,x58522),f192(x58523))+P22(f312(f312(f314(x58524),x58522),f179(x58524,x58523,x58521)))
% 155.93/155.61 [6171]~E(x61711,f189(f861(x61712,a846)))+~P22(f312(f71(x61712,x61713,x61711),x61714))
% 155.93/155.61 [6193]~P58(x61931,x61933,x61934,x61932)+P22(f312(f70(x61931),x61932))
% 155.93/155.61 [6194]~P58(x61941,x61943,x61942,x61944)+P22(f312(f70(x61941),x61942))
% 155.93/155.61 [6201]~P58(x62012,x62013,x62014,x62011)+~E(x62011,f189(f861(x62012,a846)))
% 155.93/155.61 [6228]~P105(x62281)+E(f312(f312(f115(f861(x62281,a846)),f312(f282(x62281,x62282),x62283)),f283(x62281,x62283,x62284)),f189(f861(x62281,a846)))
% 155.93/155.61 [6255]~P22(f312(f312(x62553,x62554),x62552))+P22(f312(f312(f314(x62551),x62552),f271(x62551,x62553,x62554)))
% 155.93/155.61 [6256]~P22(f312(f312(x62563,x62564),x62562))+P22(f312(f312(f314(x62561),x62562),f272(x62561,x62563,x62564)))
% 155.93/155.61 [6257]~P22(f312(f312(x62573,x62572),x62574))+P22(f312(f312(f314(x62571),x62572),f273(x62571,x62573,x62574)))
% 155.93/155.61 [6258]~P22(f312(f312(x62583,x62582),x62584))+P22(f312(f312(f314(x62581),x62582),f276(x62581,x62583,x62584)))
% 155.93/155.61 [6396]~P105(x63961)+E(f312(f312(f115(f861(x63961,a846)),f285(x63961,x63962,x63963)),f283(x63961,x63963,x63964)),f189(f861(x63961,a846)))
% 155.93/155.61 [6397]~P105(x63971)+E(f312(f312(f115(f861(x63971,a846)),f284(x63971,x63972,x63973)),f285(x63971,x63973,x63974)),f189(f861(x63971,a846)))
% 155.93/155.61 [6398]~P105(x63981)+E(f312(f312(f115(f861(x63981,a846)),f284(x63981,x63982,x63983)),f284(x63981,x63983,x63984)),f189(f861(x63981,a846)))
% 155.93/155.61 [6399]~P105(x63991)+E(f312(f312(f115(f861(x63991,a846)),f283(x63991,x63992,x63993)),f285(x63991,x63993,x63994)),f189(f861(x63991,a846)))
% 155.93/155.61 [6400]~P105(x64001)+E(f312(f312(f115(f861(x64001,a846)),f283(x64001,x64002,x64003)),f284(x64001,x64003,x64004)),f189(f861(x64001,a846)))
% 155.93/155.61 [6433]P22(f312(f312(x64331,x64332),f570(x64332,x64331)))+~P22(f312(f244(x64333,x64334,x64331),x64332))
% 155.93/155.61 [6482]~E(f312(x64821,x64822),f192(x64823))+~P22(f312(f312(f314(x64824),x64822),f179(x64824,x64823,x64821)))
% 155.93/155.61 [6511]~P103(x65112)+E(f312(f168(x65111),f144(x65111,x65112,x65113,x65114)),f312(f168(x65111),x65114))
% 155.93/155.61 [6563]~P23(x65631)+E(f191(x65631,x65632,f312(a126,x65633),x65634),f191(x65631,x65632,x65633,f312(x65632,x65634)))
% 155.93/155.61 [6622]~P22(f312(f312(f314(x66224),x66223),f271(x66224,x66221,x66222)))+P22(f312(f312(x66221,x66222),x66223))
% 155.93/155.61 [6623]~P22(f312(f312(f314(x66234),x66233),f272(x66234,x66231,x66232)))+P22(f312(f312(x66231,x66232),x66233))
% 155.93/155.61 [6624]~P22(f312(f312(f314(x66244),x66242),f273(x66244,x66241,x66243)))+P22(f312(f312(x66241,x66242),x66243))
% 155.93/155.61 [6625]~P22(f312(f312(f314(x66254),x66252),f276(x66254,x66251,x66253)))+P22(f312(f312(x66251,x66252),x66253))
% 155.93/155.61 [6701]E(f312(f53(f859(x67011,x67012)),f298(x67011,x67012,x67013,x67014)),f2(a853))+P22(f312(f70(x67012),x67014))
% 155.93/155.61 [6702]E(f312(f53(f859(x67021,x67022)),f298(x67021,x67022,x67023,x67024)),f2(a853))+P22(f312(f70(x67021),x67023))
% 155.93/155.61 [6902]~P11(x69024,x69021,x69022)+E(f312(f82(x69021,x69021,x69021,f312(x69022,x69023)),f312(x69022,x69023)),f312(x69022,x69023))
% 155.93/155.61 [7689]~P22(f312(x76891,x76894))+P22(f312(x76891,f104(x76892,a853,x76893,x76891)))
% 155.93/155.61 [7772]~E(x77722,x77723)+P22(f312(f312(f314(f860(x77721,x77721)),f312(f312(f239(x77721,x77721),x77722),x77723)),f287(x77721,x77724)))
% 155.93/155.61 [7800]~P19(x78001,x78002,x78003,f235(f861(x78001,a846)))+E(f312(f86(x78001,x78002,f235(f861(x78001,a846)),x78003),f312(x78003,x78004)),x78004)
% 155.93/155.61 [7886]~P22(f312(f312(f314(f854(x78861)),f312(f312(f147(x78861),x78864),x78862)),f157(x78861,x78863)))+P22(f312(f312(f314(f854(x78861)),x78862),f157(x78861,x78863)))
% 155.93/155.61 [7887]~P22(f312(f312(f314(f854(x78871)),f312(f312(f129(x78871),x78874),x78872)),f157(x78871,x78873)))+P22(f312(f312(f314(f854(x78871)),x78872),f157(x78871,x78873)))
% 155.93/155.61 [7888]~P22(f312(f312(f314(f854(x78881)),f312(f312(f129(x78881),x78882),x78884)),f157(x78881,x78883)))+P22(f312(f312(f314(f854(x78881)),x78882),f157(x78881,x78883)))
% 155.93/155.61 [7904]~P103(x79041)+P33(x79041,f312(f312(f150(x79042,x79041),x79043),f144(x79042,x79041,x79043,x79044)))
% 155.93/155.61 [7999]P19(x79994,x79993,x79991,x79992)+E(f312(x79991,f803(x79992,x79991,x79993,x79994)),f312(x79991,f804(x79992,x79991,x79993,x79994)))
% 155.93/155.61 [8015]E(f180(x80151,x80152,x80153,x80154),f180(x80151,x80152,x80154,x80153))+~E(f312(f312(f115(f861(x80151,a846)),f179(x80151,x80152,x80153)),f179(x80151,x80152,x80154)),f189(f861(x80151,a846)))
% 155.93/155.61 [8053]~P36(x80531,x80532,x80533,x80534)+P22(f312(f312(f227(f861(x80531,a846)),f179(x80531,x80532,x80533)),f179(x80531,x80532,x80534)))
% 155.93/155.61 [8119]~P19(x81192,x81191,x81194,x81193)+P19(x81191,x81192,f86(x81192,x81191,x81193,x81194),f312(f290(x81192,x81191,x81194),x81193))
% 155.93/155.61 [8260]P41(f860(x82602,x82604),f262(x82602,x82604,x82601,x82603))+P22(f312(x82601,f575(x82602,x82603,x82604,x82601)))
% 155.93/155.61 [8387]E(x83871,x83872)+~P22(f312(f312(f314(f860(x83873,x83873)),f312(f312(f239(x83873,x83873),x83871),x83872)),f237(x83873,x83874)))
% 155.93/155.61 [8451]~P22(f312(f70(f859(x84513,x84511)),f298(x84513,x84511,x84514,x84512)))+P22(f312(f70(x84511),x84512))
% 155.93/155.61 [8452]~P22(f312(f70(f859(x84521,x84523)),f298(x84521,x84523,x84522,x84524)))+P22(f312(f70(x84521),x84522))
% 155.93/155.61 [8463]P36(x84631,x84632,x84633,x84634)+~E(f312(x84633,f799(x84634,x84633,x84632,x84631)),f312(x84634,f799(x84634,x84633,x84632,x84631)))
% 155.93/155.61 [8627]P41(f860(x86271,x86272),f262(x86271,x86272,x86273,x86274))+~P41(x86272,f312(x86274,f575(x86271,x86274,x86272,x86273)))
% 155.93/155.61 [8770]P36(x87701,x87702,x87703,x87704)+P22(f312(f312(f314(x87701),f799(x87704,x87703,x87702,x87701)),f179(x87701,x87702,x87703)))
% 155.93/155.61 [9185]E(f312(f312(f155(x91851,x91852),f606(x91853,x91854,x91852,x91851)),f607(x91853,x91854,x91852,x91851)),x91854)+~P22(f312(f312(f314(f860(f854(x91851),f854(x91851))),f312(f312(f239(f854(x91851),f854(x91851)),x91852),x91854)),f153(x91851,x91853)))
% 155.93/155.61 [9186]~P22(f312(x91863,x91864))+P22(f312(f312(f227(a853),f312(x91861,f104(x91862,a853,x91861,x91863))),f312(x91861,x91864)))
% 155.93/155.61 [9192]~P22(f312(f312(f314(f860(f854(x91921),f854(x91921))),f312(f312(f239(f854(x91921),f854(x91921)),x91922),x91923)),f141(x91921,x91924)))+P22(f312(f312(f314(f860(f854(x91921),f854(x91921))),f312(f312(f239(f854(x91921),f854(x91921)),x91922),x91923)),f143(x91921,x91924)))
% 155.93/155.61 [9294]P22(f312(f70(x92941),x92942))+~P22(f312(f312(f314(f860(f861(x92941,a846),f861(x92941,a846))),f312(f312(f239(f861(x92941,a846),f861(x92941,a846)),x92943),x92942)),f303(x92941,x92944)))
% 155.93/155.61 [9295]P22(f312(f70(x92951),x92952))+~P22(f312(f312(f314(f860(f861(x92951,a846),f861(x92951,a846))),f312(f312(f239(f861(x92951,a846),f861(x92951,a846)),x92952),x92953)),f303(x92951,x92954)))
% 155.93/155.61 [9298]~E(x92981,f189(f861(x92982,a846)))+~P22(f312(f312(f314(f860(f861(x92982,a846),f861(x92982,a846))),f312(f312(f239(f861(x92982,a846),f861(x92982,a846)),x92983),x92981)),f303(x92982,x92984)))
% 155.93/155.61 [9935]P9(x99351,x99352,x99353,x99354)+~P22(f312(f312(f249(x99351,x99351,a846),f312(f312(f7(x99351,f861(x99351,x99352),f861(x99351,a846)),f312(f312(f8(f861(x99352,a846),f861(f861(x99351,x99352),f861(x99351,a846)),x99351),f8(x99352,a846,x99351)),f312(f312(f8(x99352,f861(x99352,a846),x99351),a309),x99354))),x99354)),f413(x99354,x99353,x99352,x99351)))
% 155.93/155.61 [4896]~E(x48964,f192(x48961))+E(f312(f312(f193(x48961,x48962),x48963),x48964),f192(x48962))
% 155.93/155.61 [4897]~E(x48974,f127(x48971))+E(f312(f312(f150(x48971,x48972),x48973),x48974),f127(x48972))
% 155.93/155.61 [4898]~E(x48982,f127(x48981))+E(f312(f312(f155(x48981,x48982),x48983),x48984),f127(x48981))
% 155.93/155.61 [5132]E(x51321,f192(x51322))+~E(f312(f312(f193(x51322,x51323),x51324),x51321),f192(x51323))
% 155.93/155.61 [5133]E(x51331,f127(x51332))+~E(f312(f312(f150(x51332,x51333),x51334),x51331),f127(x51333))
% 155.93/155.61 [5134]E(x51341,f127(x51342))+~E(f312(f312(f155(x51342,x51341),x51343),x51344),f127(x51342))
% 155.93/155.61 [5165]E(x51651,x51652)+~E(f312(f312(f129(x51653),x51654),x51651),f312(f312(f129(x51653),x51654),x51652))
% 155.93/155.61 [5166]E(x51661,x51662)+~E(f312(f312(f129(x51663),x51661),x51664),f312(f312(f129(x51663),x51662),x51664))
% 155.93/155.61 [5311]P22(f312(x53113,x53112))+E(f166(x53111,x53112,f312(f132(x53111,x53113),x53114)),f312(f132(x53111,x53113),x53114))
% 155.93/155.61 [5313]~P22(f312(x53132,x53133))+P38(x53131,x53132,f312(f312(f147(x53131),x53133),x53134))
% 155.93/155.61 [5322]E(x53221,x53222)+~E(f135(a853,f312(f282(a853,x53221),x53223)),f312(f312(f147(a853),x53222),x53224))
% 155.93/155.61 [5370]~P20(x53702,x53703)+P20(x53701,f312(f312(f83(x53702,x53701),x53703),x53704))
% 155.93/155.61 [5371]~P41(x53712,x53713)+P41(x53711,f312(f312(f266(x53712,x53711),x53713),x53714))
% 155.93/155.61 [5497]~P38(x54971,x54972,x54974)+P38(x54971,x54972,f312(f312(f147(x54971),x54973),x54974))
% 155.93/155.61 [5498]~P38(x54981,x54982,x54984)+P38(x54981,x54982,f312(f312(f129(x54981),x54983),x54984))
% 155.93/155.61 [5499]~P38(x54991,x54992,x54993)+P38(x54991,x54992,f312(f312(f129(x54991),x54993),x54994))
% 155.93/155.61 [5590]~E(x55901,f127(x55902))+~E(f312(f312(f129(x55902),x55903),f312(f312(f147(x55902),x55904),f127(x55902))),x55901)
% 155.93/155.61 [5620]E(f128(x56201,x56202),x56203)+~E(f312(f312(f129(x56201),x56203),f312(f312(f147(x56201),x56204),f127(x56201))),x56202)
% 155.93/155.61 [5621]E(f140(x56211,x56212),x56213)+~E(f312(f312(f129(x56211),x56214),f312(f312(f147(x56211),x56213),f127(x56211))),x56212)
% 155.93/155.61 [5725]~E(f135(a853,f312(f282(a853,x57251),x57252)),f312(f312(f147(a853),x57253),x57254))+P22(f312(f312(f228(a853),x57251),x57252))
% 155.93/155.61 [5927]E(x59271,f312(f312(f129(x59272),f312(f165(x59272),x59273)),f312(f312(f147(x59272),x59274),f127(x59272))))+~E(f312(f165(x59272),x59271),f312(f312(f147(x59272),x59274),x59273))
% 155.93/155.61 [6090]~P105(x60901)+E(f312(f312(f115(f861(x60901,a846)),f312(f282(x60901,x60902),x60903)),f312(f282(x60901,x60903),x60904)),f189(f861(x60901,a846)))
% 155.93/155.61 [6127]~P26(x61271)+E(f312(f162(x61271),f312(f312(f150(a1,x61271),x61272),f174(x61273,x61274))),f312(f312(f6(a1,x61271),x61272),f312(f168(a1),f174(x61273,x61274))))
% 155.93/155.61 [6128]~P26(x61281)+E(f312(f312(f6(a1,x61281),x61282),f312(f168(a1),f174(x61283,x61284))),f312(f162(x61281),f312(f312(f150(a1,x61281),x61282),f174(x61283,x61284))))
% 155.93/155.61 [6270]~E(x62702,f312(f312(f129(x62701),f312(f165(x62701),x62704)),f312(f312(f147(x62701),x62703),f127(x62701))))+E(f312(f165(x62701),x62702),f312(f312(f147(x62701),x62703),x62704))
% 155.93/155.61 [6286]~P14(x62862,x62863,x62864,x62861)+E(f312(x62861,f189(f861(x62862,a846))),f39(x62863))
% 155.93/155.61 [6307]~P105(x63071)+E(f312(f312(f115(f861(x63071,a846)),f285(x63071,x63072,x63073)),f312(f282(x63071,x63073),x63074)),f189(f861(x63071,a846)))
% 155.93/155.61 [6512]E(x65121,f189(f861(x65122,a846)))+~E(f298(x65123,x65122,x65124,x65121),f189(f861(f859(x65123,x65122),a846)))
% 155.93/155.61 [6513]E(x65131,f189(f861(x65132,a846)))+~E(f298(x65132,x65133,x65131,x65134),f189(f861(f859(x65132,x65133),a846)))
% 155.93/155.61 [6585]~P103(x65852)+E(f312(f190(f854(x65851)),f144(x65851,x65852,x65853,x65854)),f312(f190(f854(x65851)),x65854))
% 155.93/155.61 [6598]~P22(f312(f245(x65983,x65984,x65981),x65982))+P22(f312(f312(x65981,f555(x65982,x65981)),x65982))
% 155.93/155.61 [6635]~P22(f312(f70(x66352),x66354))+P22(f312(f70(x66351),f312(f290(x66352,x66351,x66353),x66354)))
% 155.93/155.61 [6859]~P19(x68592,x68591,x68593,x68594)+E(f312(f53(x68591),f312(f290(x68592,x68591,x68593),x68594)),f312(f53(x68592),x68594))
% 155.93/155.61 [6877]E(f312(f290(x68771,x68772,x68773),f312(f291(x68771,x68772,x68773),x68774)),x68774)+~E(f312(f290(x68771,x68772,x68773),f235(f861(x68771,a846))),f235(f861(x68772,a846)))
% 155.93/155.61 [7282]~P19(x72821,x72822,x72823,f235(f861(x72821,a846)))+E(f312(f291(x72821,x72822,x72823),f312(f290(x72821,x72822,x72823),x72824)),x72824)
% 155.93/155.61 [7610]P22(f312(x76101,x76102))+~P22(f312(f312(f314(x76103),x76102),f312(f168(x76103),f172(x76103,x76101,x76104))))
% 155.93/155.61 [7721]~P22(f312(f312(f314(f854(x77211)),f312(f312(f147(x77211),x77212),x77214)),f157(x77211,x77213)))+P22(f312(f312(f314(x77211),x77212),x77213))
% 155.93/155.61 [7841]~P22(f312(f312(f314(x78411),x78412),f312(f168(x78411),f166(x78411,x78414,x78413))))+P22(f312(f312(f314(x78411),x78412),f312(f168(x78411),x78413)))
% 155.93/155.61 [7843]~P22(f312(f312(f314(x78431),x78432),f312(f168(x78431),f170(x78431,x78433,x78434))))+P22(f312(f312(f314(x78431),x78432),f312(f168(x78431),x78433)))
% 155.93/155.61 [7844]~P22(f312(f312(f314(x78441),x78442),f312(f168(x78441),f172(x78441,x78444,x78443))))+P22(f312(f312(f314(x78441),x78442),f312(f168(x78441),x78443)))
% 155.93/155.61 [7854]E(f312(f190(f854(x78541)),x78542),x78543)+~P22(f312(f312(f314(f854(x78541)),x78542),f312(f168(f854(x78541)),f63(x78541,x78543,x78544))))
% 155.93/155.61 [7950]P22(f312(x79503,x79502))+E(f312(f132(x79501,f312(f312(f8(a846,a846,x79501),a307),f312(a309,x79502))),f312(f132(x79501,x79503),x79504)),f312(f132(x79501,x79503),x79504))
% 155.93/155.61 [8069]E(f312(f312(f161(x80691),f172(x80691,x80692,x80693)),x80694),f312(f312(f161(x80691),x80693),x80694))+~P22(f312(f312(f228(a853),x80694),f312(f190(f854(x80691)),f172(x80691,x80692,x80693))))
% 155.93/155.61 [8155]~P26(x81551)+E(f312(f312(f6(a853,x81551),f312(f312(f8(a853,x81551,a853),x81552),a126)),f312(f282(a853,x81553),x81554)),f312(f312(f6(a853,x81551),x81552),f312(f282(a853,f312(a126,x81553)),f312(a126,x81554))))
% 155.93/155.61 [8164]~P26(x81641)+E(f312(f312(f6(a853,x81641),f312(f312(f8(a853,x81641,a853),x81642),a126)),f283(a853,x81643,x81644)),f312(f312(f6(a853,x81641),x81642),f283(a853,f312(a126,x81643),f312(a126,x81644))))
% 155.93/155.61 [8296]~P19(x82961,x82963,x82964,f235(f861(x82961,a846)))+P19(x82961,f861(x82962,x82963),f312(f312(f8(x82963,f861(x82962,x82963),x82961),f16(x82963,x82962)),x82964),f235(f861(x82961,a846)))
% 155.93/155.61 [8395]~P19(x83952,x83951,x83954,x83953)+E(f312(f290(x83951,x83952,f86(x83952,x83951,x83953,x83954)),f312(f290(x83952,x83951,x83954),x83953)),x83953)
% 155.93/155.61 [8453]~P22(f312(f312(f314(f860(x84531,x84531)),f312(f312(f239(x84531,x84531),x84532),x84534)),f237(x84531,x84533)))+P22(f312(f312(f314(x84531),x84532),x84533))
% 155.93/155.61 [8542]E(f312(f312(f312(f81(x85421,f857(x85422)),f312(f16(f857(x85422),x85421),f192(x85422))),x85423),f312(f219(x85422),f758(x85423,x85424,x85422,x85421))),x85424)+~E(f179(x85421,x85422,x85424),f312(f312(f289(x85421),x85423),f189(f861(x85421,a846))))
% 155.93/155.61 [8664]~E(f312(f312(f6(x86641,a853),x86644),x86643),f312(a126,x86642))+P22(f312(f312(f314(x86641),f720(x86642,x86643,x86644,x86641)),x86643))
% 155.93/155.61 [8683]~E(f312(f312(f6(x86834,a853),x86831),x86833),f312(a126,x86832))+P22(f312(f312(f228(a853),f2(a853)),f312(x86831,f720(x86832,x86833,x86831,x86834))))
% 155.93/155.61 [8694]~P22(f312(f70(x86942),x86944))+P22(f312(f312(f227(a853),f312(f53(x86941),f312(f290(x86942,x86941,x86943),x86944))),f312(f53(x86942),x86944)))
% 155.93/155.61 [8702]P19(x87021,x87022,x87023,x87024)+P22(f312(f312(f314(x87021),f803(x87024,x87023,x87022,x87021)),x87024))
% 155.93/155.61 [8703]P19(x87031,x87032,x87033,x87034)+P22(f312(f312(f314(x87031),f804(x87034,x87033,x87032,x87031)),x87034))
% 155.93/155.61 [8763]P9(x87631,x87632,x87633,x87634)+P22(f312(f312(f314(f860(x87631,x87631)),f413(x87634,x87633,x87632,x87631)),x87633))
% 155.93/155.61 [8822]P22(f312(x88221,x88222))+~P22(f312(x88221,f312(f312(f239(x88223,x88224),f343(x88224,x88223,x88221)),f344(x88224,x88223,x88221))))
% 155.93/155.61 [8839]E(f312(f190(f854(x88391)),x88392),f312(f190(f854(x88391)),x88393))+~P22(f312(f312(f314(f860(f854(x88391),f854(x88391))),f312(f312(f239(f854(x88391),f854(x88391)),x88392),x88393)),f141(x88391,x88394)))
% 155.93/155.61 [8842]E(f312(f190(f854(x88421)),x88422),f312(f190(f854(x88421)),x88423))+~P22(f312(f312(f314(f860(f854(x88421),f854(x88421))),f312(f312(f239(f854(x88421),f854(x88421)),x88422),x88423)),f154(x88421,x88424)))
% 155.93/155.61 [8843]E(f312(f190(f854(x88431)),x88432),f312(f190(f854(x88431)),x88433))+~P22(f312(f312(f314(f860(f854(x88431),f854(x88431))),f312(f312(f239(f854(x88431),f854(x88431)),x88432),x88433)),f153(x88431,x88434)))
% 155.93/155.61 [8922]P22(f312(f312(f227(a853),f151(x89221,x89222,x89223)),f151(x89221,x89224,x89223)))+P22(f312(f312(f314(x89221),f604(x89224,x89222,x89223,x89221)),f312(f168(x89221),x89223)))
% 155.93/155.61 [8925]E(f312(f190(f854(x89251)),x89252),f312(f190(f854(x89251)),x89253))+~P22(f312(f312(f314(f860(f854(x89251),f854(x89251))),f312(f312(f239(f854(x89251),f854(x89251)),x89252),x89253)),f287(f854(x89251),f153(x89251,x89254))))
% 155.93/155.61 [9155]~P19(x91551,x91552,x91553,x91554)+~P22(f312(f312(f228(a853),f312(f53(x91552),f312(f290(x91551,x91552,x91553),x91554))),f312(f53(x91551),x91554)))
% 155.93/155.61 [9203]~P22(f312(f312(f314(f860(f854(x92031),f854(x92031))),f312(f312(f239(f854(x92031),f854(x92031)),x92032),x92033)),f153(x92031,x92034)))+P22(f312(f312(f314(f860(f854(x92031),f854(x92031))),f312(f312(f239(f854(x92031),f854(x92031)),x92032),x92033)),f154(x92031,f287(x92031,x92034))))
% 155.93/155.61 [9207]~P22(f312(f312(f314(f860(f854(x92071),f854(x92071))),f312(f312(f239(f854(x92071),f854(x92071)),x92072),x92073)),f154(x92071,x92074)))+P22(f312(f312(f314(f860(f854(x92071),f854(x92071))),f312(f312(f239(f854(x92071),f854(x92071)),x92072),x92073)),f287(f854(x92071),f153(x92071,x92074))))
% 155.93/155.61 [9223]P22(f312(f312(f314(f860(x92231,x92231)),f312(f312(f239(x92231,x92231),x92232),x92233)),f287(x92231,x92234)))+~P22(f312(f312(f314(f860(x92231,x92231)),f312(f312(f239(x92231,x92231),x92232),x92233)),f312(f312(f267(x92231,x92231,x92231),x92234),f287(x92231,x92234))))
% 155.93/155.61 [9405]E(f312(f312(f129(x94051),f625(x94052,x94053,x94054,x94051)),f312(f312(f147(x94051),f626(x94052,x94053,x94054,x94051)),f628(x94052,x94053,x94054,x94051))),x94054)+~P22(f312(f312(f314(f860(f854(x94051),f854(x94051))),f312(f312(f239(f854(x94051),f854(x94051)),x94054),x94053)),f153(x94051,x94052)))
% 155.93/155.61 [9406]E(f312(f312(f129(x94061),f625(x94062,x94063,x94064,x94061)),f312(f312(f147(x94061),f627(x94062,x94063,x94064,x94061)),f628(x94062,x94063,x94064,x94061))),x94063)+~P22(f312(f312(f314(f860(f854(x94061),f854(x94061))),f312(f312(f239(f854(x94061),f854(x94061)),x94064),x94063)),f153(x94061,x94062)))
% 155.93/155.61 [9479]P22(f312(f312(f314(f860(x94791,x94791)),f312(f312(f239(x94791,x94791),x94792),f779(x94793,x94794,x94792,x94791))),f287(x94791,x94793)))+~P22(f312(f312(f314(f860(x94791,x94791)),f312(f312(f239(x94791,x94791),x94792),x94794)),f312(f312(f267(x94791,x94791,x94791),x94793),f287(x94791,x94793))))
% 155.93/155.61 [9544]P22(f312(f312(f227(a853),f151(x95441,x95442,x95443)),f151(x95441,x95444,x95443)))+~P22(f312(f312(f228(a853),f312(x95442,f604(x95444,x95442,x95443,x95441))),f312(x95444,f604(x95444,x95442,x95443,x95441))))
% 155.93/155.61 [9610]P22(f312(f312(f314(f860(x96101,x96101)),f312(f312(f239(x96101,x96101),f775(x96102,x96103,x96104,x96101)),x96103)),f287(x96101,x96102)))+~P22(f312(f312(f314(f860(x96101,x96101)),f312(f312(f239(x96101,x96101),x96104),x96103)),f312(f312(f267(x96101,x96101,x96101),x96102),f287(x96101,x96102))))
% 155.93/155.61 [5148]~E(x51482,x51483)+E(f166(x51481,x51482,f312(f312(f147(x51481),x51483),x51484)),x51484)
% 155.93/155.61 [5269]P22(f312(x52692,x52693))+E(f172(x52691,x52692,f312(f312(f147(x52691),x52693),x52694)),f127(x52691))
% 155.93/155.61 [5334]~P79(x53342)+E(f312(f312(f88(f861(x53341,x53342)),x53343),x53344),f312(f88(x53342),f312(x53343,x53344)))
% 155.93/155.61 [5346]~E(x53462,f2(a853))+E(f312(f312(f134(x53461),x53462),f312(f312(f147(x53461),x53463),x53464)),f312(f312(f147(x53461),x53463),x53464))
% 155.93/155.61 [5347]P22(f312(x53472,x53473))+E(f312(f132(x53471,x53472),f312(f312(f147(x53471),x53473),x53474)),f312(f132(x53471,x53472),x53474))
% 155.93/155.61 [5480]~E(x54802,x54804)+P22(f312(f312(f312(f289(x54801),x54802),x54803),x54804))
% 155.93/155.61 [5488]E(x54881,f127(x54882))+E(f140(x54883,f312(f312(f150(x54882,x54883),x54884),x54881)),f312(x54884,f140(x54882,x54881)))
% 155.93/155.61 [5502]~E(x55021,f72(x55022,x55024))+E(f312(x55021,f312(f312(f289(x55022),x55023),f189(f861(x55022,a846)))),x55023)
% 155.93/155.61 [5540]E(x55401,f127(x55402))+E(f312(f137(x55403),f312(f312(f150(x55402,x55403),x55404),x55401)),f312(x55404,f312(f137(x55402),x55401)))
% 155.93/155.61 [5640]~P22(f312(x56403,x56404))+P22(f312(f312(f312(f289(x56401),x56402),x56403),x56404))
% 155.93/155.61 [5747]~P13(x57472,x57474,x57471)+E(f312(x57471,f312(f312(f289(x57472),x57473),f189(f861(x57472,a846)))),x57473)
% 155.93/155.61 [5770]~E(x57702,x57703)+P22(f312(f312(f314(x57701),x57702),f312(f312(f289(x57701),x57703),x57704)))
% 155.93/155.61 [5776]~P107(x57761)+E(f312(f312(f89(x57761),x57762),f312(f312(f89(x57761),x57763),x57764)),f312(f312(f89(x57761),x57763),f312(f312(f89(x57761),x57762),x57764)))
% 155.93/155.61 [5777]~P87(x57771)+E(f312(f312(f124(x57771),x57772),f312(f312(f124(x57771),x57773),x57774)),f312(f312(f124(x57771),x57773),f312(f312(f124(x57771),x57772),x57774)))
% 155.93/155.61 [5779]~P98(x57791)+E(f312(f312(f124(x57791),x57792),f312(f312(f124(x57791),x57793),x57794)),f312(f312(f124(x57791),x57793),f312(f312(f124(x57791),x57792),x57794)))
% 155.93/155.61 [5780]~P87(x57801)+E(f312(f312(f115(x57801),x57802),f312(f312(f115(x57801),x57803),x57804)),f312(f312(f115(x57801),x57803),f312(f312(f115(x57801),x57802),x57804)))
% 155.93/155.61 [5782]~P99(x57821)+E(f312(f312(f115(x57821),x57822),f312(f312(f115(x57821),x57823),x57824)),f312(f312(f115(x57821),x57823),f312(f312(f115(x57821),x57822),x57824)))
% 155.93/155.61 [5783]~P107(x57831)+E(f312(f312(f90(x57831),x57832),f312(f312(f90(x57831),x57833),x57834)),f312(f312(f90(x57831),x57833),f312(f312(f90(x57831),x57832),x57834)))
% 155.93/155.61 [5785]~P103(x57851)+E(f312(f312(f225(x57851),x57852),f312(f312(f225(x57851),x57853),x57854)),f312(f312(f225(x57851),x57853),f312(f312(f225(x57851),x57852),x57854)))
% 155.93/155.61 [5787]~P103(x57871)+E(f312(f312(f226(x57871),x57872),f312(f312(f226(x57871),x57873),x57874)),f312(f312(f226(x57871),x57873),f312(f312(f226(x57871),x57872),x57874)))
% 155.93/155.61 [5792]E(x57921,x57922)+E(f166(x57923,x57921,f312(f312(f147(x57923),x57922),x57924)),f312(f312(f147(x57923),x57922),f166(x57923,x57921,x57924)))
% 155.93/155.61 [5805]~P22(f312(x58052,x58053))+E(f312(f132(x58051,x58052),f312(f312(f147(x58051),x58053),x58054)),f312(f312(f147(x58051),x58053),f312(f132(x58051,x58052),x58054)))
% 155.93/155.61 [5946]~P22(f312(x59462,x59463))+E(f172(x59461,x59462,f312(f312(f147(x59461),x59463),x59464)),f312(f312(f147(x59461),x59463),f172(x59461,x59462,x59464)))
% 155.93/155.61 [5992]P18(x59921,x59922,x59923)+~P18(x59921,x59922,f312(f312(f289(f852(x59921)),x59924),x59923))
% 155.93/155.61 [6003]E(x60031,f189(f861(x60032,a846)))+E(f312(f312(f50(x60032,f861(x60033,a846)),x60031),f312(f16(f861(x60033,a846),x60032),x60034)),x60034)
% 155.93/155.61 [6004]E(x60041,f189(f861(x60042,a846)))+E(f312(f312(f51(x60042,f861(x60043,a846)),x60041),f312(f16(f861(x60043,a846),x60042),x60044)),x60044)
% 155.93/155.61 [6012]~E(x60124,f189(f861(x60122,a846)))+E(f312(f312(f247(x60121,x60122),x60123),f312(f16(f861(x60122,a846),x60121),x60124)),f189(f861(f860(x60121,x60122),a846)))
% 155.93/155.61 [6013]~E(x60133,f189(f861(x60131,a846)))+E(f312(f312(f247(x60131,x60132),x60133),f312(f16(f861(x60132,a846),x60131),x60134)),f189(f861(f860(x60131,x60132),a846)))
% 155.93/155.61 [6058]E(x60581,f2(a853))+E(f312(f312(f134(x60582),x60581),f312(f312(f147(x60582),x60583),x60584)),f312(f312(f134(x60582),f312(f312(f21(a853),x60581),f87(a853))),x60584))
% 155.93/155.61 [6084]E(x60841,f189(f861(x60842,a846)))+E(f312(f290(x60842,x60843,f312(f16(x60843,x60842),x60844)),x60841),f312(f312(f289(x60843),x60844),f189(f861(x60843,a846))))
% 155.93/155.61 [6087]E(f312(f291(x60871,x60872,f312(f16(x60872,x60871),x60873)),x60874),f189(f861(x60871,a846)))+P22(f312(f312(f314(x60872),x60873),x60874))
% 155.93/155.61 [6155]~E(x61553,f189(f861(x61551,a846)))+E(f312(f312(f50(x61551,f861(x61552,a846)),x61553),f312(f16(f861(x61552,a846),x61551),x61554)),f189(f861(x61552,a846)))
% 155.93/155.61 [6156]~E(x61563,f189(f861(x61561,a846)))+E(f312(f312(f51(x61561,f861(x61562,a846)),x61563),f312(f16(f861(x61562,a846),x61561),x61564)),f235(f861(x61562,a846)))
% 155.93/155.61 [6158]~P60(x61581)+E(f54(x61581,f312(f312(f90(x61581),x61582),x61583),f312(f312(f90(x61581),x61582),x61584)),f312(f312(f90(x61581),x61582),f54(x61581,x61583,x61584)))
% 155.93/155.61 [6319]E(f312(f291(x63191,x63192,f312(f16(x63192,x63191),x63193)),x63194),f235(f861(x63191,a846)))+~P22(f312(f312(f314(x63192),x63193),x63194))
% 155.93/155.61 [6343]~P22(f312(f312(f314(x63431),x63432),x63434))+P22(f312(f312(f314(x63431),x63432),f312(f312(f289(x63431),x63433),x63434)))
% 155.93/155.61 [6348]P22(f312(x63481,x63482))+~P22(f312(f156(x63483,x63481),f312(f312(f147(x63483),x63482),x63484)))
% 155.93/155.61 [6356]~E(x63563,f312(f312(f21(a853),f312(f190(f854(x63561)),x63562)),f87(a853)))+E(f128(x63561,f312(f312(f155(x63561,x63562),x63563),x63564)),f128(x63561,x63562))
% 155.93/155.61 [6375]~P103(x63751)+E(f312(f312(f115(f861(x63751,a846)),f312(f281(x63751),x63752)),f283(x63751,x63753,x63754)),f283(x63751,x63753,f312(f312(f225(x63751),x63752),x63754)))
% 155.93/155.61 [6376]~P103(x63761)+E(f312(f312(f115(f861(x63761,a846)),f312(f234(x63761),x63762)),f283(x63761,x63763,x63764)),f283(x63761,f312(f312(f226(x63761),x63762),x63763),x63764))
% 155.93/155.61 [6391]E(f312(f312(f115(f861(x63911,a846)),x63912),f312(f312(f289(x63911),x63913),x63914)),f312(f312(f115(f861(x63911,a846)),x63912),x63914))+P22(f312(f312(f314(x63911),x63913),x63912))
% 155.93/155.61 [6403]E(f166(x64031,x64032,f312(f312(f129(x64031),x64033),x64034)),f312(f312(f129(x64031),x64033),f166(x64031,x64032,x64034)))+P22(f312(f312(f314(x64031),x64032),f312(f168(x64031),x64033)))
% 155.93/155.61 [6407]~P78(x64071)+E(f312(f312(f90(x64071),f312(f312(f240(x64071),x64072),x64073)),f312(f312(f240(x64071),x64072),x64074)),f312(f312(f240(x64071),x64072),f312(f312(f89(a853),x64073),x64074)))
% 155.93/155.61 [6408]~P107(x64081)+E(f312(f312(f90(x64081),f312(f312(f240(x64081),x64082),x64083)),f312(f312(f240(x64081),x64082),x64084)),f312(f312(f240(x64081),x64082),f312(f312(f89(a853),x64083),x64084)))
% 155.93/155.61 [6440]~P96(x64401)+E(f312(f312(f115(x64401),f312(f312(f124(x64401),x64402),x64403)),f312(f312(f124(x64401),x64402),x64404)),f312(f312(f124(x64401),x64402),f312(f312(f115(x64401),x64403),x64404)))
% 155.93/155.61 [6441]~P96(x64411)+E(f312(f312(f124(x64411),f312(f312(f115(x64411),x64412),x64413)),f312(f312(f115(x64411),x64412),x64414)),f312(f312(f115(x64411),x64412),f312(f312(f124(x64411),x64413),x64414)))
% 155.93/155.61 [6442]~P107(x64421)+E(f312(f312(f89(x64421),f312(f312(f90(x64421),x64422),x64423)),f312(f312(f90(x64421),x64422),x64424)),f312(f312(f90(x64421),x64422),f312(f312(f89(x64421),x64423),x64424)))
% 155.93/155.61 [6443]~P103(x64431)+E(f312(f312(f226(x64431),f312(f312(f225(x64431),x64432),x64433)),f312(f312(f225(x64431),x64432),x64434)),f312(f312(f225(x64431),x64432),f312(f312(f226(x64431),x64433),x64434)))
% 155.93/155.61 [6444]~P103(x64441)+E(f312(f312(f225(x64441),f312(f312(f226(x64441),x64442),x64443)),f312(f312(f226(x64441),x64442),x64444)),f312(f312(f226(x64441),x64442),f312(f312(f225(x64441),x64443),x64444)))
% 155.93/155.61 [6478]~P60(x64781)+E(f54(x64781,f312(f312(f90(x64781),x64782),x64783),f312(f312(f90(x64781),x64784),x64783)),f312(f312(f90(x64781),f54(x64781,x64782,x64784)),x64783))
% 155.93/155.61 [6479]~E(f312(f190(f854(x64791)),x64793),f312(f190(f854(x64792)),x64794))+E(f312(f312(f150(f860(x64791,x64792),x64792),f248(x64791,x64792)),f312(f312(f177(x64791,x64792),x64793),x64794)),x64794)
% 155.93/155.61 [6480]~E(f312(f190(f854(x64801)),x64803),f312(f190(f854(x64802)),x64804))+E(f312(f312(f150(f860(x64801,x64802),x64801),f246(x64801,x64802)),f312(f312(f177(x64801,x64802),x64803),x64804)),x64803)
% 155.93/155.61 [6486]P22(f312(f156(x64861,x64862),x64863))+~P22(f312(f156(x64861,x64862),f312(f312(f147(x64861),x64864),x64863)))
% 155.93/155.61 [6487]P22(f312(f156(x64871,x64872),x64873))+~P22(f312(f156(x64871,x64872),f312(f312(f129(x64871),x64874),x64873)))
% 155.93/155.61 [6488]P22(f312(f156(x64881,x64882),x64883))+~P22(f312(f156(x64881,x64882),f312(f312(f129(x64881),x64883),x64884)))
% 155.93/155.61 [6494]~P61(x64941)+E(f54(x64941,f312(f312(f21(x64941),x64942),f54(x64941,x64943,x64944)),x64944),f54(x64941,f312(f312(f21(x64941),x64942),x64943),x64944))
% 155.93/155.61 [6495]~P60(x64951)+E(f54(x64951,f312(f312(f90(x64951),x64952),f54(x64951,x64953,x64954)),x64954),f54(x64951,f312(f312(f90(x64951),x64952),x64953),x64954))
% 155.93/155.61 [6496]~P60(x64961)+E(f54(x64961,f312(f312(f89(x64961),x64962),f54(x64961,x64963,x64964)),x64964),f54(x64961,f312(f312(f89(x64961),x64962),x64963),x64964))
% 155.93/155.61 [6575]~P103(x65751)+E(f312(f312(f115(f861(x65751,a846)),f283(x65751,x65752,x65753)),f312(f281(x65751),x65754)),f283(x65751,x65752,f312(f312(f225(x65751),x65753),x65754)))
% 155.93/155.61 [6576]~P103(x65761)+E(f312(f312(f115(f861(x65761,a846)),f283(x65761,x65762,x65763)),f312(f234(x65761),x65764)),f283(x65761,f312(f312(f226(x65761),x65762),x65764),x65763))
% 155.93/155.61 [6581]~E(f312(f190(f854(x65811)),x65813),f312(f190(f854(x65812)),x65814))+E(f312(f312(f177(x65811,x65812),f312(f165(x65811),x65813)),f312(f165(x65812),x65814)),f312(f165(f860(x65811,x65812)),f312(f312(f177(x65811,x65812),x65813),x65814)))
% 155.93/155.61 [6594]E(x65941,f312(f312(f21(a853),f312(f190(f854(x65942)),x65943)),f87(a853)))+E(f128(x65942,f312(f312(f155(x65942,x65943),x65941),x65944)),f312(f312(f155(x65942,f128(x65942,x65943)),x65941),x65944))
% 155.93/155.61 [6605]~P22(f312(f133(x66052),x66054))+P22(f312(f133(f860(x66051,x66052)),f312(f312(f177(x66051,x66052),x66053),x66054)))
% 155.93/155.61 [6606]~P22(f312(f133(x66061),x66063))+P22(f312(f133(f860(x66061,x66062)),f312(f312(f177(x66061,x66062),x66063),x66064)))
% 155.93/155.61 [6695]E(x66951,f312(f312(f312(a201,x66952),x66953),f312(x66954,x66952)))+~P22(f312(f312(f195(f28(x66953,x66954)),x66952),x66951))
% 155.93/155.61 [6841]E(f312(f47(a853,x68411),x68412),x68413)+~P22(f312(f56(x68411,x68412),f312(f312(f239(a853,a853),x68413),x68414)))
% 155.93/155.61 [6887]E(f54(a853,x68871,x68872),x68873)+~P22(f312(f56(x68871,x68872),f312(f312(f239(a853,a853),x68874),x68873)))
% 155.93/155.61 [6890]P22(f312(f133(x68901),x68902))+~P22(f312(f133(x68903),f312(f312(f150(x68901,x68903),x68904),x68902)))
% 155.93/155.61 [6898]~P18(x68981,x68982,f312(f312(f289(f852(x68981)),x68983),x68984))+P18(x68981,x68982,f312(f312(f289(f852(x68981)),x68983),f189(f861(f852(x68981),a846))))
% 155.93/155.61 [6906]P22(f312(f312(f195(x69061),x69062),x69063))+~P22(f312(f312(f312(f312(a198,x69061),x69062),x69064),x69063))
% 155.93/155.61 [6977]E(f166(x69771,x69772,f312(f312(f129(x69771),x69773),x69774)),f312(f312(f129(x69771),f166(x69771,x69772,x69773)),x69774))+~P22(f312(f312(f314(x69771),x69772),f312(f168(x69771),x69773)))
% 155.93/155.61 [7071]~P61(x70711)+E(f54(x70711,f312(f312(f21(x70711),f54(x70711,x70712,x70713)),x70714),x70713),f54(x70711,f312(f312(f21(x70711),x70712),x70714),x70713))
% 155.93/155.61 [7073]~P60(x70731)+E(f54(x70731,f312(f312(f89(x70731),f54(x70731,x70732,x70733)),x70734),x70733),f54(x70731,f312(f312(f89(x70731),x70732),x70734),x70733))
% 155.93/155.61 [7074]~P60(x70741)+E(f54(x70741,f312(f312(f90(x70741),f54(x70741,x70742,x70743)),x70744),x70743),f54(x70741,f312(f312(f90(x70741),x70742),x70744),x70743))
% 155.93/155.61 [7255]~E(x72551,f312(f312(f147(x72552),x72553),x72554))+~P22(f312(f312(f227(a853),f312(f190(f854(x72552)),x72551)),f312(f190(f854(x72552)),x72554)))
% 155.93/155.61 [7328]~E(f312(f173(x73281,x73282),x73283),f312(f173(x73281,x73282),x73284))+E(f312(f290(f860(x73281,x73282),x73281,f246(x73281,x73282)),f312(f168(f860(x73281,x73282)),x73283)),f312(f290(f860(x73281,x73282),x73281,f246(x73281,x73282)),f312(f168(f860(x73281,x73282)),x73284)))
% 155.93/155.61 [7460]P19(x74601,x74602,x74603,f312(f168(x74601),x74604))+~P22(f312(f133(x74602),f312(f312(f150(x74601,x74602),x74603),x74604)))
% 155.93/155.61 [7535]~P22(f312(f312(f227(f861(x75351,a846)),x75352),x75354))+P22(f312(f312(f227(f861(x75351,a846)),x75352),f312(f312(f289(x75351),x75353),x75354)))
% 155.93/155.61 [7566]~P60(x75661)+E(f54(x75661,f312(f312(f89(x75661),f54(x75661,x75662,x75663)),f54(x75661,x75664,x75663)),x75663),f54(x75661,f312(f312(f89(x75661),x75662),x75664),x75663))
% 155.93/155.61 [7567]~P61(x75671)+E(f54(x75671,f312(f312(f21(x75671),f54(x75671,x75672,x75673)),f54(x75671,x75674,x75673)),x75673),f54(x75671,f312(f312(f21(x75671),x75672),x75674),x75673))
% 155.93/155.61 [7568]~P60(x75681)+E(f54(x75681,f312(f312(f90(x75681),f54(x75681,x75682,x75683)),f54(x75681,x75684,x75683)),x75683),f54(x75681,f312(f312(f90(x75681),x75682),x75684),x75683))
% 155.93/155.61 [7667]P22(f312(f312(f312(f312(a198,x76671),x76672),f312(a126,x76673)),x76674))+~P22(f312(f312(f312(f312(a198,x76671),x76672),x76673),x76674))
% 155.93/155.61 [7675]~E(f312(x76754,f399(x76754,x76753,x76751,x76752)),f189(f861(x76752,a846)))+E(f312(f312(f50(x76751,f861(x76752,a846)),x76753),x76754),f189(f861(x76752,a846)))
% 155.93/155.61 [7676]~E(f312(x76764,f634(x76764,x76763,x76761,x76762)),f235(f861(x76762,a846)))+E(f312(f312(f51(x76761,f861(x76762,a846)),x76763),x76764),f235(f861(x76762,a846)))
% 155.93/155.61 [7677]~E(f312(x76774,f412(x76774,x76773,x76772,x76771)),f189(f861(x76772,a846)))+E(f312(f312(f50(x76771,f861(x76772,a846)),x76773),x76774),f189(f861(x76772,a846)))
% 155.93/155.61 [7678]~E(f312(x76784,f635(x76784,x76783,x76782,x76781)),f235(f861(x76782,a846)))+E(f312(f312(f51(x76781,f861(x76782,a846)),x76783),x76784),f235(f861(x76782,a846)))
% 155.93/155.61 [8070]P22(f312(x80701,x80702))+~P22(f312(f312(f314(x80703),x80702),f312(f312(f115(f861(x80703,a846)),x80704),f312(f233(x80703),x80701))))
% 155.93/155.61 [8108]~P22(f312(f312(f227(f861(x81081,a846)),x81083),x81084))+P22(f312(f312(f227(f861(x81081,a846)),f312(f312(f289(x81081),x81082),x81083)),f312(f312(f289(x81081),x81082),x81084)))
% 155.93/155.61 [8278]P22(f312(f312(f195(x82781),x82782),f828(x82783,x82782,x82784,x82781)))+~P22(f312(f312(f195(f36(x82781,x82784)),x82782),x82783))
% 155.93/155.61 [8279]P22(f312(f312(f195(x82791),x82792),f837(x82793,x82792,x82794,x82791)))+~P22(f312(f312(f195(f36(x82791,x82794)),x82792),x82793))
% 155.93/155.61 [8288]P22(f312(x82882,x82883))+E(f312(f312(f134(x82881),f312(f190(f854(x82881)),f172(x82881,x82882,f312(f312(f147(x82881),x82883),x82884)))),f312(f312(f147(x82881),x82883),x82884)),f312(f312(f147(x82881),x82883),x82884))
% 155.93/155.61 [8409]~P22(f312(f312(f228(a853),f312(x84094,x84092)),f312(x84094,x84093)))+P22(f312(f312(f314(f860(x84091,x84091)),f312(f312(f239(x84091,x84091),x84092),x84093)),f312(f312(f266(a853,x84091),a232),x84094)))
% 155.93/155.61 [8504]~P22(f312(x85042,f721(x85044,x85042,x85043,x85041)))+E(f172(x85041,x85042,f312(f312(f129(x85041),x85043),x85044)),f312(f312(f129(x85041),x85043),f172(x85041,x85042,x85044)))
% 155.93/155.61 [8567]P19(f854(x85671),f854(x85672),f312(f150(x85671,x85672),x85673),x85674)+~P19(x85671,x85672,x85673,f48(f861(x85671,a846),f312(f290(f854(x85671),f861(x85671,a846),f168(x85671)),x85674)))
% 155.93/155.61 [8634]~P22(f312(x86342,x86343))+E(f312(f312(f134(x86341),f312(f190(f854(x86341)),f172(x86341,x86342,f312(f312(f147(x86341),x86343),x86344)))),f312(f312(f147(x86341),x86343),x86344)),f312(f312(f134(x86341),f312(f190(f854(x86341)),f172(x86341,x86342,x86344))),x86344))
% 155.93/155.61 [8675]~E(x86752,x86753)+E(f312(f132(x86751,f312(f312(f8(a846,a846,x86751),a307),f312(a309,x86752))),f312(f312(f147(x86751),x86753),x86754)),f312(f132(x86751,f312(f312(f8(a846,a846,x86751),a307),f312(a309,x86752))),x86754))
% 155.93/155.61 [8684]E(f312(f312(f50(x86841,f861(x86842,a846)),x86843),x86844),f189(f861(x86842,a846)))+P22(f312(f312(f314(x86841),f399(x86844,x86843,x86841,x86842)),x86843))
% 155.93/155.61 [8685]E(f312(f312(f51(x86851,f861(x86852,a846)),x86853),x86854),f235(f861(x86852,a846)))+P22(f312(f312(f314(x86851),f634(x86854,x86853,x86851,x86852)),x86853))
% 155.93/155.61 [8686]E(f312(f312(f50(x86861,f861(x86862,a846)),x86863),x86864),f189(f861(x86862,a846)))+P22(f312(f312(f314(x86861),f412(x86864,x86863,x86862,x86861)),x86863))
% 155.93/155.61 [8687]E(f312(f312(f51(x86871,f861(x86872,a846)),x86873),x86874),f235(f861(x86872,a846)))+P22(f312(f312(f314(x86871),f635(x86874,x86873,x86872,x86871)),x86873))
% 155.93/155.61 [8722]P22(f312(f312(f228(a853),f312(x87221,x87222)),f312(x87221,x87223)))+~P22(f312(f312(f314(f860(x87224,x87224)),f312(f312(f239(x87224,x87224),x87222),x87223)),f312(f312(f266(a853,x87224),a232),x87221)))
% 155.93/155.61 [8743]E(f172(x87431,x87432,f312(f312(f129(x87431),x87433),x87434)),f312(f312(f129(x87431),x87433),f172(x87431,x87432,x87434)))+P22(f312(f312(f314(x87431),f721(x87434,x87432,x87433,x87431)),f312(f168(x87431),x87433)))
% 155.93/155.61 [8779]P22(f312(f312(f195(x87791),f828(x87792,x87793,x87791,x87794)),x87792))+~P22(f312(f312(f195(f36(x87794,x87791)),x87793),x87792))
% 155.93/155.61 [8780]P22(f312(f312(f195(x87801),f837(x87802,x87803,x87801,x87804)),x87802))+~P22(f312(f312(f195(f36(x87804,x87801)),x87803),x87802))
% 155.93/155.61 [8889]~P60(x88891)+E(f312(f312(f89(x88891),f312(f312(f89(x88891),f312(f312(f90(x88891),x88892),f312(f47(x88891,x88893),x88892))),f54(x88891,x88893,x88892))),x88894),f312(f312(f89(x88891),x88893),x88894))
% 155.93/155.61 [8911]P22(f312(f312(f314(x89111),f373(x89112,x89113,x89114,x89111)),x89113))+~P22(f312(f312(f314(f861(x89111,a846)),x89114),f312(f312(f69(x89111),x89113),x89112)))
% 155.93/155.61 [8914]E(x89141,x89142)+~P22(f312(f312(f314(f860(x89143,x89143)),f312(f312(f239(x89143,x89143),x89141),x89142)),f312(f312(f184(f860(x89143,x89143),a846),f2(a853)),x89144)))
% 155.93/155.61 [8990]E(f312(f264(x89901,x89901,x89902),f312(f312(f289(x89901),f373(x89902,x89903,x89904,x89901)),f189(f861(x89901,a846)))),x89904)+~P22(f312(f312(f314(f861(x89901,a846)),x89904),f312(f312(f69(x89901),x89903),x89902)))
% 155.93/155.61 [8995]~P22(f312(f312(f314(f860(x89951,x89951)),f312(f312(f239(x89951,x89951),x89953),x89952)),f287(x89951,x89954)))+P22(f312(f312(f314(f860(x89951,x89951)),f312(f312(f239(x89951,x89951),x89952),x89953)),f287(x89951,f312(f265(x89951,x89951),x89954))))
% 155.93/155.61 [9018]~P22(f312(f312(f314(x90181),x90183),x90184))+P22(f312(f312(f314(f861(x90181,a846)),f312(f264(x90181,x90181,x90182),f312(f312(f289(x90181),x90183),f189(f861(x90181,a846))))),f312(f312(f69(x90181),x90184),x90182)))
% 155.93/155.61 [9029]P22(f312(f312(f314(f860(x90291,x90291)),f312(f312(f239(x90291,x90291),x90292),x90293)),f287(x90291,x90294)))+~P22(f312(f312(f314(f860(x90291,x90291)),f312(f312(f239(x90291,x90291),x90293),x90292)),f287(x90291,f312(f265(x90291,x90291),x90294))))
% 155.93/155.61 [9118]E(f312(f312(f155(x91181,f312(f165(x91181),x91182)),f312(f312(f21(a853),f312(f312(f21(a853),f312(f190(f854(x91181)),x91182)),x91183)),f87(a853))),x91184),f312(f165(x91181),f312(f312(f155(x91181,x91182),x91183),x91184)))+~P22(f312(f312(f228(a853),x91183),f312(f190(f854(x91181)),x91182)))
% 155.93/155.61 [9122]~P22(f312(x91222,f712(x91224,x91222,x91223,x91221)))+E(f312(f312(f134(x91221),f312(f190(f854(x91221)),f172(x91221,x91222,f312(f312(f129(x91221),x91223),x91224)))),f312(f312(f129(x91221),x91223),x91224)),f312(f312(f134(x91221),f312(f190(f854(x91221)),f172(x91221,x91222,x91224))),x91224))
% 155.93/155.61 [9161]~P19(x91612,x91611,x91613,f235(f861(x91612,a846)))+P22(f312(f312(f227(f861(x91611,a846)),f312(f290(x91612,x91611,x91613),f312(f88(f861(x91612,a846)),x91614))),f312(f88(f861(x91611,a846)),f312(f290(x91612,x91611,x91613),x91614))))
% 155.93/155.61 [9171]~P60(x91711)+E(f312(f312(f89(x91711),f312(f312(f89(x91711),f312(f312(f90(x91711),f312(f47(x91711,x91712),x91713)),x91713)),f54(x91711,x91712,x91713))),x91714),f312(f312(f89(x91711),x91712),x91714))
% 155.93/155.61 [9176]~P31(x91761)+E(f312(f138(x91761,x91762,f312(f7(x91762,x91761,x91761),f312(f312(f8(x91761,f861(x91761,x91761),x91762),f124(x91761)),x91763)),f189(x91761)),x91764),f312(f312(f50(x91762,x91761),f312(f168(x91762),x91764)),x91763))
% 155.93/155.61 [9177]~P31(x91771)+E(f312(f138(x91771,x91772,f312(f7(x91772,x91771,x91771),f312(f312(f8(x91771,f861(x91771,x91771),x91772),f115(x91771)),x91773)),f235(x91771)),x91774),f312(f312(f51(x91772,x91771),f312(f168(x91772),x91774)),x91773))
% 155.93/155.61 [9189]E(f312(f312(f134(x91891),f312(f190(f854(x91891)),f172(x91891,x91892,f312(f312(f129(x91891),x91893),x91894)))),f312(f312(f129(x91891),x91893),x91894)),f312(f312(f134(x91891),f312(f190(f854(x91891)),f172(x91891,x91892,x91894))),x91894))+P22(f312(f312(f314(x91891),f712(x91894,x91892,x91893,x91891)),f312(f168(x91891),x91893)))
% 155.93/155.61 [9254]~P22(f312(f312(f314(f860(f854(x92544),f854(x92544))),f312(f312(f239(f854(x92544),f854(x92544)),x92543),x92542)),f153(x92544,x92541)))+P22(f312(f312(f228(a853),f606(x92541,x92542,x92543,x92544)),f312(f190(f854(x92544)),x92543)))
% 155.93/155.61 [9282]~P22(f312(f312(f314(f860(f854(x92821),f854(x92821))),f312(f312(f239(f854(x92821),f854(x92821)),x92822),x92823)),f312(f265(f854(x92821),f854(x92821)),f153(x92821,x92824))))+P22(f312(f312(f314(f860(f854(x92821),f854(x92821))),f312(f312(f239(f854(x92821),f854(x92821)),x92822),x92823)),f153(x92821,f312(f265(x92821,x92821),x92824))))
% 155.93/155.61 [9283]P22(f312(f312(f314(f860(f854(x92831),f854(x92831))),f312(f312(f239(f854(x92831),f854(x92831)),x92832),x92833)),f312(f265(f854(x92831),f854(x92831)),f153(x92831,x92834))))+~P22(f312(f312(f314(f860(f854(x92831),f854(x92831))),f312(f312(f239(f854(x92831),f854(x92831)),x92832),x92833)),f153(x92831,f312(f265(x92831,x92831),x92834))))
% 155.93/155.61 [9318]~P22(f312(f312(f314(x93181),x93183),f312(f238(x93181,x93182),x93184)))+P22(f312(f312(f314(f860(x93181,x93182)),f312(f312(f239(x93181,x93182),x93183),f574(x93184,x93182,x93183,x93181))),x93184))
% 155.93/155.61 [9319]~P22(f312(f312(f314(x93191),x93193),f312(f238(x93191,x93192),x93194)))+P22(f312(f312(f314(f860(x93191,x93192)),f312(f312(f239(x93191,x93192),x93193),f576(x93194,x93192,x93193,x93191))),x93194))
% 155.93/155.61 [9429]~P22(f312(f70(f857(x94291)),f312(f290(x94292,f857(x94291),x94293),f235(f861(x94292,a846)))))+P22(f312(f70(f857(x94291)),f312(f290(x94292,f857(x94291),f180(x94292,x94291,x94293,f312(f173(x94292,x94291),x94294))),f235(f861(x94292,a846)))))
% 155.93/155.61 [9474]~P22(f312(f312(f314(f860(x94741,x94741)),f312(f312(f239(x94741,x94741),x94742),x94744)),f312(f312(f267(x94741,x94741,x94741),x94743),f287(x94741,x94743))))+P22(f312(f312(f314(f860(x94741,x94741)),f312(f312(f239(x94741,x94741),x94742),f775(x94743,x94744,x94742,x94741))),x94743))
% 155.93/155.61 [9664]~P22(f312(f312(f314(f860(f854(x96641),f854(x96641))),f312(f312(f239(f854(x96641),f854(x96641)),x96644),x96643)),f153(x96641,x96642)))+P22(f312(f312(f314(f860(x96641,x96641)),f312(f312(f239(x96641,x96641),f626(x96642,x96643,x96644,x96641)),f627(x96642,x96643,x96644,x96641))),x96642))
% 155.93/155.61 [9759]~P22(f312(f312(f314(f860(f854(x97591),f854(x97591))),f312(f312(f239(f854(x97591),f854(x97591)),x97592),x97594)),f153(x97591,x97593)))+P22(f312(f312(f314(f860(x97591,x97591)),f312(f312(f239(x97591,x97591),f312(f312(f161(x97591),x97592),f606(x97593,x97594,x97592,x97591))),f607(x97593,x97594,x97592,x97591))),x97593))
% 155.93/155.61 [9781]~P22(f312(f70(x97812),x97814))+E(f312(f312(f312(f74(f861(x97811,a846),x97812,f124(f861(x97811,a846))),f312(f312(f7(x97812,f861(x97811,a846),f861(x97811,a846)),f312(f312(f8(x97811,f861(f861(x97811,a846),f861(x97811,a846)),x97812),f289(x97811)),x97813)),f189(f861(x97811,a846)))),f189(f861(x97811,a846))),x97814),f312(f290(x97812,x97811,x97813),x97814))
% 155.93/155.61 [9887]~P19(x98871,x98872,x98873,f235(f861(x98871,a846)))+P22(f312(f312(f227(f861(x98871,a846)),f312(f291(x98871,x98872,x98873),f312(f312(f289(x98872),x98874),f189(f861(x98872,a846))))),f312(f312(f289(x98871),f94(x98871,f312(f312(f7(x98871,x98872,a846),f312(f312(f8(x98872,f861(x98872,a846),x98871),a309),x98873)),x98874))),f189(f861(x98871,a846)))))
% 155.93/155.61 [5551]~E(f312(f312(f129(x55511),x55512),x55514),x55513)+E(f312(f312(f169(x55511),f312(f190(f854(x55511)),x55512)),x55513),x55512)
% 155.93/155.61 [5552]~E(f312(f312(f129(x55522),x55523),x55521),x55524)+E(x55521,f312(f312(f134(x55522),f312(f190(f854(x55522)),x55523)),x55524))
% 155.93/155.61 [5563]~E(x55634,f2(a853))+E(f312(f312(f161(x55631),f312(f312(f147(x55631),x55632),x55633)),x55634),x55632)
% 155.93/155.61 [6068]~P107(x60681)+E(f312(f312(f240(x60681),f312(f312(f240(x60681),x60682),x60683)),x60684),f312(f312(f240(x60681),x60682),f312(f312(f90(a853),x60683),x60684)))
% 155.93/155.61 [6069]~P78(x60691)+E(f312(f312(f240(x60691),f312(f312(f240(x60691),x60692),x60693)),x60694),f312(f312(f240(x60691),x60692),f312(f312(f90(a853),x60693),x60694)))
% 155.93/155.61 [6085]E(x60851,f2(a853))+E(f312(f312(f161(x60852),f312(f312(f147(x60852),x60853),x60854)),x60851),f312(f312(f161(x60852),x60854),f312(f312(f21(a853),x60851),f87(a853))))
% 155.93/155.61 [6111]~P114(x61111)+E(f312(f312(f268(x61111),f312(f312(f90(x61111),x61112),x61113)),x61114),f312(f312(f90(x61111),x61112),f312(f312(f268(x61111),x61113),x61114)))
% 155.93/155.61 [6112]~P107(x61121)+E(f312(f312(f89(x61121),f312(f312(f89(x61121),x61122),x61123)),x61124),f312(f312(f89(x61121),x61122),f312(f312(f89(x61121),x61123),x61124)))
% 155.93/155.61 [6113]~P29(x61131)+E(f312(f312(f89(x61131),f312(f312(f89(x61131),x61132),x61133)),x61134),f312(f312(f89(x61131),x61132),f312(f312(f89(x61131),x61133),x61134)))
% 155.93/155.61 [6114]~P87(x61141)+E(f312(f312(f124(x61141),f312(f312(f124(x61141),x61142),x61143)),x61144),f312(f312(f124(x61141),x61142),f312(f312(f124(x61141),x61143),x61144)))
% 155.93/155.61 [6116]~P98(x61161)+E(f312(f312(f124(x61161),f312(f312(f124(x61161),x61162),x61163)),x61164),f312(f312(f124(x61161),x61162),f312(f312(f124(x61161),x61163),x61164)))
% 155.93/155.61 [6117]~P87(x61171)+E(f312(f312(f115(x61171),f312(f312(f115(x61171),x61172),x61173)),x61174),f312(f312(f115(x61171),x61172),f312(f312(f115(x61171),x61173),x61174)))
% 155.93/155.61 [6119]~P99(x61191)+E(f312(f312(f115(x61191),f312(f312(f115(x61191),x61192),x61193)),x61194),f312(f312(f115(x61191),x61192),f312(f312(f115(x61191),x61193),x61194)))
% 155.93/155.61 [6120]~P107(x61201)+E(f312(f312(f90(x61201),f312(f312(f90(x61201),x61202),x61203)),x61204),f312(f312(f90(x61201),x61202),f312(f312(f90(x61201),x61203),x61204)))
% 155.93/155.61 [6121]~P68(x61211)+E(f312(f312(f90(x61211),f312(f312(f90(x61211),x61212),x61213)),x61214),f312(f312(f90(x61211),x61212),f312(f312(f90(x61211),x61213),x61214)))
% 155.93/155.61 [6124]~P103(x61241)+E(f312(f312(f225(x61241),f312(f312(f225(x61241),x61242),x61243)),x61244),f312(f312(f225(x61241),x61242),f312(f312(f225(x61241),x61243),x61244)))
% 155.93/155.61 [6126]~P103(x61261)+E(f312(f312(f226(x61261),f312(f312(f226(x61261),x61262),x61263)),x61264),f312(f312(f226(x61261),x61262),f312(f312(f226(x61261),x61263),x61264)))
% 155.93/155.61 [6141]~P60(x61411)+E(f54(x61411,f312(f312(f89(x61411),x61412),f312(f312(f90(x61411),x61413),x61414)),x61414),f54(x61411,x61412,x61414))
% 155.93/155.61 [6142]~P60(x61421)+E(f54(x61421,f312(f312(f89(x61421),x61422),f312(f312(f90(x61421),x61423),x61424)),x61423),f54(x61421,x61422,x61423))
% 155.93/155.61 [6271]E(f312(f312(f161(x62711),f312(f312(f169(x62711),x62712),x62713)),x62714),f312(f312(f161(x62711),x62713),x62714))+~P22(f312(f312(f228(a853),x62714),x62712))
% 155.93/155.61 [6438]~P107(x64381)+E(f312(f312(f89(x64381),f312(f312(f89(x64381),x64382),x64383)),x64384),f312(f312(f89(x64381),f312(f312(f89(x64381),x64382),x64384)),x64383))
% 155.93/155.61 [6439]~P107(x64391)+E(f312(f312(f90(x64391),f312(f312(f90(x64391),x64392),x64393)),x64394),f312(f312(f90(x64391),f312(f312(f90(x64391),x64392),x64394)),x64393))
% 155.93/155.61 [6499]~P23(x64992)+E(f312(f312(f6(x64991,x64992),f312(f16(x64992,x64991),x64993)),x64994),f312(f312(f90(x64992),f312(f114(x64992),f312(f53(x64991),x64994))),x64993))
% 155.93/155.61 [6668]E(f312(f312(f115(f861(x66681,a846)),f312(f312(f289(x66681),x66682),x66683)),x66684),f312(f312(f115(f861(x66681,a846)),x66683),x66684))+P22(f312(f312(f314(x66681),x66682),x66684))
% 155.93/155.61 [6731]~P81(x67311)+E(f312(f312(f225(x67311),f312(f312(f89(x67311),x67312),x67313)),f312(f312(f89(x67311),x67314),x67313)),f312(f312(f89(x67311),f312(f312(f225(x67311),x67312),x67314)),x67313))
% 155.93/155.61 [6732]~P81(x67321)+E(f312(f312(f226(x67321),f312(f312(f89(x67321),x67322),x67323)),f312(f312(f89(x67321),x67324),x67323)),f312(f312(f89(x67321),f312(f312(f226(x67321),x67322),x67324)),x67323))
% 155.93/155.61 [6733]~P76(x67331)+E(f312(f312(f225(x67331),f312(f312(f21(x67331),x67332),x67333)),f312(f312(f21(x67331),x67334),x67333)),f312(f312(f21(x67331),f312(f312(f225(x67331),x67332),x67334)),x67333))
% 155.93/155.61 [6734]~P76(x67341)+E(f312(f312(f226(x67341),f312(f312(f21(x67341),x67342),x67343)),f312(f312(f21(x67341),x67344),x67343)),f312(f312(f21(x67341),f312(f312(f226(x67341),x67342),x67344)),x67343))
% 155.93/155.61 [6735]~P96(x67351)+E(f312(f312(f115(x67351),f312(f312(f124(x67351),x67352),x67353)),f312(f312(f124(x67351),x67354),x67353)),f312(f312(f124(x67351),f312(f312(f115(x67351),x67352),x67354)),x67353))
% 155.93/155.61 [6736]~P96(x67361)+E(f312(f312(f124(x67361),f312(f312(f115(x67361),x67362),x67363)),f312(f312(f115(x67361),x67364),x67363)),f312(f312(f115(x67361),f312(f312(f124(x67361),x67362),x67364)),x67363))
% 155.93/155.61 [6738]~P110(x67381)+E(f312(f312(f89(x67381),f312(f312(f90(x67381),x67382),x67383)),f312(f312(f90(x67381),x67384),x67383)),f312(f312(f90(x67381),f312(f312(f89(x67381),x67382),x67384)),x67383))
% 155.93/155.61 [6739]~P107(x67391)+E(f312(f312(f90(x67391),f312(f312(f240(x67391),x67392),x67393)),f312(f312(f240(x67391),x67394),x67393)),f312(f312(f240(x67391),f312(f312(f90(x67391),x67392),x67394)),x67393))
% 155.93/155.61 [6740]~P72(x67401)+E(f312(f312(f90(x67401),f312(f312(f240(x67401),x67402),x67403)),f312(f312(f240(x67401),x67404),x67403)),f312(f312(f240(x67401),f312(f312(f90(x67401),x67402),x67404)),x67403))
% 155.93/155.61 [6741]~P64(x67411)+E(f312(f312(f268(x67411),f312(f312(f240(x67411),x67412),x67413)),f312(f312(f240(x67411),x67414),x67413)),f312(f312(f240(x67411),f312(f312(f268(x67411),x67412),x67414)),x67413))
% 155.93/155.61 [6742]~P103(x67421)+E(f312(f312(f226(x67421),f312(f312(f225(x67421),x67422),x67423)),f312(f312(f225(x67421),x67424),x67423)),f312(f312(f225(x67421),f312(f312(f226(x67421),x67422),x67424)),x67423))
% 155.93/155.61 [6743]~P103(x67431)+E(f312(f312(f225(x67431),f312(f312(f226(x67431),x67432),x67433)),f312(f312(f226(x67431),x67434),x67433)),f312(f312(f226(x67431),f312(f312(f225(x67431),x67432),x67434)),x67433))
% 155.93/155.61 [6744]~P114(x67441)+E(f312(f312(f89(x67441),f312(f312(f268(x67441),x67442),x67443)),f312(f312(f268(x67441),x67444),x67443)),f312(f312(f268(x67441),f312(f312(f89(x67441),x67442),x67444)),x67443))
% 155.93/155.61 [6745]~P114(x67451)+E(f312(f312(f21(x67451),f312(f312(f268(x67451),x67452),x67453)),f312(f312(f268(x67451),x67454),x67453)),f312(f312(f268(x67451),f312(f312(f21(x67451),x67452),x67454)),x67453))
% 155.93/155.61 [6746]~P107(x67461)+E(f312(f312(f89(x67461),f312(f312(f90(x67461),x67462),x67463)),f312(f312(f90(x67461),x67464),x67463)),f312(f312(f90(x67461),f312(f312(f89(x67461),x67462),x67464)),x67463))
% 155.93/155.61 [6777]E(f312(f312(f155(x67771,x67772),x67773),x67774),x67772)+~P22(f312(f312(f227(a853),f312(f190(f854(x67771)),x67772)),x67773))
% 155.93/155.61 [6799]~P22(f312(x67993,x67994))+P22(f312(f312(f312(f124(f861(x67991,a846)),x67992),x67993),x67994))
% 155.93/155.61 [6801]~P22(f312(x68012,x68014))+P22(f312(f312(f312(f124(f861(x68011,a846)),x68012),x68013),x68014))
% 155.93/155.61 [6822]E(f312(f312(f161(x68221),f312(f312(f129(x68221),x68222),x68223)),x68224),f312(f312(f161(x68221),x68222),x68224))+~P22(f312(f312(f228(a853),x68224),f312(f190(f854(x68221)),x68222)))
% 155.93/155.61 [6834]E(f312(f312(f21(f861(x68341,a846)),f312(f312(f289(x68341),x68342),x68343)),x68344),f312(f312(f21(f861(x68341,a846)),x68343),x68344))+~P22(f312(f312(f314(x68341),x68342),x68344))
% 155.93/155.61 [6875]~E(f135(a853,f312(f282(a853,x68751),x68752)),f312(f312(f147(a853),x68754),x68753))+E(f135(a853,f312(f282(a853,f312(f312(f89(a853),x68751),f87(a853))),x68752)),x68753)
% 155.93/155.61 [6952]E(x69521,f2(a853))+E(f312(f312(f147(x69522),x69523),f312(f312(f169(x69522),f312(f312(f21(a853),x69521),f87(a853))),x69524)),f312(f312(f169(x69522),x69521),f312(f312(f147(x69522),x69523),x69524)))
% 155.93/155.61 [7051]E(f312(f312(f161(x70511),x70512),f312(f312(f21(a853),x70513),f312(f190(f854(x70511)),x70514))),f312(f312(f161(x70511),f312(f312(f129(x70511),x70514),x70512)),x70513))+P22(f312(f312(f228(a853),x70513),f312(f190(f854(x70511)),x70514)))
% 155.93/155.61 [7084]E(f312(f312(f115(f861(x70841,a846)),x70842),f312(f312(f289(x70841),x70843),x70844)),f312(f312(f289(x70841),x70843),f312(f312(f115(f861(x70841,a846)),x70842),x70844)))+~P22(f312(f312(f314(x70841),x70843),x70842))
% 155.93/155.61 [7119]E(f312(f312(f161(x71191),f312(f312(f155(x71191,x71192),x71193),x71194)),x71193),x71194)+~P22(f312(f312(f228(a853),x71193),f312(f190(f854(x71191)),x71192)))
% 155.93/155.61 [7138]E(x71381,f189(f861(x71382,a846)))+E(f312(f290(f860(x71383,x71382),x71383,f246(x71383,x71382)),f312(f312(f247(x71383,x71382),x71384),f312(f16(f861(x71382,a846),x71383),x71381))),x71384)
% 155.93/155.61 [7139]E(x71391,f189(f861(x71392,a846)))+E(f312(f290(f860(x71392,x71393),x71393,f248(x71392,x71393)),f312(f312(f247(x71392,x71393),x71391),f312(f16(f861(x71393,a846),x71392),x71394))),x71394)
% 155.93/155.61 [7196]E(f312(f312(f21(f861(x71961,a846)),f312(f312(f289(x71961),x71962),x71963)),x71964),f312(f312(f289(x71961),x71962),f312(f312(f21(f861(x71961,a846)),x71963),x71964)))+P22(f312(f312(f314(x71961),x71962),x71964))
% 155.93/155.61 [7232]P22(f312(x72321,x72322))+P22(f312(f312(f312(f312(a198,f35(x72321,x72323)),x72322),x72324),x72322))
% 155.93/155.61 [7239]~E(x72394,f189(f861(x72392,a846)))+E(f312(f290(f860(x72391,x72392),x72391,f246(x72391,x72392)),f312(f312(f247(x72391,x72392),x72393),f312(f16(f861(x72392,a846),x72391),x72394))),f189(f861(x72391,a846)))
% 155.93/155.61 [7240]~E(x72403,f189(f861(x72401,a846)))+E(f312(f290(f860(x72401,x72402),x72402,f248(x72401,x72402)),f312(f312(f247(x72401,x72402),x72403),f312(f16(f861(x72402,a846),x72401),x72404))),f189(f861(x72402,a846)))
% 155.93/155.61 [7295]~P22(f312(f312(f314(x72951),x72952),x72954))+P22(f312(f312(f314(x72951),x72952),f312(f312(f124(f861(x72951,a846)),x72953),x72954)))
% 155.93/155.61 [7298]~P22(f312(f312(f314(x72981),x72982),x72983))+P22(f312(f312(f314(x72981),x72982),f312(f312(f124(f861(x72981,a846)),x72983),x72984)))
% 155.93/155.62 [7316]E(f312(f312(f115(f861(x73161,a846)),f312(f312(f289(x73161),x73162),x73163)),x73164),f312(f312(f289(x73161),x73162),f312(f312(f115(f861(x73161,a846)),x73163),x73164)))+~P22(f312(f312(f314(x73161),x73162),x73164))
% 155.93/155.62 [7590]P22(f312(x75901,x75902))+~P22(f312(f312(f312(f115(f861(x75903,a846)),x75904),x75901),x75902))
% 155.93/155.62 [7591]P22(f312(x75911,x75912))+~P22(f312(f312(f312(f115(f861(x75913,a846)),x75911),x75914),x75912))
% 155.93/155.62 [7594]E(f312(f312(f6(x75941,a853),x75942),f312(f312(f21(f861(x75941,a846)),x75943),f312(f312(f289(x75941),x75944),f189(f861(x75941,a846))))),f312(f312(f6(x75941,a853),x75942),x75943))+P22(f312(f312(f314(x75941),x75944),x75943))
% 155.93/155.62 [7599]~P26(x75991)+E(f312(f162(x75991),f312(f312(f150(a853,x75991),x75992),f135(a853,f312(f282(a853,x75993),x75994)))),f312(f312(f6(a853,x75991),x75992),f312(f168(a853),f135(a853,f312(f282(a853,x75993),x75994)))))
% 155.93/155.62 [7600]~P26(x76001)+E(f312(f312(f6(a853,x76001),x76002),f312(f168(a853),f135(a853,f312(f282(a853,x76003),x76004)))),f312(f162(x76001),f312(f312(f150(a853,x76001),x76002),f135(a853,f312(f282(a853,x76003),x76004)))))
% 155.93/155.62 [7714]~E(x77143,x77144)+P22(f312(f71(x77141,x77142,f312(f312(f289(x77141),x77143),f189(f861(x77141,a846)))),x77144))
% 155.93/155.62 [7806]P22(f312(f312(f314(x78061),x78062),f312(f168(x78061),x78063)))+~P22(f312(f312(f314(x78061),x78062),f312(f168(x78061),f312(f312(f169(x78061),x78064),x78063))))
% 155.93/155.62 [7807]P22(f312(f312(f314(x78071),x78072),f312(f168(x78071),x78073)))+~P22(f312(f312(f314(x78071),x78072),f312(f168(x78071),f312(f312(f134(x78071),x78074),x78073))))
% 155.93/155.62 [7876]P22(f312(f312(f314(x78761),x78762),x78763))+~P22(f312(f312(f314(x78761),x78762),f312(f312(f21(f861(x78761,a846)),x78763),x78764)))
% 155.93/155.62 [7878]P22(f312(f312(f314(x78781),x78782),x78783))+~P22(f312(f312(f314(x78781),x78782),f312(f312(f115(f861(x78781,a846)),x78784),x78783)))
% 155.93/155.62 [7881]P22(f312(f312(f314(x78811),x78812),x78813))+~P22(f312(f312(f314(x78811),x78812),f312(f312(f115(f861(x78811,a846)),x78813),x78814)))
% 155.93/155.62 [7899]E(f312(f312(f129(x78991),f312(f312(f169(x78991),x78992),x78993)),f312(f312(f147(x78991),x78994),f312(f312(f134(x78991),f312(a126,x78992)),x78993))),f312(f312(f155(x78991,x78993),x78992),x78994))+~P22(f312(f312(f228(a853),x78992),f312(f190(f854(x78991)),x78993)))
% 155.93/155.62 [7922]P22(f312(f312(f314(x79221),x79222),x79223))+~P22(f312(f312(f227(f861(x79221,a846)),f312(f312(f289(x79221),x79222),x79224)),x79223))
% 155.93/155.62 [7955]~P22(f312(f312(f314(x79551),x79552),x79553))+~P22(f312(f312(f314(x79551),x79552),f312(f312(f21(f861(x79551,a846)),x79554),x79553)))
% 155.93/155.62 [7988]~P22(f312(f312(f228(a853),x79884),f312(f190(f854(x79881)),x79883)))+P22(f312(f312(f314(x79881),x79882),f312(f168(x79881),f312(f312(f155(x79881,x79883),x79884),x79882))))
% 155.93/155.62 [8046]E(f312(f312(f161(x80461),f312(f312(f134(x80461),x80462),x80463)),x80464),f312(f312(f161(x80461),x80463),f312(f312(f89(a853),x80462),x80464)))+~P22(f312(f312(f227(a853),f312(f312(f89(a853),x80462),x80464)),f312(f190(f854(x80461)),x80463)))
% 155.93/155.62 [8057]~P23(x80572)+E(f312(f312(f6(x80571,x80572),f312(f312(f8(a853,x80572,x80571),f114(x80572)),x80573)),x80574),f312(f114(x80572),f312(f312(f6(x80571,a853),x80573),x80574)))
% 155.93/155.62 [8058]~P111(x80582)+E(f312(f312(f6(x80581,x80582),f312(f312(f8(a1,x80582,x80581),f116(x80582)),x80583)),x80584),f312(f116(x80582),f312(f312(f6(x80581,a1),x80583),x80584)))
% 155.93/155.62 [8110]~P67(x81102)+E(f312(f312(f9(x81101,x81102),f312(f312(f8(x81102,x81102,x81101),f84(x81102)),x81103)),x81104),f312(f84(x81102),f312(f312(f9(x81101,x81102),x81103),x81104)))
% 155.93/155.62 [8111]~P30(x81112)+E(f312(f312(f6(x81111,x81112),f312(f312(f8(x81112,x81112,x81111),f88(x81112)),x81113)),x81114),f312(f88(x81112),f312(f312(f6(x81111,x81112),x81113),x81114)))
% 155.93/155.62 [8113]E(f312(f312(f6(x81131,a853),x81132),f312(f312(f21(f861(x81131,a846)),x81133),f312(f312(f289(x81131),x81134),f189(f861(x81131,a846))))),f312(f312(f21(a853),f312(f312(f6(x81131,a853),x81132),x81133)),f312(x81132,x81134)))+~P22(f312(f312(f314(x81131),x81134),x81133))
% 155.93/155.62 [8133]P22(f312(f312(f227(f861(x81331,a846)),x81332),x81333))+~P22(f312(f312(f227(f861(x81331,a846)),f312(f312(f289(x81331),x81334),x81332)),x81333))
% 155.93/155.62 [8348]E(f312(a126,f425(x83481,x83482,x83483,x83484)),x83482)+~P22(f312(f312(f312(f312(a198,f312(a27,x83484)),x83483),x83482),x83481))
% 155.93/155.62 [8350]E(f312(f312(f173(x83501,x83502),x83503),x83504),f192(x83502))+P22(f312(f312(f314(x83501),x83504),f312(f290(f860(x83501,x83502),x83501,f246(x83501,x83502)),f312(f168(f860(x83501,x83502)),x83503))))
% 155.93/155.62 [8351]P41(x83511,x83512)+~P41(x83511,f312(f312(f289(f860(x83511,x83511)),f312(f312(f239(x83511,x83511),x83513),x83514)),x83512))
% 155.93/155.62 [8352]P57(x83521,x83522)+~P57(x83521,f312(f312(f289(f860(x83521,x83521)),f312(f312(f239(x83521,x83521),x83523),x83524)),x83522))
% 155.93/155.62 [8361]~P103(x83611)+E(f312(f312(f145(x83611,x83611,f5(x83611)),x83612),f312(f312(f145(x83611,x83611,f5(x83611)),x83613),x83614)),f312(f312(f145(x83611,x83611,f5(x83611)),x83613),f312(f312(f145(x83611,x83611,f5(x83611)),x83612),x83614)))
% 155.93/155.62 [8370]E(x83701,x83702)+~P22(f312(f71(x83703,x83704,f312(f312(f289(x83703),x83701),f189(f861(x83703,a846)))),x83702))
% 155.93/155.62 [8383]E(f312(f312(f129(x83831),f312(f312(f169(x83831),x83832),x83833)),f312(f312(f169(x83831),x83834),f312(f312(f134(x83831),x83832),x83833))),f312(f312(f169(x83831),f312(f312(f89(a853),x83832),x83834)),x83833))+~P22(f312(f312(f227(a853),f312(f312(f89(a853),x83832),x83834)),f312(f190(f854(x83831)),x83833)))
% 155.93/155.62 [8422]P22(f312(f70(x84221),x84222))+~E(x84222,f312(f290(a853,x84221,x84223),f312(f233(a853),f312(f312(f7(a853,a853,a846),f228(a853)),x84224))))
% 155.93/155.62 [8443]~P86(x84431)+E(f312(f138(x84431,x84431,f89(x84431),f312(f312(f89(x84431),x84432),x84433)),x84434),f312(f312(f89(x84431),x84432),f312(f138(x84431,x84431,f89(x84431),x84433),x84434)))
% 155.93/155.62 [8480]P22(f312(f312(f227(f861(x84801,a846)),f312(f238(x84801,x84802),x84803)),f312(f238(x84801,x84802),x84804)))+~P22(f312(f312(f227(f861(f860(x84801,x84802),a846)),x84803),x84804))
% 155.93/155.62 [8495]~P22(f312(f312(f227(a853),x84952),x84954))+P22(f312(f312(f227(f861(x84951,a846)),f312(f168(x84951),f312(f312(f169(x84951),x84952),x84953))),f312(f168(x84951),f312(f312(f169(x84951),x84954),x84953))))
% 155.93/155.62 [8496]~P22(f312(f312(f227(a853),x84964),x84962))+P22(f312(f312(f227(f861(x84961,a846)),f312(f168(x84961),f312(f312(f134(x84961),x84962),x84963))),f312(f168(x84961),f312(f312(f134(x84961),x84964),x84963))))
% 155.93/155.62 [8544]~P22(f312(f70(x85441),f312(f312(f21(f861(x85441,a846)),x85442),x85444)))+P22(f312(f70(x85441),f312(f312(f21(f861(x85441,a846)),x85442),f312(f312(f289(x85441),x85443),x85444))))
% 155.93/155.62 [8578]P22(f312(f312(f314(f860(x85781,x85781)),x85782),f287(x85781,x85783)))+~P22(f312(f312(f314(f860(x85781,x85781)),x85782),f312(f312(f184(f860(x85781,x85781),a846),x85784),x85783)))
% 155.93/155.62 [8657]~P22(f312(f70(x86571),f312(f312(f21(f861(x86571,a846)),x86572),f312(f312(f289(x86571),x86574),x86573))))+P22(f312(f70(x86571),f312(f312(f21(f861(x86571,a846)),x86572),x86573)))
% 155.93/155.62 [8799]~E(f312(f312(f173(x87991,x87992),x87993),x87994),f192(x87992))+~P22(f312(f312(f314(x87991),x87994),f312(f290(f860(x87991,x87992),x87991,f246(x87991,x87992)),f312(f168(f860(x87991,x87992)),x87993))))
% 155.93/155.62 [8866]~P87(x88661)+P22(f312(f312(f227(x88661),f312(f312(f124(x88661),x88662),f312(f312(f115(x88661),x88663),x88664))),f312(f312(f115(x88661),f312(f312(f124(x88661),x88662),x88663)),f312(f312(f124(x88661),x88662),x88664))))
% 155.93/155.62 [8867]~P103(x88671)+P22(f312(f312(f227(x88671),f312(f312(f226(x88671),x88672),f312(f312(f225(x88671),x88673),x88674))),f312(f312(f225(x88671),f312(f312(f226(x88671),x88672),x88673)),f312(f312(f226(x88671),x88672),x88674))))
% 155.93/155.62 [9013]E(x90131,x90132)+~P22(f312(f312(f314(f860(x90133,x90133)),f312(f312(f239(x90133,x90133),x90131),x90132)),f312(f168(f860(x90133,x90133)),f312(f312(f177(x90133,x90133),x90134),x90134))))
% 155.93/155.62 [9047]~P22(f312(f312(f314(f860(x90471,x90471)),f312(f312(f239(x90471,x90471),x90473),x90472)),f287(x90471,x90474)))+~P41(x90471,f312(f312(f289(f860(x90471,x90471)),f312(f312(f239(x90471,x90471),x90472),x90473)),x90474))
% 155.93/155.62 [9048]~P22(f312(f312(f314(f860(x90481,x90481)),f312(f312(f239(x90481,x90481),x90483),x90482)),f287(x90481,x90484)))+~P57(x90481,f312(f312(f289(f860(x90481,x90481)),f312(f312(f239(x90481,x90481),x90482),x90483)),x90484))
% 155.93/155.62 [9051]E(x90511,x90512)+E(f312(f132(x90513,f312(f312(f8(a846,a846,x90513),a307),f312(a309,x90511))),f312(f312(f147(x90513),x90512),x90514)),f312(f312(f147(x90513),x90512),f312(f132(x90513,f312(f312(f8(a846,a846,x90513),a307),f312(a309,x90511))),x90514)))
% 155.93/155.62 [9094]~P87(x90941)+P22(f312(f312(f227(x90941),f312(f312(f124(x90941),f312(f312(f115(x90941),x90942),x90943)),f312(f312(f115(x90941),x90942),x90944))),f312(f312(f115(x90941),x90942),f312(f312(f124(x90941),x90943),x90944))))
% 155.93/155.62 [9095]~P103(x90951)+P22(f312(f312(f227(x90951),f312(f312(f226(x90951),f312(f312(f225(x90951),x90952),x90953)),f312(f312(f225(x90951),x90952),x90954))),f312(f312(f225(x90951),x90952),f312(f312(f226(x90951),x90953),x90954))))
% 155.93/155.62 [9170]~E(f312(f290(x91702,x91701,x91703),f235(f861(x91702,a846))),f235(f861(x91701,a846)))+P22(f312(f312(f227(f861(x91701,a846)),f312(f88(f861(x91701,a846)),f312(f290(x91702,x91701,x91703),x91704))),f312(f290(x91702,x91701,x91703),f312(f88(f861(x91702,a846)),x91704))))
% 155.93/155.62 [9247]P22(f312(f312(f312(f312(a198,f312(f223(a847),f312(a30,x92471))),x92472),f425(x92473,x92474,x92472,x92471)),x92473))+~P22(f312(f312(f312(f312(a198,f312(a27,x92471)),x92472),x92474),x92473))
% 155.93/155.62 [9489]P22(f312(f312(f314(f860(x94891,x94891)),f312(f312(f239(x94891,x94891),x94892),x94893)),f312(f265(x94891,x94891),f312(f312(f267(x94891,x94891,x94891),x94894),f287(x94891,x94894)))))+~P22(f312(f312(f314(f860(x94891,x94891)),f312(f312(f239(x94891,x94891),x94892),x94893)),f312(f312(f267(x94891,x94891,x94891),f312(f265(x94891,x94891),x94894)),f287(x94891,f312(f265(x94891,x94891),x94894)))))
% 155.93/155.62 [9490]~P22(f312(f312(f314(f860(x94901,x94901)),f312(f312(f239(x94901,x94901),x94902),x94903)),f312(f265(x94901,x94901),f312(f312(f267(x94901,x94901,x94901),x94904),f287(x94901,x94904)))))+P22(f312(f312(f314(f860(x94901,x94901)),f312(f312(f239(x94901,x94901),x94902),x94903)),f312(f312(f267(x94901,x94901,x94901),f312(f265(x94901,x94901),x94904)),f287(x94901,f312(f265(x94901,x94901),x94904)))))
% 155.93/155.62 [9512]~P22(f312(f312(f314(x95122),x95124),f312(f236(x95121,x95122),x95123)))+P22(f312(f312(f314(f860(x95121,x95122)),f312(f312(f239(x95121,x95122),f567(x95123,x95121,x95124,x95122)),x95124)),x95123))
% 155.93/155.62 [9513]~P22(f312(f312(f314(x95132),x95134),f312(f236(x95131,x95132),x95133)))+P22(f312(f312(f314(f860(x95131,x95132)),f312(f312(f239(x95131,x95132),f568(x95133,x95131,x95134,x95132)),x95134)),x95133))
% 155.93/155.62 [9532]~P22(f312(f312(f314(x95321),x95324),f312(f312(f124(f861(x95321,a846)),x95322),x95323)))+P22(f312(f312(f312(f124(f861(x95321,a846)),f312(f312(f7(x95321,f861(x95321,a846),a846),f314(x95321)),x95322)),f312(f312(f7(x95321,f861(x95321,a846),a846),f314(x95321)),x95323)),x95324))
% 155.93/155.62 [9533]~P22(f312(f312(f314(x95331),x95334),f312(f312(f115(f861(x95331,a846)),x95332),x95333)))+P22(f312(f312(f312(f115(f861(x95331,a846)),f312(f312(f7(x95331,f861(x95331,a846),a846),f314(x95331)),x95332)),f312(f312(f7(x95331,f861(x95331,a846),a846),f314(x95331)),x95333)),x95334))
% 155.93/155.62 [9608]~P22(f312(f312(f314(f860(x96081,x96081)),f312(f312(f239(x96081,x96081),x96084),x96083)),f312(f312(f267(x96081,x96081,x96081),x96082),f287(x96081,x96082))))+P22(f312(f312(f314(f860(x96081,x96081)),f312(f312(f239(x96081,x96081),f779(x96082,x96083,x96084,x96081)),x96083)),x96082))
% 155.93/155.62 [9653]P22(f312(f312(f314(x96531),x96532),f312(f312(f124(f861(x96531,a846)),x96533),x96534)))+~P22(f312(f312(f312(f124(f861(x96531,a846)),f312(f312(f7(x96531,f861(x96531,a846),a846),f314(x96531)),x96533)),f312(f312(f7(x96531,f861(x96531,a846),a846),f314(x96531)),x96534)),x96532))
% 155.93/155.62 [9654]P22(f312(f312(f314(x96541),x96542),f312(f312(f115(f861(x96541,a846)),x96543),x96544)))+~P22(f312(f312(f312(f115(f861(x96541,a846)),f312(f312(f7(x96541,f861(x96541,a846),a846),f314(x96541)),x96543)),f312(f312(f7(x96541,f861(x96541,a846),a846),f314(x96541)),x96544)),x96542))
% 155.93/155.62 [9940]P37(x99401,f312(f312(f7(x99401,f861(f860(x99401,x99401),a846),f861(x99401,a846)),f312(f312(f8(f861(x99401,f861(f861(f860(x99401,x99401),a846),a846)),f861(f861(f860(x99401,x99401),a846),f861(x99401,a846)),x99401),f7(x99401,f861(f860(x99401,x99401),a846),a846)),f312(f312(f8(f861(x99401,f860(x99401,x99401)),f861(x99401,f861(f861(f860(x99401,x99401),a846),a846)),x99401),f312(f8(f860(x99401,x99401),f861(f861(f860(x99401,x99401),a846),a846),x99401),f314(f860(x99401,x99401)))),f239(x99401,x99401)))),x99402),x99403,x99404)+~P22(f312(f312(f314(f860(f854(x99401),f854(x99401))),f312(f312(f239(f854(x99401),f854(x99401)),x99403),x99404)),f154(x99401,x99402)))
% 155.93/155.62 [9944]P58(x99441,f312(f312(f7(x99441,f861(f860(x99441,x99441),a846),f861(x99441,a846)),f312(f312(f8(f861(x99441,f861(f861(f860(x99441,x99441),a846),a846)),f861(f861(f860(x99441,x99441),a846),f861(x99441,a846)),x99441),f7(x99441,f861(f860(x99441,x99441),a846),a846)),f312(f312(f8(f861(x99441,f860(x99441,x99441)),f861(x99441,f861(f861(f860(x99441,x99441),a846),a846)),x99441),f312(f8(f860(x99441,x99441),f861(f861(f860(x99441,x99441),a846),a846),x99441),f314(f860(x99441,x99441)))),f239(x99441,x99441)))),x99442),x99443,x99444)+~P22(f312(f312(f314(f860(f861(x99441,a846),f861(x99441,a846))),f312(f312(f239(f861(x99441,a846),f861(x99441,a846)),x99443),x99444)),f303(x99441,x99442)))
% 155.93/155.62 [9972]E(x99721,x99722)+~E(f312(f312(f7(x99723,f861(f860(x99723,x99724),a846),f861(x99724,a846)),f312(f312(f8(f861(x99724,f861(f861(f860(x99723,x99724),a846),a846)),f861(f861(f860(x99723,x99724),a846),f861(x99724,a846)),x99723),f7(x99724,f861(f860(x99723,x99724),a846),a846)),f312(f312(f8(f861(x99724,f860(x99723,x99724)),f861(x99724,f861(f861(f860(x99723,x99724),a846),a846)),x99723),f312(f8(f860(x99723,x99724),f861(f861(f860(x99723,x99724),a846),a846),x99724),f314(f860(x99723,x99724)))),f239(x99723,x99724)))),x99721),f312(f312(f7(x99723,f861(f860(x99723,x99724),a846),f861(x99724,a846)),f312(f312(f8(f861(x99724,f861(f861(f860(x99723,x99724),a846),a846)),f861(f861(f860(x99723,x99724),a846),f861(x99724,a846)),x99723),f7(x99724,f861(f860(x99723,x99724),a846),a846)),f312(f312(f8(f861(x99724,f860(x99723,x99724)),f861(x99724,f861(f861(f860(x99723,x99724),a846),a846)),x99723),f312(f8(f860(x99723,x99724),f861(f861(f860(x99723,x99724),a846),a846),x99724),f314(f860(x99723,x99724)))),f239(x99723,x99724)))),x99722))
% 155.93/155.62 [9976]~P37(x99761,f312(f312(f7(x99761,f861(f860(x99761,x99761),a846),f861(x99761,a846)),f312(f312(f8(f861(x99761,f861(f861(f860(x99761,x99761),a846),a846)),f861(f861(f860(x99761,x99761),a846),f861(x99761,a846)),x99761),f7(x99761,f861(f860(x99761,x99761),a846),a846)),f312(f312(f8(f861(x99761,f860(x99761,x99761)),f861(x99761,f861(f861(f860(x99761,x99761),a846),a846)),x99761),f312(f8(f860(x99761,x99761),f861(f861(f860(x99761,x99761),a846),a846),x99761),f314(f860(x99761,x99761)))),f239(x99761,x99761)))),x99764),x99762,x99763)+P22(f312(f312(f314(f860(f854(x99761),f854(x99761))),f312(f312(f239(f854(x99761),f854(x99761)),x99762),x99763)),f154(x99761,x99764)))
% 155.93/155.62 [9977]~P58(x99771,f312(f312(f7(x99771,f861(f860(x99771,x99771),a846),f861(x99771,a846)),f312(f312(f8(f861(x99771,f861(f861(f860(x99771,x99771),a846),a846)),f861(f861(f860(x99771,x99771),a846),f861(x99771,a846)),x99771),f7(x99771,f861(f860(x99771,x99771),a846),a846)),f312(f312(f8(f861(x99771,f860(x99771,x99771)),f861(x99771,f861(f861(f860(x99771,x99771),a846),a846)),x99771),f312(f8(f860(x99771,x99771),f861(f861(f860(x99771,x99771),a846),a846),x99771),f314(f860(x99771,x99771)))),f239(x99771,x99771)))),x99774),x99772,x99773)+P22(f312(f312(f314(f860(f861(x99771,a846),f861(x99771,a846))),f312(f312(f239(f861(x99771,a846),f861(x99771,a846)),x99772),x99773)),f303(x99771,x99774)))
% 155.93/155.62 [7367]~P90(x73671)+E(f312(f312(f89(x73671),f312(f117(x73671),x73672)),f312(f312(f89(x73671),f312(f117(x73671),x73673)),x73674)),f312(f312(f89(x73671),f312(f117(x73671),f312(f312(f89(a1),x73672),x73673))),x73674))
% 155.93/155.62 [7368]~P90(x73681)+E(f312(f312(f89(x73681),f312(f117(x73681),x73682)),f312(f312(f21(x73681),f312(f117(x73681),x73683)),x73684)),f312(f312(f21(x73681),f312(f117(x73681),f312(f312(f89(a1),x73682),x73683))),x73684))
% 155.93/155.62 [7369]~P90(x73691)+E(f312(f312(f90(x73691),f312(f117(x73691),x73692)),f312(f312(f90(x73691),f312(f117(x73691),x73693)),x73694)),f312(f312(f90(x73691),f312(f117(x73691),f312(f312(f90(a1),x73692),x73693))),x73694))
% 155.93/155.62 [7411]~P23(x74111)+E(f312(f162(x74111),f312(f312(f150(x74112,x74111),f312(f16(x74111,x74112),x74113)),x74114)),f312(f312(f90(x74111),f312(f114(x74111),f312(f190(f854(x74112)),x74114))),x74113))
% 155.93/155.62 [7646]E(f312(f256(x76461,f312(f312(f147(f860(a113,x76461)),x76462),x76463)),x76464),f312(f248(a113,x76461),x76462))+~P22(f312(f312(f228(a113),x76464),f312(f246(a113,x76461),x76462)))
% 155.93/155.62 [7691]~P90(x76911)+E(f312(f312(f89(x76911),f312(f117(x76911),x76912)),f312(f312(f21(x76911),x76913),f312(f117(x76911),x76914))),f312(f312(f89(x76911),f312(f117(x76911),f312(f312(f89(a1),x76912),f312(f88(a1),x76914)))),x76913))
% 155.93/155.62 [7817]E(f312(f256(x78171,x78172),f312(f312(f21(a113),x78173),f312(f246(a113,x78171),x78174))),f312(f256(x78171,f312(f312(f147(f860(a113,x78171)),x78174),x78172)),x78173))+P22(f312(f312(f228(a113),x78173),f312(f246(a113,x78171),x78174)))
% 155.93/155.62 [8263]~P22(f312(f312(f314(x82631),x82632),f312(f168(x82631),f128(x82631,x82634))))+P22(f312(f312(f314(x82631),x82632),f312(f168(x82631),f128(x82631,f312(f312(f129(x82631),x82633),x82634)))))
% 155.93/155.62 [8264]~P22(f312(f312(f314(x82641),x82642),f312(f168(x82641),f128(x82641,x82643))))+P22(f312(f312(f314(x82641),x82642),f312(f168(x82641),f128(x82641,f312(f312(f129(x82641),x82643),x82644)))))
% 155.93/155.62 [8283]E(f312(f312(f124(f861(x82831,a846)),f312(f312(f115(f861(x82831,a846)),x82832),x82833)),x82834),f312(f312(f115(f861(x82831,a846)),x82832),f312(f312(f124(f861(x82831,a846)),x82833),x82834)))+~P22(f312(f312(f227(f861(x82831,a846)),x82834),x82832))
% 155.93/155.62 [8591]~E(f312(f312(f124(f861(x85911,a846)),f312(f312(f115(f861(x85911,a846)),x85913),x85914)),x85912),f312(f312(f115(f861(x85911,a846)),x85913),f312(f312(f124(f861(x85911,a846)),x85914),x85912)))+P22(f312(f312(f227(f861(x85911,a846)),x85912),x85913))
% 155.93/155.62 [8873]~P22(f312(f312(f227(f861(x88731,a846)),x88732),f312(f312(f124(f861(x88731,a846)),x88733),x88734)))+P22(f312(f312(f227(f861(x88731,a846)),f312(f312(f21(f861(x88731,a846)),x88732),x88733)),x88734))
% 155.93/155.62 [8935]~P22(f312(f312(f312(f312(a198,f312(a27,x89351)),x89352),f312(a126,x89353)),x89354))+P22(f312(f312(f312(f312(a198,f312(f223(a847),f312(a30,x89351))),x89352),x89353),x89354))
% 155.93/155.62 [8992]P22(f312(f312(f227(f861(x89921,a846)),x89922),f312(f312(f124(f861(x89921,a846)),x89923),x89924)))+~P22(f312(f312(f227(f861(x89921,a846)),f312(f312(f21(f861(x89921,a846)),x89922),x89923)),x89924))
% 155.93/155.62 [9046]P22(f312(f312(f312(f312(a198,f312(a27,x90461)),x90462),f312(a126,x90463)),x90464))+~P22(f312(f312(f312(f312(a198,f312(f223(a847),f312(a30,x90461))),x90462),x90463),x90464))
% 155.93/155.62 [9075]~P83(x90751)+E(f312(f84(x90751),f312(f312(f6(x90752,x90751),f312(f312(f8(x90751,x90751,x90752),f84(x90751)),x90753)),x90754)),f312(f312(f6(x90752,x90751),f312(f312(f8(x90751,x90751,x90752),f84(x90751)),x90753)),x90754))
% 155.93/155.62 [9245]~P83(x92451)+P22(f312(f312(f227(x92451),f2(x92451)),f312(f312(f6(x92452,x92451),f312(f312(f8(x92451,x92451,x92452),f84(x92451)),x92453)),x92454)))
% 155.93/155.62 [9250]~P30(x92501)+E(f312(f162(x92501),f312(f312(f150(x92502,x92501),f312(f82(x92501,x92501,x92502,f88(x92501)),x92503)),x92504)),f312(f88(x92501),f312(f162(x92501),f312(f312(f150(x92502,x92501),x92503),x92504))))
% 155.93/155.62 [9383]~P83(x93831)+P22(f312(f312(f227(x93831),f312(f84(x93831),f312(f312(f6(x93832,x93831),x93833),x93834))),f312(f312(f6(x93832,x93831),f312(f312(f8(x93831,x93831,x93832),f84(x93831)),x93833)),x93834)))
% 155.93/155.62 [9414]~E(f312(f312(f89(a853),x94141),x94144),f312(f312(f89(a853),x94143),x94142))+P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),f312(f312(f239(a853,a853),x94141),x94142)),f312(f312(f239(a853,a853),x94143),x94144))),a122))
% 155.93/155.62 [9415]~P22(f312(f312(f228(a853),x94151),x94153))+P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),f312(f312(f239(a853,a853),x94151),x94152)),f312(f312(f239(a853,a853),x94153),x94154))),a45))
% 155.93/155.62 [9416]~P22(f312(f312(f228(a853),x94161),x94163))+P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),f312(f312(f239(a853,a853),x94161),x94162)),f312(f312(f239(a853,a853),x94163),x94164))),a79))
% 155.93/155.62 [9557]E(f312(f312(f89(a853),x95571),x95572),f312(f312(f89(a853),x95573),x95574))+~P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),f312(f312(f239(a853,a853),x95571),x95574)),f312(f312(f239(a853,a853),x95573),x95572))),a122))
% 155.93/155.62 [9582]E(f312(f312(f161(x95821),f312(f312(f134(x95821),f312(f190(f854(x95821)),f172(x95821,x95822,x95823))),x95823)),x95824),f312(f312(f161(x95821),x95823),f312(f312(f89(a853),x95824),f312(f190(f854(x95821)),f172(x95821,x95822,x95823)))))+~P22(f312(f312(f228(a853),x95824),f312(f190(f854(x95821)),f312(f312(f134(x95821),f312(f190(f854(x95821)),f172(x95821,x95822,x95823))),x95823))))
% 155.93/155.62 [9599]~P22(f312(f312(f314(x95992),x95994),f312(f312(f50(x95991,f861(x95992,a846)),f235(f861(x95991,a846))),x95993)))+P22(f312(f312(f312(f50(x95991,f861(x95992,a846)),f235(f861(x95991,a846))),f312(f312(f8(f861(x95992,a846),f861(x95992,a846),x95991),f312(f7(x95992,f861(x95992,a846),a846),f314(x95992))),x95993)),x95994))
% 155.93/155.62 [9600]~P22(f312(f312(f314(x96002),x96004),f312(f312(f51(x96001,f861(x96002,a846)),f235(f861(x96001,a846))),x96003)))+P22(f312(f312(f312(f51(x96001,f861(x96002,a846)),f235(f861(x96001,a846))),f312(f312(f8(f861(x96002,a846),f861(x96002,a846),x96001),f312(f7(x96002,f861(x96002,a846),a846),f314(x96002))),x96003)),x96004))
% 155.93/155.62 [9680]~P22(f312(f57(x96801,x96802),f312(f312(f239(a1,a1),x96804),x96803)))+P22(f312(f57(f312(f88(a1),x96801),x96802),f312(f312(f239(a1,a1),f312(f312(f312(f108(a1),f312(f312(a309,x96803),f2(a1))),f312(f88(a1),x96804)),f312(f312(f21(a1),f312(f88(a1),x96804)),f87(a1)))),f312(f312(f312(f108(a1),f312(f312(a309,x96803),f2(a1))),f2(a1)),f312(f312(f21(a1),x96802),x96803)))))
% 155.93/155.62 [9689]P22(f312(f312(f314(x96891),x96892),f312(f312(f50(x96893,f861(x96891,a846)),f235(f861(x96893,a846))),x96894)))+~P22(f312(f312(f312(f50(x96893,f861(x96891,a846)),f235(f861(x96893,a846))),f312(f312(f8(f861(x96891,a846),f861(x96891,a846),x96893),f312(f7(x96891,f861(x96891,a846),a846),f314(x96891))),x96894)),x96892))
% 155.93/155.62 [9690]P22(f312(f312(f314(x96901),x96902),f312(f312(f51(x96903,f861(x96901,a846)),f235(f861(x96903,a846))),x96904)))+~P22(f312(f312(f312(f51(x96903,f861(x96901,a846)),f235(f861(x96903,a846))),f312(f312(f8(f861(x96901,a846),f861(x96901,a846),x96903),f312(f7(x96901,f861(x96901,a846),a846),f314(x96901))),x96904)),x96902))
% 155.93/155.62 [9700]E(f312(f312(f50(a853,f861(x97001,a846)),f235(f861(a853,a846))),x97002),f312(f312(f50(a853,f861(x97001,a846)),f235(f861(a853,a846))),x97003))+~E(f312(f312(f50(a853,f861(x97001,a846)),f312(f282(a853,f2(a853)),f490(x97002,x97004,x97003,x97001))),x97003),f312(f312(f50(a853,f861(x97001,a846)),f312(f282(a853,f2(a853)),f312(f312(f89(a853),f490(x97002,x97004,x97003,x97001)),x97004))),x97002))
% 155.93/155.62 [10033]~P22(f312(f312(f227(f861(f860(x100331,x100332),a846)),x100333),x100334))+P22(f312(f312(f227(f861(x100331,f861(x100332,a846))),f312(f312(f7(x100331,f861(f860(x100331,x100332),a846),f861(x100332,a846)),f312(f312(f8(f861(x100332,f861(f861(f860(x100331,x100332),a846),a846)),f861(f861(f860(x100331,x100332),a846),f861(x100332,a846)),x100331),f7(x100332,f861(f860(x100331,x100332),a846),a846)),f312(f312(f8(f861(x100332,f860(x100331,x100332)),f861(x100332,f861(f861(f860(x100331,x100332),a846),a846)),x100331),f312(f8(f860(x100331,x100332),f861(f861(f860(x100331,x100332),a846),a846),x100332),f314(f860(x100331,x100332)))),f239(x100331,x100332)))),x100333)),f312(f312(f7(x100331,f861(f860(x100331,x100332),a846),f861(x100332,a846)),f312(f312(f8(f861(x100332,f861(f861(f860(x100331,x100332),a846),a846)),f861(f861(f860(x100331,x100332),a846),f861(x100332,a846)),x100331),f7(x100332,f861(f860(x100331,x100332),a846),a846)),f312(f312(f8(f861(x100332,f860(x100331,x100332)),f861(x100332,f861(f861(f860(x100331,x100332),a846),a846)),x100331),f312(f8(f860(x100331,x100332),f861(f861(f860(x100331,x100332),a846),a846),x100332),f314(f860(x100331,x100332)))),f239(x100331,x100332)))),x100334)))
% 155.93/155.62 [10049]P22(f312(f312(f227(f861(f860(x100491,x100492),a846)),x100493),x100494))+~P22(f312(f312(f227(f861(x100491,f861(x100492,a846))),f312(f312(f7(x100491,f861(f860(x100491,x100492),a846),f861(x100492,a846)),f312(f312(f8(f861(x100492,f861(f861(f860(x100491,x100492),a846),a846)),f861(f861(f860(x100491,x100492),a846),f861(x100492,a846)),x100491),f7(x100492,f861(f860(x100491,x100492),a846),a846)),f312(f312(f8(f861(x100492,f860(x100491,x100492)),f861(x100492,f861(f861(f860(x100491,x100492),a846),a846)),x100491),f312(f8(f860(x100491,x100492),f861(f861(f860(x100491,x100492),a846),a846),x100492),f314(f860(x100491,x100492)))),f239(x100491,x100492)))),x100493)),f312(f312(f7(x100491,f861(f860(x100491,x100492),a846),f861(x100492,a846)),f312(f312(f8(f861(x100492,f861(f861(f860(x100491,x100492),a846),a846)),f861(f861(f860(x100491,x100492),a846),f861(x100492,a846)),x100491),f7(x100492,f861(f860(x100491,x100492),a846),a846)),f312(f312(f8(f861(x100492,f860(x100491,x100492)),f861(x100492,f861(f861(f860(x100491,x100492),a846),a846)),x100491),f312(f8(f860(x100491,x100492),f861(f861(f860(x100491,x100492),a846),a846),x100492),f314(f860(x100491,x100492)))),f239(x100491,x100492)))),x100494)))
% 155.93/155.62 [9125]~P22(f312(f312(f314(f860(x91251,x91251)),x91252),f287(x91251,x91254)))+P22(f312(f312(f314(f860(x91251,x91251)),x91252),f287(x91251,f312(f312(f124(f861(f860(x91251,x91251),a846)),x91253),x91254))))
% 155.93/155.62 [9126]~P22(f312(f312(f314(f860(x91261,x91261)),x91262),f287(x91261,x91263)))+P22(f312(f312(f314(f860(x91261,x91261)),x91262),f287(x91261,f312(f312(f124(f861(f860(x91261,x91261),a846)),x91263),x91264))))
% 155.93/155.62 [9480]~E(f312(f168(x94801),x94804),f179(x94801,x94802,x94803))+E(f312(f173(x94801,x94802),f312(f312(f150(x94801,f860(x94801,x94802)),f312(f312(f18(x94801,x94802,f860(x94801,x94802)),f239(x94801,x94802)),f312(f312(f8(f857(x94802),x94802,x94801),f223(x94802)),x94803))),x94804)),x94803)
% 155.93/155.62 [9799]~P22(f312(f312(f228(a853),f312(f312(f89(a853),x97991),x97994)),f312(f312(f89(a853),x97993),x97992)))+P22(f312(f312(f228(a1),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x97991),x97992)),f189(f861(f860(a853,a853),a846)))))),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x97993),x97994)),f189(f861(f860(a853,a853),a846)))))))
% 155.93/155.62 [9800]~P22(f312(f312(f227(a853),f312(f312(f89(a853),x98001),x98004)),f312(f312(f89(a853),x98003),x98002)))+P22(f312(f312(f227(a1),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x98001),x98002)),f189(f861(f860(a853,a853),a846)))))),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x98003),x98004)),f189(f861(f860(a853,a853),a846)))))))
% 155.93/155.62 [9882]P22(f312(f312(f228(a853),f312(f312(f89(a853),x98821),x98822)),f312(f312(f89(a853),x98823),x98824)))+~P22(f312(f312(f228(a1),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x98821),x98824)),f189(f861(f860(a853,a853),a846)))))),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x98823),x98822)),f189(f861(f860(a853,a853),a846)))))))
% 155.93/155.62 [9883]P22(f312(f312(f227(a853),f312(f312(f89(a853),x98831),x98832)),f312(f312(f89(a853),x98833),x98834)))+~P22(f312(f312(f227(a1),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x98831),x98834)),f189(f861(f860(a853,a853),a846)))))),f312(a98,f312(f264(f860(a853,a853),f860(a853,a853),a122),f312(f312(f289(f860(a853,a853)),f312(f312(f239(a853,a853),x98833),x98832)),f189(f861(f860(a853,a853),a846)))))))
% 155.93/155.62 [9925]P22(f312(f312(f227(f861(x99251,a846)),f312(f312(f50(a853,f861(x99251,a846)),f235(f861(a853,a846))),x99252)),f312(f312(f50(a853,f861(x99251,a846)),f235(f861(a853,a846))),x99253)))+~P22(f312(f312(f227(f861(x99251,a846)),f312(f312(f50(a853,f861(x99251,a846)),f312(f282(a853,f2(a853)),f491(x99253,x99254,x99252,x99251))),x99252)),f312(f312(f50(a853,f861(x99251,a846)),f312(f282(a853,f2(a853)),f312(f312(f89(a853),f491(x99253,x99254,x99252,x99251)),x99254))),x99253)))
% 155.93/155.62 [10024]~P22(f312(f312(f314(x100242),x100244),f312(f236(x100241,x100242),x100243)))+P22(f312(f245(x100241,x100242,f312(f312(f7(x100241,f861(f860(x100241,x100242),a846),f861(x100242,a846)),f312(f312(f8(f861(x100242,f861(f861(f860(x100241,x100242),a846),a846)),f861(f861(f860(x100241,x100242),a846),f861(x100242,a846)),x100241),f7(x100242,f861(f860(x100241,x100242),a846),a846)),f312(f312(f8(f861(x100242,f860(x100241,x100242)),f861(x100242,f861(f861(f860(x100241,x100242),a846),a846)),x100241),f312(f8(f860(x100241,x100242),f861(f861(f860(x100241,x100242),a846),a846),x100242),f314(f860(x100241,x100242)))),f239(x100241,x100242)))),x100243)),x100244))
% 155.93/155.62 [10025]~P22(f312(f312(f314(x100251),x100254),f312(f238(x100251,x100252),x100253)))+P22(f312(f244(x100251,x100252,f312(f312(f7(x100251,f861(f860(x100251,x100252),a846),f861(x100252,a846)),f312(f312(f8(f861(x100252,f861(f861(f860(x100251,x100252),a846),a846)),f861(f861(f860(x100251,x100252),a846),f861(x100252,a846)),x100251),f7(x100252,f861(f860(x100251,x100252),a846),a846)),f312(f312(f8(f861(x100252,f860(x100251,x100252)),f861(x100252,f861(f861(f860(x100251,x100252),a846),a846)),x100251),f312(f8(f860(x100251,x100252),f861(f861(f860(x100251,x100252),a846),a846),x100252),f314(f860(x100251,x100252)))),f239(x100251,x100252)))),x100253)),x100254))
% 155.93/155.62 [10036]P22(f312(f312(f314(x100361),x100362),f312(f236(x100363,x100361),x100364)))+~P22(f312(f245(x100363,x100361,f312(f312(f7(x100363,f861(f860(x100363,x100361),a846),f861(x100361,a846)),f312(f312(f8(f861(x100361,f861(f861(f860(x100363,x100361),a846),a846)),f861(f861(f860(x100363,x100361),a846),f861(x100361,a846)),x100363),f7(x100361,f861(f860(x100363,x100361),a846),a846)),f312(f312(f8(f861(x100361,f860(x100363,x100361)),f861(x100361,f861(f861(f860(x100363,x100361),a846),a846)),x100363),f312(f8(f860(x100363,x100361),f861(f861(f860(x100363,x100361),a846),a846),x100361),f314(f860(x100363,x100361)))),f239(x100363,x100361)))),x100364)),x100362))
% 155.93/155.62 [10037]P22(f312(f312(f314(x100371),x100372),f312(f238(x100371,x100373),x100374)))+~P22(f312(f244(x100371,x100373,f312(f312(f7(x100371,f861(f860(x100371,x100373),a846),f861(x100373,a846)),f312(f312(f8(f861(x100373,f861(f861(f860(x100371,x100373),a846),a846)),f861(f861(f860(x100371,x100373),a846),f861(x100373,a846)),x100371),f7(x100373,f861(f860(x100371,x100373),a846),a846)),f312(f312(f8(f861(x100373,f860(x100371,x100373)),f861(x100373,f861(f861(f860(x100371,x100373),a846),a846)),x100371),f312(f8(f860(x100371,x100373),f861(f861(f860(x100371,x100373),a846),a846),x100373),f314(f860(x100371,x100373)))),f239(x100371,x100373)))),x100374)),x100372))
% 155.93/155.62 [9710]P22(f312(f156(x97101,x97102),x97103))+~P22(f312(f156(x97101,f312(f312(f18(x97101,a846,a846),f312(f312(f8(a846,f861(a846,a846),x97101),a310),x97104)),x97102)),x97103))
% 155.93/155.62 [9711]P22(f312(f156(x97111,x97112),x97113))+~P22(f312(f156(x97111,f312(f312(f18(x97111,a846,a846),f312(f312(f8(a846,f861(a846,a846),x97111),a310),x97112)),x97114)),x97113))
% 155.93/155.62 [9802]~P107(x98021)+E(f312(f312(f90(x98021),f312(f312(f89(x98021),f87(x98021)),f87(x98021))),f312(f312(f6(a853,x98021),f312(f312(f8(x98021,x98021,a853),f312(f89(x98021),x98022)),f312(f312(f7(a853,x98021,x98021),f312(f312(f8(x98021,f861(x98021,x98021),a853),f90(x98021)),f114(x98021))),x98023))),f312(f279(a853),x98024))),f312(f312(f90(x98021),f312(f114(x98021),x98024)),f312(f312(f89(x98021),x98022),f312(f312(f89(x98021),x98022),f312(f312(f90(x98021),f312(f114(x98021),f312(f312(f21(a853),x98024),f87(a853)))),x98023)))))
% 155.93/155.62 [9947]P22(f312(x99471,f577(x99472,x99473,x99474,x99471)))+P41(x99472,f312(f233(f860(x99472,x99472)),f312(f249(x99472,x99472,a846),f312(f312(f8(f861(x99472,a846),f861(x99472,a846),x99472),f312(f18(x99472,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99472),a310),x99471))),f312(f312(f7(x99472,f861(x99472,x99472),f861(x99472,a846)),f312(f312(f8(f861(x99472,a846),f861(f861(x99472,x99472),f861(x99472,a846)),x99472),f8(x99472,a846,x99472)),a309)),x99473)))))
% 155.93/155.62 [9962]~P22(f312(f312(f228(a853),f312(x99624,f312(x99623,f577(x99621,x99623,x99624,x99622)))),f312(x99624,f577(x99621,x99623,x99624,x99622))))+P41(x99621,f312(f233(f860(x99621,x99621)),f312(f249(x99621,x99621,a846),f312(f312(f8(f861(x99621,a846),f861(x99621,a846),x99621),f312(f18(x99621,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99621),a310),x99622))),f312(f312(f7(x99621,f861(x99621,x99621),f861(x99621,a846)),f312(f312(f8(f861(x99621,a846),f861(f861(x99621,x99621),f861(x99621,a846)),x99621),f8(x99621,a846,x99621)),a309)),x99623)))))
% 155.93/155.62 [10066]~P22(f312(f312(f314(f860(x100661,x100661)),f312(f312(f239(x100661,x100661),x100663),x100664)),f312(f312(f124(f861(f860(x100661,x100661),a846)),x100662),f287(x100661,f189(f861(f860(x100661,x100661),a846))))))+P22(f312(f312(f312(f312(f124(f861(x100661,f861(x100661,a846))),f312(f312(f7(x100661,f861(f860(x100661,x100661),a846),f861(x100661,a846)),f312(f312(f8(f861(x100661,f861(f861(f860(x100661,x100661),a846),a846)),f861(f861(f860(x100661,x100661),a846),f861(x100661,a846)),x100661),f7(x100661,f861(f860(x100661,x100661),a846),a846)),f312(f312(f8(f861(x100661,f860(x100661,x100661)),f861(x100661,f861(f861(f860(x100661,x100661),a846),a846)),x100661),f312(f8(f860(x100661,x100661),f861(f861(f860(x100661,x100661),a846),a846),x100661),f314(f860(x100661,x100661)))),f239(x100661,x100661)))),x100662)),a309),x100663),x100664))
% 155.93/155.62 [10076]P22(f312(f312(f314(f860(x100761,x100761)),f312(f312(f239(x100761,x100761),x100762),x100763)),f312(f312(f124(f861(f860(x100761,x100761),a846)),x100764),f287(x100761,f189(f861(f860(x100761,x100761),a846))))))+~P22(f312(f312(f312(f312(f124(f861(x100761,f861(x100761,a846))),f312(f312(f7(x100761,f861(f860(x100761,x100761),a846),f861(x100761,a846)),f312(f312(f8(f861(x100761,f861(f861(f860(x100761,x100761),a846),a846)),f861(f861(f860(x100761,x100761),a846),f861(x100761,a846)),x100761),f7(x100761,f861(f860(x100761,x100761),a846),a846)),f312(f312(f8(f861(x100761,f860(x100761,x100761)),f861(x100761,f861(f861(f860(x100761,x100761),a846),a846)),x100761),f312(f8(f860(x100761,x100761),f861(f861(f860(x100761,x100761),a846),a846),x100761),f314(f860(x100761,x100761)))),f239(x100761,x100761)))),x100764)),a309),x100762),x100763))
% 155.93/155.62 [9933]~P104(x99333)+E(f99(x99331,f312(f312(f18(x99331,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99331),a310),x99332)),f312(f312(f8(f861(x99331,a846),a846,x99331),f97(x99331)),f312(f312(f8(f861(x99331,a846),f861(x99331,a846),x99331),f312(f18(x99331,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99331),a315),x99332))),f312(f312(f8(x99333,f861(x99331,a846),x99331),f312(f7(x99331,x99333,a846),f312(f312(f8(x99333,f861(x99333,a846),x99331),f227(x99333)),x99334))),x99334))))),f312(f101(x99331,x99333,x99334),x99332))
% 155.93/155.62 [9975]~P104(x99753)+E(f99(x99751,f312(f312(f18(x99751,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99751),a310),x99752)),f312(f312(f8(f861(x99751,a846),a846,x99751),f97(x99751)),f312(f312(f8(f861(x99751,a846),f861(x99751,a846),x99751),f312(f18(x99751,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99751),a315),x99752))),f312(f312(f7(x99751,f861(x99751,x99753),f861(x99751,a846)),f312(f312(f8(f861(x99753,a846),f861(f861(x99751,x99753),f861(x99751,a846)),x99751),f8(x99753,a846,x99751)),f312(f312(f8(x99753,f861(x99753,a846),x99751),f227(x99753)),x99754))),x99754))))),f104(x99751,x99753,x99754,x99752))
% 155.93/155.62 [10022]E(f312(f312(f147(f854(x100221)),f312(f312(f147(x100221),x100222),f312(f138(f854(x100221),f854(x100221),f129(x100221),f127(x100221)),f312(f312(f150(f854(x100221),f854(x100221)),f152(f854(x100221),x100221,f127(x100221),f312(f312(f8(f854(x100221),f861(f854(x100221),f854(x100221)),x100221),f16(f854(x100221),f854(x100221))),f312(f312(f7(x100221,f854(x100221),f854(x100221)),f147(x100221)),f127(x100221))))),x100223)))),f175(x100221,f312(f312(f147(f854(x100221)),x100224),f312(f138(f854(f854(x100221)),f854(f854(x100221)),f129(f854(x100221)),f127(f854(x100221))),f312(f312(f150(f854(x100221),f854(f854(x100221))),f152(f854(f854(x100221)),x100221,f127(f854(x100221)),f312(f16(f861(f854(x100221),f854(f854(x100221))),x100221),f312(f312(f7(f854(x100221),f854(f854(x100221)),f854(f854(x100221))),f147(f854(x100221))),f127(f854(x100221)))))),x100223))))),f175(x100221,f312(f312(f147(f854(x100221)),f312(f312(f147(x100221),x100222),x100224)),x100223)))+~P22(f312(f300(f854(f854(x100221)),f176(x100221)),f312(f312(f147(f854(x100221)),f312(f312(f147(x100221),x100222),x100224)),x100223)))
% 155.93/155.62 [10065]~P22(f312(f70(x100652),f312(f233(x100652),x100654)))+P22(f312(f70(x100651),f312(f233(x100651),f312(f312(f8(f861(x100652,a846),a846,x100651),f96(x100652)),f312(f312(f7(x100651,f861(x100652,a846),f861(x100652,a846)),f312(f312(f8(f861(x100652,f861(a846,a846)),f861(f861(x100652,a846),f861(x100652,a846)),x100651),f18(x100652,a846,a846)),f312(f312(f8(f861(x100652,a846),f861(x100652,f861(a846,a846)),x100651),f312(f8(a846,f861(a846,a846),x100652),a310)),f312(f312(f7(x100651,f861(x100652,x100651),f861(x100652,a846)),f312(f312(f8(f861(x100651,a846),f861(f861(x100652,x100651),f861(x100652,a846)),x100651),f8(x100651,a846,x100652)),a309)),x100653)))),x100654)))))
% 155.93/155.62 [8153]P36(x81531,x81532,x81533,x81534)+~P36(x81531,x81532,f180(x81531,x81532,x81535,x81533),x81534)
% 155.93/155.62 [5578]E(f312(f312(f289(x55781),x55782),f179(x55781,x55783,x55784)),f179(x55781,x55783,x55784))+~E(f312(x55784,x55782),f312(f219(x55783),x55785))
% 155.93/155.62 [5971]P22(f312(f245(x59711,x59712,x59713),x59714))+~P22(f312(f312(x59713,x59715),x59714))
% 155.93/155.62 [5973]P22(f312(f244(x59731,x59732,x59733),x59734))+~P22(f312(f312(x59733,x59734),x59735))
% 155.93/155.62 [5976]~E(f312(x59764,x59762),f312(f219(x59763),x59765))+P22(f312(f312(f314(x59761),x59762),f179(x59761,x59763,x59764)))
% 155.93/155.62 [5977]~E(f312(x59774,x59775),f312(f219(x59771),x59772))+P22(f312(f312(f314(x59771),x59772),f181(x59773,x59771,x59774)))
% 155.93/155.62 [6564]~E(x65643,f2(a113))+E(f312(f259(x65641,x65642,x65643,x65644),x65645),f312(f239(x65641,x65642),x65645))
% 155.93/155.62 [6638]~E(f312(x66384,x66385),f192(x66382))+E(f312(f221(f857(x66381),x66382,f192(x66381),x66383),f312(x66384,x66385)),f192(x66381))
% 155.93/155.62 [7251]E(f312(x72511,x72512),f192(x72513))+~E(f312(f180(x72514,x72513,x72515,x72511),x72512),f192(x72513))
% 155.93/155.62 [7252]E(f312(x72521,x72522),f192(x72523))+~E(f312(f180(x72524,x72523,x72521,x72525),x72522),f192(x72523))
% 155.93/155.62 [7287]E(f312(f180(x72871,x72872,x72873,x72874),x72875),f312(x72873,x72875))+P22(f312(f312(f314(x72871),x72875),f179(x72871,x72872,x72874)))
% 155.93/155.62 [7288]E(f312(f180(x72881,x72882,x72883,x72884),x72885),f312(x72884,x72885))+P22(f312(f312(f314(x72881),x72885),f179(x72881,x72882,x72883)))
% 155.93/155.62 [7604]~P15(x76044,x76041,x76042,x76045)+E(f312(f82(x76041,x76041,x76041,f312(x76042,x76043)),f312(x76042,x76043)),f312(x76042,x76043))
% 155.93/155.62 [7651]E(f312(f180(x76511,x76512,x76513,x76514),x76515),f312(x76514,x76515))+~P22(f312(f312(f314(x76511),x76515),f179(x76511,x76512,x76514)))
% 155.93/155.62 [8327]P22(f312(f312(f314(f860(x83271,x83271)),f312(f312(f239(x83271,x83271),x83272),x83273)),f306(x83271,x83274,x83275)))+~P22(f312(f312(f228(a853),f312(x83274,x83272)),f312(x83274,x83273)))
% 155.93/155.62 [8428]~P22(f312(f312(f314(x84284),x84283),f277(x84284,x84281,x84282,x84285)))+P22(f312(f312(x84281,x84282),x84283))
% 155.93/155.62 [8429]~P22(f312(f312(f314(x84294),x84293),f274(x84294,x84291,x84292,x84295)))+P22(f312(f312(x84291,x84292),x84293))
% 155.93/155.62 [8430]~P22(f312(f312(f314(x84304),x84302),f277(x84304,x84301,x84305,x84303)))+P22(f312(f312(x84301,x84302),x84303))
% 155.93/155.62 [8431]~P22(f312(f312(f314(x84314),x84312),f274(x84314,x84311,x84315,x84313)))+P22(f312(f312(x84311,x84312),x84313))
% 155.93/155.62 [8568]~P56(x85682,x85681,x85685,x85683,x85684)+E(f312(f290(x85681,x85682,x85683),x85684),f235(f861(x85682,a846)))
% 155.93/155.62 [9003]~P39(x90031,x90032,x90033,x90034,x90035)+P39(x90031,x90032,x90033,f312(f165(x90031),x90034),f312(f165(x90032),x90035))
% 155.93/155.62 [9005]~P39(x90051,x90052,x90053,f312(f165(x90051),x90054),x90055)+P39(x90051,x90052,x90053,x90054,f312(f165(x90052),x90055))
% 155.93/155.62 [9006]~P39(x90061,x90062,x90063,x90064,f312(f165(x90062),x90065))+P39(x90061,x90062,x90063,f312(f165(x90061),x90064),x90065)
% 155.93/155.62 [9011]P39(x90111,x90112,x90113,x90114,x90115)+~P39(x90111,x90112,x90113,f312(f165(x90111),x90114),f312(f165(x90112),x90115))
% 155.93/155.62 [9407]P22(f312(f312(f314(f860(f854(x94071),f854(x94071))),f312(f312(f239(f854(x94071),f854(x94071)),f312(f312(f147(x94071),x94072),x94073)),f312(f312(f147(x94071),x94072),x94074))),f153(x94071,x94075)))+~P22(f312(f312(f314(f860(f854(x94071),f854(x94071))),f312(f312(f239(f854(x94071),f854(x94071)),x94073),x94074)),f153(x94071,x94075)))
% 155.93/155.62 [9408]P22(f312(f312(f314(f860(f854(x94081),f854(x94081))),f312(f312(f239(f854(x94081),f854(x94081)),f312(f312(f129(x94081),x94082),x94083)),f312(f312(f129(x94081),x94082),x94084))),f143(x94081,x94085)))+~P22(f312(f312(f314(f860(f854(x94081),f854(x94081))),f312(f312(f239(f854(x94081),f854(x94081)),x94083),x94084)),f143(x94081,x94085)))
% 155.93/155.62 [9587]E(f312(f312(f147(x95871),f592(x95872,x95873,x95874,x95875,x95871)),f593(x95872,x95873,x95874,x95875,x95871)),x95875)+~P22(f312(f312(f314(f860(f854(x95871),f854(x95871))),f312(f312(f239(f854(x95871),f854(x95871)),x95875),f312(f312(f147(x95871),x95874),x95873))),f154(x95871,x95872)))
% 155.93/155.62 [9611]E(f312(f312(f147(x96111),f594(x96112,x96113,x96114,x96115,x96111)),f595(x96112,x96113,x96114,x96115,x96111)),x96113)+~P22(f312(f312(f314(f860(f854(x96111),f854(x96111))),f312(f312(f239(f854(x96111),f854(x96111)),f312(f312(f147(x96111),x96115),x96114)),x96113)),f154(x96111,x96112)))
% 155.93/155.62 [9771]~P22(f312(f312(f314(f860(f854(x97711),f854(x97711))),f312(f312(f239(f854(x97711),f854(x97711)),f312(f312(f147(x97711),x97715),x97712)),x97714)),f154(x97711,x97713)))+P22(f312(f312(f314(f860(f854(x97711),f854(x97711))),f312(f312(f239(f854(x97711),f854(x97711)),x97712),f595(x97713,x97714,x97712,x97715,x97711))),f154(x97711,x97713)))
% 155.93/155.62 [9846]~P22(f312(f312(f314(f860(f854(x98461),f854(x98461))),f312(f312(f239(f854(x98461),f854(x98461)),x98465),f312(f312(f147(x98461),x98464),x98463))),f154(x98461,x98462)))+P22(f312(f312(f314(f860(f854(x98461),f854(x98461))),f312(f312(f239(f854(x98461),f854(x98461)),f593(x98462,x98463,x98464,x98465,x98461)),x98463)),f154(x98461,x98462)))
% 155.93/155.62 [10016]P22(f312(f312(f314(f860(x100161,x100161)),f312(f312(f239(x100161,x100161),f312(x100162,f312(f312(f89(a853),x100163),x100164))),f312(x100162,x100163))),f287(x100161,x100165)))+~P22(f312(f312(f314(f860(x100161,x100161)),f312(f312(f239(x100161,x100161),f312(x100162,f312(a126,f755(x100164,x100163,x100165,x100162,x100161)))),f312(x100162,f755(x100164,x100163,x100165,x100162,x100161)))),f287(x100161,x100165)))
% 155.93/155.62 [10039]E(x100391,f2(a113))+E(f312(f221(f860(f854(x100392),x100393),f860(x100392,x100393),f312(f312(f239(f854(x100392),x100393),f127(x100392)),x100394),f312(f249(x100392,x100393,f860(f854(x100392),x100393)),f312(f312(f7(x100392,f861(x100393,f860(f854(x100392),x100393)),f861(x100393,f860(f854(x100392),x100393))),f312(f312(f8(f861(f860(f854(x100392),x100393),f860(f854(x100392),x100393)),f861(f861(x100393,f860(f854(x100392),x100393)),f861(x100393,f860(f854(x100392),x100393))),x100392),f8(f860(f854(x100392),x100393),f860(f854(x100392),x100393),x100393)),f312(f312(f8(f861(f854(x100392),f861(x100393,f860(f854(x100392),x100393))),f861(f860(f854(x100392),x100393),f860(f854(x100392),x100393)),x100392),f249(f854(x100392),x100393,f860(f854(x100392),x100393))),f312(f312(f8(f861(f854(x100392),f854(x100392)),f861(f854(x100392),f861(x100393,f860(f854(x100392),x100393))),x100392),f312(f8(f854(x100392),f861(x100393,f860(f854(x100392),x100393)),f854(x100392)),f239(f854(x100392),x100393))),f147(x100392))))),f131(x100393,x100392,x100395,f312(f312(f21(a113),x100391),f87(a113)))))),f312(x100395,x100394)),f312(f131(x100393,x100392,x100395,x100391),x100394))
% 155.93/155.62 [5167]E(x51671,x51672)+~E(f312(f312(f147(x51673),x51674),x51671),f312(f312(f147(x51673),x51675),x51672))
% 155.93/155.62 [5168]E(x51681,x51682)+~E(f312(f312(f147(x51683),x51681),x51684),f312(f312(f147(x51683),x51682),x51685))
% 155.93/155.62 [5218]P22(f312(x52181,x52182))+~E(f312(f132(x52183,x52181),x52184),f312(f312(f147(x52183),x52182),x52185))
% 155.93/155.62 [5219]P22(f312(x52191,x52192))+~E(f312(f312(f147(x52193),x52192),x52194),f312(f132(x52193,x52191),x52195))
% 155.93/155.62 [5367]~E(f312(f312(f134(x53671),x53673),x53672),f312(f312(f147(x53671),x53674),x53675))+E(f312(f312(f161(x53671),x53672),x53673),x53674)
% 155.93/155.62 [5501]~P11(x55014,x55015,x55011)+E(f312(f312(x55011,x55012),f312(f312(x55011,x55012),x55013)),f312(f312(x55011,x55012),x55013))
% 155.93/155.62 [6093]~P103(x60932)+~E(f312(f312(f145(x60931,x60932,x60933),x60934),x60935),f127(x60931))
% 155.93/155.62 [6467]E(x64671,x64672)+~E(f312(f312(f129(x64673),x64674),f312(f312(f147(x64673),x64671),f127(x64673))),f312(f312(f129(x64673),x64675),f312(f312(f147(x64673),x64672),f127(x64673))))
% 155.93/155.62 [6468]E(x64681,x64682)+~E(f312(f312(f129(x64683),x64681),f312(f312(f147(x64683),x64684),f127(x64683))),f312(f312(f129(x64683),x64682),f312(f312(f147(x64683),x64685),f127(x64683))))
% 155.93/155.62 [6717]E(f312(f183(x67171,x67172,x67173,x67174),x67175),f192(x67172))+P22(f312(f312(f314(x67171),x67175),x67174))
% 155.93/155.62 [6775]E(f312(f312(f289(x67751),f312(x67752,x67753)),f312(f290(x67754,x67751,x67752),x67755)),f312(f290(x67754,x67751,x67752),x67755))+~P22(f312(f312(f314(x67754),x67753),x67755))
% 155.93/155.62 [6782]~P22(f312(x67824,f312(x67823,x67825)))+P22(f312(f312(f291(x67821,x67822,x67823),x67824),x67825))
% 155.93/155.62 [6786]~E(x67864,f2(a113))+E(f312(f131(x67861,x67862,x67863,x67864),x67865),f312(f312(f239(f854(x67862),x67861),f127(x67862)),x67865))
% 155.93/155.62 [6879]~E(f312(f290(x68791,x68792,x68793),x68794),x68795)+E(f312(f290(f861(x68791,a846),f861(x68792,a846),f290(x68791,x68792,x68793)),f312(f288(x68791),x68794)),f312(f288(x68792),x68795))
% 155.93/155.62 [6916]E(f312(f183(x69161,x69162,x69163,x69164),x69165),f312(x69163,x69165))+~P22(f312(f312(f314(x69161),x69165),x69164))
% 155.93/155.62 [7207]P19(x72071,x72072,x72073,x72074)+~P19(x72071,x72072,x72073,f312(f312(f289(x72071),x72075),x72074))
% 155.93/155.62 [7276]P22(f312(x72761,x72762))+~P22(f312(f312(f103(x72763,x72764,x72761),x72765),x72762))
% 155.93/155.62 [7319]~P22(f312(f312(f314(x73194),x73193),x73195))+P22(f312(f312(f314(x73191),f312(x73192,x73193)),f312(f290(x73194,x73191,x73192),x73195)))
% 155.93/155.62 [7342]~P103(x73422)+E(f144(x73421,x73422,x73423,f312(f132(x73421,x73424),x73425)),f312(f132(x73421,x73424),f144(x73421,x73422,x73423,x73425)))
% 155.93/155.62 [7376]P22(f312(x73761,f312(x73762,x73763)))+~P22(f312(f312(f291(x73764,x73765,x73762),x73761),x73763))
% 155.93/155.62 [7377]P22(f312(f312(x73771,x73772),x73773))+~P22(f312(f312(f103(x73774,x73771,x73775),x73772),x73773))
% 155.93/155.62 [7440]~P22(f312(f312(f314(x74403),f312(x74404,x74402)),x74405))+P22(f312(f312(f314(x74401),x74402),f312(f291(x74401,x74403,x74404),x74405)))
% 155.93/155.62 [7831]~P22(f312(f312(f314(x78315),x78313),f312(f291(x78315,x78311,x78312),x78314)))+P22(f312(f312(f314(x78311),f312(x78312,x78313)),x78314))
% 155.93/155.62 [8059]~E(x80593,f312(f312(f312(f81(x80591,f857(x80592)),f312(f16(f857(x80592),x80591),f192(x80592))),x80594),f312(f219(x80592),x80595)))+E(f179(x80591,x80592,x80593),f312(f312(f289(x80591),x80594),f189(f861(x80591,a846))))
% 155.93/155.62 [8158]E(f312(x81581,f798(x81582,x81581,x81583,x81584)),x81584)+~P22(f312(f312(f314(x81585),x81584),f312(f290(x81583,x81585,x81581),x81582)))
% 155.93/155.62 [8478]~E(x84782,f312(f312(f147(x84781),x84784),x84785))+P22(f312(f312(f314(f860(f854(x84781),f854(x84781))),f312(f312(f239(f854(x84781),f854(x84781)),f127(x84781)),x84782)),f143(x84781,x84783)))
% 155.93/155.62 [8528]~P39(x85281,x85283,x85285,x85282,x85284)+E(f312(f190(f854(x85281)),x85282),f312(f190(f854(x85283)),x85284))
% 155.93/155.62 [8538]P22(f312(f312(f227(f861(x85381,a846)),f312(f312(f51(x85382,f861(x85381,a846)),x85383),x85384)),f312(x85384,x85385)))+~P22(f312(f312(f314(x85382),x85385),x85383))
% 155.93/155.62 [8584]~P56(x85841,x85842,x85843,x85845,x85844)+E(f312(f290(x85841,x85842,x85843),f235(f861(x85841,a846))),x85844)
% 155.93/155.62 [8788]E(f312(f312(f312(f81(x87881,f857(x87882)),f183(x87881,x87882,x87883,x87884)),x87885),f192(x87882)),f183(x87881,x87882,x87883,x87884))+P22(f312(f312(f314(x87881),x87885),x87884))
% 155.93/155.62 [8790]E(f312(f132(x87901,x87902),f727(x87903,x87904,x87905,x87902,x87901)),x87903)+~E(f312(f132(x87901,x87902),x87905),f312(f312(f147(x87901),x87904),x87903))
% 155.93/155.62 [8791]E(f312(f132(x87911,x87912),f729(x87913,x87912,x87914,x87915,x87911)),x87914)+~E(f312(f312(f147(x87911),x87915),x87914),f312(f132(x87911,x87912),x87913))
% 155.93/155.62 [8792]E(f312(x87921,f740(x87922,x87923,x87921,x87924,x87925)),x87922)+~E(f312(f312(f193(x87925,x87924),x87921),x87923),f312(f219(x87924),x87922))
% 155.93/155.62 [8796]E(f312(f219(x87961),f740(x87962,x87963,x87964,x87965,x87961)),x87963)+~E(f312(f312(f193(x87961,x87965),x87964),x87963),f312(f219(x87965),x87962))
% 155.93/155.62 [8898]E(f312(f190(f854(x88981)),x88982),x88983)+~P22(f312(f312(f314(f860(f854(x88981),f854(x88981))),f312(f312(f239(f854(x88981),f854(x88981)),x88984),x88982)),f312(f139(x88981,x88985),x88983)))
% 155.93/155.62 [8899]E(f312(f190(f854(x88991)),x88992),x88993)+~P22(f312(f312(f314(f860(f854(x88991),f854(x88991))),f312(f312(f239(f854(x88991),f854(x88991)),x88992),x88994)),f312(f139(x88991,x88995),x88993)))
% 155.93/155.62 [8965]P22(f312(f312(f314(x89651),f798(x89652,x89653,x89651,x89654)),x89652))+~P22(f312(f312(f314(x89655),x89654),f312(f290(x89651,x89655,x89653),x89652)))
% 155.93/155.62 [9121]~P49(f861(x91213,a846),f861(x91211,a846),x91212)+P22(f312(f312(f227(f861(x91211,a846)),f312(x91212,f312(f312(f115(f861(x91213,a846)),x91214),x91215))),f312(f312(f115(f861(x91211,a846)),f312(x91212,x91214)),f312(x91212,x91215))))
% 155.93/155.62 [9123]E(f312(f290(x91231,x91232,x91233),f816(x91234,x91233,x91231,x91235,x91232)),x91235)+~P22(f312(f312(f227(f861(x91232,a846)),x91235),f312(f290(x91231,x91232,x91233),x91234)))
% 155.93/155.62 [9373]E(f312(x93731,f800(x93732,x93731,x93733,x93734,x93735)),f312(f219(x93735),x93734))+~P22(f312(f312(f314(x93735),x93734),f181(x93733,x93735,f183(x93733,x93735,x93731,x93732))))
% 155.93/155.62 [9421]P22(f312(f312(f314(f860(f854(x94211),f854(x94211))),f312(f312(f239(f854(x94211),f854(x94211)),f312(f312(f147(x94211),x94212),x94213)),f312(f312(f147(x94211),x94212),x94214))),f287(f854(x94211),f153(x94211,x94215))))+~P22(f312(f312(f314(f860(f854(x94211),f854(x94211))),f312(f312(f239(f854(x94211),f854(x94211)),x94213),x94214)),f287(f854(x94211),f153(x94211,x94215))))
% 155.93/155.62 [9451]~E(f312(x94513,f586(x94515,x94514,x94513,x94512,x94511)),f312(x94515,f586(x94515,x94514,x94513,x94512,x94511)))+E(f312(f312(f150(x94511,x94512),x94513),x94514),f312(f312(f150(x94511,x94512),x94515),x94514))
% 155.93/155.62 [9527]~E(f312(f132(x95271,x95275),x95274),f312(f312(f147(x95271),x95273),x95272))+E(f312(f312(f129(x95271),f728(x95272,x95273,x95274,x95275,x95271)),f312(f312(f147(x95271),x95273),f727(x95272,x95273,x95274,x95275,x95271))),x95274)
% 155.93/155.62 [9528]~E(f312(f312(f147(x95281),x95285),x95284),f312(f132(x95281,x95283),x95282))+E(f312(f312(f129(x95281),f730(x95282,x95283,x95284,x95285,x95281)),f312(f312(f147(x95281),x95285),f729(x95282,x95283,x95284,x95285,x95281))),x95282)
% 155.93/155.62 [9529]E(f312(f312(f150(x95291,x95292),x95293),x95294),f312(f312(f150(x95291,x95292),x95295),x95294))+P22(f312(f312(f314(x95291),f586(x95293,x95294,x95295,x95292,x95291)),f312(f168(x95291),x95294)))
% 155.93/155.62 [9558]~P22(f312(f312(f314(x95585),x95584),f312(f264(x95581,x95585,x95583),x95582)))+P22(f312(f312(f314(x95581),f359(x95582,x95583,x95581,x95584,x95585)),x95582))
% 155.93/155.62 [9559]~P22(f312(f312(f314(x95595),x95594),f312(f264(x95591,x95595,x95593),x95592)))+P22(f312(f312(f314(x95591),f369(x95592,x95593,x95591,x95594,x95595)),x95592))
% 155.93/155.62 [9583]~P22(f312(f312(f227(f861(x95835,a846)),x95834),f312(f290(x95831,x95835,x95833),x95832)))+P22(f312(f312(f227(f861(x95831,a846)),f816(x95832,x95833,x95831,x95834,x95835)),x95832))
% 155.93/155.62 [9635]~P22(f312(f312(f314(x96355),x96354),f181(x96351,x96355,f183(x96351,x96355,x96353,x96352))))+P22(f312(f312(f314(x96351),f800(x96352,x96353,x96351,x96354,x96355)),x96352))
% 155.93/155.62 [5381]~E(f312(x53813,x53814),x53815)+E(f312(f312(f312(f81(x53811,x53812),x53813),x53814),x53815),x53813)
% 155.93/155.62 [5815]E(f312(x58151,x58152),x58153)+~E(f312(f312(f312(f81(x58154,x58155),x58151),x58152),x58153),x58151)
% 155.93/155.62 [5913]E(x59131,x59132)+~E(f312(f248(x59133,x59134),f312(f312(f239(x59133,x59134),x59135),x59131)),x59132)
% 155.93/155.62 [5914]E(x59141,x59142)+~E(f312(f246(x59143,x59144),f312(f312(f239(x59143,x59144),x59141),x59145)),x59142)
% 155.93/155.62 [6170]~E(x61703,f312(f312(f129(x61701),x61704),f312(f312(f147(x61701),x61702),x61705)))+P22(f312(f312(f314(x61701),x61702),f312(f168(x61701),x61703)))
% 155.93/155.62 [6551]E(f312(f290(x65511,x65512,f312(f16(x65512,x65511),x65513)),x65514),f312(f312(f289(x65512),x65513),f189(f861(x65512,a846))))+~P22(f312(f312(f314(x65511),x65515),x65514))
% 155.93/155.62 [6621]E(f312(f312(f124(f861(x66211,a846)),f312(f168(x66211),x66212)),f312(f168(x66211),x66213)),f312(f168(x66211),x66214))+~E(f163(x66211,x66215,x66214),f312(f312(f239(f854(x66211),f854(x66211)),x66212),x66213))
% 155.93/155.62 [6721]~P103(x67212)+E(f312(f190(f854(x67211)),f312(f312(f145(x67211,x67212,x67213),x67214),x67215)),f312(a126,f312(f190(f854(x67211)),x67215)))
% 155.93/155.62 [6730]~P103(x67302)+E(f312(f168(x67301),f312(f312(f145(x67301,x67302,x67303),x67304),x67305)),f312(f312(f289(x67301),x67304),f312(f168(x67301),x67305)))
% 155.93/155.62 [7008]~P107(x70081)+E(f312(f312(f89(x70081),f312(f312(f89(x70081),x70082),x70083)),f312(f312(f89(x70081),x70084),x70085)),f312(f312(f89(x70081),f312(f312(f89(x70081),x70082),x70084)),f312(f312(f89(x70081),x70083),x70085)))
% 155.93/155.62 [7009]~P107(x70091)+E(f312(f312(f90(x70091),f312(f312(f90(x70091),x70092),x70093)),f312(f312(f90(x70091),x70094),x70095)),f312(f312(f90(x70091),f312(f312(f90(x70091),x70092),x70094)),f312(f312(f90(x70091),x70093),x70095)))
% 155.93/155.62 [7010]~P64(x70101)+E(f312(f312(f268(x70101),f312(f312(f90(x70101),x70102),x70103)),f312(f312(f90(x70101),x70104),x70105)),f312(f312(f90(x70101),f312(f312(f268(x70101),x70102),x70104)),f312(f312(f268(x70101),x70103),x70105)))
% 155.93/155.62 [7022]~P103(x70221)+E(f285(x70221,f312(f312(f226(x70221),x70222),x70223),f312(f312(f225(x70221),x70224),x70225)),f312(f312(f115(f861(x70221,a846)),f285(x70221,x70222,x70224)),f285(x70221,x70223,x70225)))
% 155.93/155.62 [7023]~P103(x70231)+E(f284(x70231,f312(f312(f226(x70231),x70232),x70233),f312(f312(f225(x70231),x70234),x70235)),f312(f312(f115(f861(x70231,a846)),f284(x70231,x70232,x70234)),f284(x70231,x70233,x70235)))
% 155.93/155.62 [7024]~P103(x70241)+E(f283(x70241,f312(f312(f226(x70241),x70242),x70243),f312(f312(f225(x70241),x70244),x70245)),f312(f312(f115(f861(x70241,a846)),f283(x70241,x70242,x70244)),f283(x70241,x70243,x70245)))
% 155.93/155.62 [7025]~P103(x70251)+E(f312(f312(f115(f861(x70251,a846)),f312(f282(x70251,x70252),x70253)),f312(f282(x70251,x70254),x70255)),f312(f282(x70251,f312(f312(f226(x70251),x70252),x70254)),f312(f312(f225(x70251),x70253),x70255)))
% 155.93/155.62 [7140]~P22(f312(x71401,f340(x71403,x71402,x71401)))+P22(f312(x71401,f312(f312(f239(x71402,x71403),x71404),x71405)))
% 155.93/155.62 [7219]~E(f312(x72193,x72194),f192(x72192))+E(f181(x72191,x72192,f312(f312(f312(f81(x72191,f857(x72192)),x72193),x72194),f312(f219(x72192),x72195))),f312(f312(f289(x72192),x72195),f181(x72191,x72192,x72193)))
% 155.93/155.62 [7242]~E(x72422,f312(x72424,x72425))+P22(f312(f312(f314(x72421),x72422),f312(f290(x72423,x72421,x72424),f235(f861(x72423,a846)))))
% 155.93/155.62 [7299]~E(f312(x72993,x72994),f192(x72992))+E(f312(f312(f21(f861(x72991,a846)),f179(x72991,x72992,x72993)),f312(f312(f289(x72991),x72994),x72995)),f312(f312(f21(f861(x72991,a846)),f179(x72991,x72992,x72993)),x72995))
% 155.93/155.62 [7317]~P11(x73173,x73172,x73174)+P11(x73171,x73172,f312(f312(f8(x73173,f861(x73172,x73172),x73171),x73174),x73175))
% 155.93/155.62 [7457]~P19(x74571,x74572,x74573,x74574)+P19(x74571,x74572,x74573,f312(f312(f21(f861(x74571,a846)),x74574),x74575))
% 155.93/155.62 [7612]~P22(f312(f312(x76123,x76124),x76125))+P22(f312(f312(f249(x76121,x76122,a846),x76123),f312(f312(f239(x76121,x76122),x76124),x76125)))
% 155.93/155.62 [7727]~P22(f312(x77272,x77274))+~E(f312(f312(f134(x77271),f312(f190(f854(x77271)),f172(x77271,x77272,x77273))),x77273),f312(f312(f147(x77271),x77274),x77275))
% 155.93/155.62 [7748]P19(x77481,x77482,x77483,x77484)+~P19(x77481,x77482,x77483,f312(f312(f124(f861(x77481,a846)),x77485),x77484))
% 155.93/155.62 [7749]P19(x77491,x77492,x77493,x77494)+~P19(x77491,x77492,x77493,f312(f312(f124(f861(x77491,a846)),x77494),x77495))
% 155.93/155.62 [7793]~P103(x77932)+E(f312(f312(f145(x77931,x77932,x77933),x77934),f144(x77931,x77932,x77933,x77935)),f144(x77931,x77932,x77933,f312(f312(f147(x77931),x77934),x77935)))
% 155.93/155.62 [7948]~P34(x79481,f312(a126,x79482),f312(f312(f312(f100(x79481),x79483),f312(a27,x79484)),x79485))+P34(x79481,x79482,f312(f312(f312(f100(x79481),x79483),f312(f223(a847),f312(a30,x79484))),x79485))
% 155.93/155.62 [8085]P34(x80851,f312(a126,x80852),f312(f312(f312(f100(x80851),x80853),f312(a27,x80854)),x80855))+~P34(x80851,x80852,f312(f312(f312(f100(x80851),x80853),f312(f223(a847),f312(a30,x80854))),x80855))
% 155.93/155.62 [8114]~P11(x81142,x81141,x81143)+E(f312(f138(x81141,x81142,f312(f7(x81142,x81141,x81141),x81143),x81144),x81145),f312(f312(f73(x81142,x81141,x81143),x81144),f312(f168(x81142),x81145)))
% 155.93/155.62 [8144]~E(f312(f312(f134(x81441),f312(f190(f854(x81441)),f172(x81441,x81442,x81443))),x81443),f312(f312(f147(x81441),x81444),x81445))+E(f312(f312(f129(x81441),f172(x81441,x81442,x81443)),f312(f312(f147(x81441),x81444),x81445)),x81443)
% 155.93/155.62 [8168]P22(f312(f312(x81681,x81682),x81683))+~P22(f312(f312(f249(x81684,x81685,a846),x81681),f312(f312(f239(x81684,x81685),x81682),x81683)))
% 155.93/155.62 [8234]~E(f312(f312(f173(x82341,x82342),x82345),x82343),f312(f219(x82342),x82344))+P22(f312(f312(f314(f860(x82341,x82342)),f312(f312(f239(x82341,x82342),x82343),x82344)),f312(f168(f860(x82341,x82342)),x82345)))
% 155.93/155.62 [8640]P22(f312(f312(f227(f861(x86401,a846)),f312(f290(x86402,x86401,x86403),x86404)),f312(f290(x86402,x86401,x86403),x86405)))+~P22(f312(f312(f227(f861(x86402,a846)),x86404),x86405))
% 155.93/155.62 [8641]P22(f312(f312(f227(f861(x86411,a846)),f312(f291(x86411,x86412,x86413),x86414)),f312(f291(x86411,x86412,x86413),x86415)))+~P22(f312(f312(f227(f861(x86412,a846)),x86414),x86415))
% 155.93/155.62 [8715]E(x87151,f2(a113))+E(f312(f312(f251(x87152,x87153,x87152,f860(x87153,x87152)),f312(x87154,x87155)),f259(x87153,x87152,f312(f312(f21(a113),x87151),f87(a113)),x87154)),f312(f259(x87153,x87152,x87151,x87154),x87155))
% 155.93/155.62 [9034]P34(x90341,x90342,f312(f312(f312(f100(x90341),x90343),x90344),x90345))+P22(f312(f312(x90343,f562(x90345,x90344,x90343,x90342)),f571(x90345,x90344,x90343,x90342)))
% 155.93/155.62 [9042]~P22(f312(f312(f195(x90423),f312(f312(f312(a201,x90424),f40(x90421)),f312(x90422,x90424))),x90425))+P22(f312(f312(f195(f32(x90421,x90422,x90423)),x90424),f312(f312(f312(a201,x90425),f40(x90421)),f312(f312(a202,x90424),x90421))))
% 155.93/155.62 [9233]E(f312(f219(x92331),f589(x92332,x92333,x92334,x92331,x92335)),f312(f312(f173(x92335,x92331),x92332),x92334))+~P22(f312(f312(f314(f860(x92335,x92331)),f312(f312(f239(x92335,x92331),x92334),x92333)),f312(f168(f860(x92335,x92331)),x92332)))
% 155.93/155.62 [9275]P34(x92751,x92752,f312(f312(f312(f100(x92751),x92753),x92754),x92755))+~P22(f312(f312(x92755,f562(x92755,x92754,x92753,x92752)),f585(x92755,x92754,x92753,x92752)))
% 155.93/155.62 [9337]P34(x93371,x93372,f312(f312(f312(f100(x93371),x93373),x93374),x93375))+P22(f312(f312(f312(f312(a198,x93374),f571(x93375,x93374,x93373,x93372)),x93372),f585(x93375,x93374,x93373,x93372)))
% 155.93/155.62 [9340]~P18(x93401,x93402,f312(f312(f289(f852(x93401)),f312(f312(f312(f100(x93401),x93403),f312(f223(a847),f312(a30,x93404))),x93405)),f189(f861(f852(x93401),a846))))+P18(x93401,x93402,f312(f312(f289(f852(x93401)),f312(f312(f312(f100(x93401),x93403),f312(a27,x93404)),x93405)),f189(f861(f852(x93401),a846))))
% 155.93/155.62 [9365]~P22(f312(f70(x93653),f312(f290(x93652,x93653,x93655),f235(f861(x93652,a846)))))+P22(f312(f70(x93651),f312(f290(x93652,x93651,f312(f312(f8(x93653,x93651,x93652),x93654),x93655)),f235(f861(x93652,a846)))))
% 155.93/155.62 [9386]P22(f312(f312(f227(f861(f861(x93861,a846),a846)),f312(f290(f861(x93862,a846),f861(x93861,a846),f290(x93862,x93861,x93863)),f312(f288(x93862),x93864))),f312(f288(x93861),x93865)))+~P22(f312(f312(f227(f861(x93861,a846)),f312(f290(x93862,x93861,x93863),x93864)),x93865))
% 155.93/155.62 [9403]~P22(f312(f70(f857(x94031)),f312(f290(x94032,f857(x94031),x94033),f235(f861(x94032,a846)))))+P22(f312(f70(f857(x94031)),f312(f290(x94032,f857(x94031),f312(f312(f312(f81(x94032,f857(x94031)),x94033),x94034),f312(f219(x94031),x94035))),f235(f861(x94032,a846)))))
% 155.93/155.62 [9435]P22(f312(f312(f195(x94351),f312(f312(f312(a201,x94352),f40(x94353)),f312(x94354,x94352))),f477(x94355,x94352,x94351,x94354,x94353)))+~P22(f312(f312(f195(f32(x94353,x94354,x94351)),x94352),x94355))
% 155.93/155.62 [9460]E(x94601,x94602)+~P22(f312(f75(x94603,x94604,x94605,x94601,f189(f861(x94603,a846))),x94602))
% 155.93/155.62 [9475]E(f312(f312(f239(x94751,x94752),f532(x94753,x94754,x94755,x94752,x94751)),f533(x94753,x94754,x94755,x94752,x94751)),x94755)+~P22(f312(f312(f314(f860(x94751,x94752)),x94755),f312(f312(f247(x94751,x94752),x94754),x94753)))
% 155.93/155.62 [9486]P22(f312(f312(f195(x94861),f312(f312(f312(a201,x94862),f40(x94863)),f312(x94864,x94862))),f444(x94865,x94862,x94861,x94864,x94863)))+~P22(f312(f312(f195(f32(x94863,x94864,x94861)),x94862),f312(f312(f312(a201,x94865),f40(x94863)),f312(f312(a202,x94862),x94863))))
% 155.93/155.62 [9492]~P22(f312(f312(f195(f312(a27,x94922)),f312(f312(f312(a201,f312(f312(a203,x94924),a204)),f40(a26)),f312(x94923,x94924))),x94925))+P22(f312(f312(f195(f31(x94921,x94922,x94923)),x94924),f312(f312(f312(a201,f312(f312(a203,x94925),f312(a202,x94924))),x94921),f312(f312(a202,x94925),a25))))
% 155.93/155.62 [9522]P22(f312(f312(f195(f312(a27,x95221)),f312(f312(f312(a201,f312(f312(a203,x95222),a204)),f40(a26)),f312(x95223,x95222))),f609(x95224,x95222,x95223,x95221,x95225)))+~P22(f312(f312(f195(f31(x95225,x95221,x95223)),x95222),x95224))
% 155.93/155.62 [9563]P22(f312(f312(f314(x95631),f532(x95632,x95633,x95634,x95635,x95631)),x95633))+~P22(f312(f312(f314(f860(x95631,x95635)),x95634),f312(f312(f247(x95631,x95635),x95633),x95632)))
% 155.93/155.62 [9589]E(f312(f312(f312(a201,f477(x95891,x95892,x95893,x95894,x95895)),f40(x95895)),f312(f312(a202,x95892),x95895)),x95891)+~P22(f312(f312(f195(f32(x95895,x95894,x95893)),x95892),x95891))
% 155.93/155.62 [9612]E(f312(f312(f312(a201,f444(x96121,x96122,x96123,x96124,x96125)),f40(x96125)),f312(f312(a202,x96122),x96125)),f312(f312(f312(a201,x96121),f40(x96125)),f312(f312(a202,x96122),x96125)))+~P22(f312(f312(f195(f32(x96125,x96124,x96123)),x96122),f312(f312(f312(a201,x96121),f40(x96125)),f312(f312(a202,x96122),x96125))))
% 155.93/155.62 [9640]P22(f312(f312(f195(f312(a27,x96401)),f312(f312(f312(a201,f312(f312(a203,x96402),a204)),f40(a26)),f312(x96403,x96402))),f517(x96404,x96402,x96403,x96401,x96405)))+~P22(f312(f312(f195(f31(x96405,x96401,x96403)),x96402),f312(f312(f312(a201,f312(f312(a203,x96404),f312(a202,x96402))),x96405),f312(f312(a202,x96404),a25))))
% 155.93/155.62 [9670]P18(x96705,x96704,f312(f312(f289(f852(x96705)),f312(f312(f312(f100(x96705),x96701),x96703),x96702)),f189(f861(f852(x96705),a846))))+P22(f312(f312(x96701,f673(x96702,x96703,x96704,x96705,x96701)),f685(x96702,x96703,x96704,x96705,x96701)))
% 155.93/155.62 [9718]P22(f312(f312(f314(x97181),f533(x97182,x97183,x97184,x97181,x97185)),f312(x97182,f532(x97182,x97183,x97184,x97181,x97185))))+~P22(f312(f312(f314(f860(x97185,x97181)),x97184),f312(f312(f247(x97185,x97181),x97183),x97182)))
% 155.93/155.62 [9748]P22(f312(f312(f314(f860(x97481,x97481)),f312(f312(f239(x97481,x97481),x97482),f776(x97483,x97484,x97485,x97482,x97481))),x97483))+~P22(f312(f312(f314(f860(x97481,x97481)),f312(f312(f239(x97481,x97481),x97482),x97485)),f312(f312(f184(f860(x97481,x97481),a846),f312(a126,x97484)),x97483)))
% 155.93/155.62 [9749]P22(f312(f312(f314(f860(x97491,x97491)),f312(f312(f239(x97491,x97491),x97492),f778(x97493,x97494,x97495,x97492,x97491))),x97493))+~P22(f312(f312(f314(f860(x97491,x97491)),f312(f312(f239(x97491,x97491),x97492),x97495)),f312(f312(f184(f860(x97491,x97491),a846),f312(a126,x97494)),x97493)))
% 155.93/155.62 [9766]~P22(f312(f312(f314(f860(f854(x97661),f854(x97661))),f312(f312(f239(f854(x97661),f854(x97661)),f312(f312(f147(x97661),x97662),x97665)),x97664)),f154(x97661,x97663)))+P22(f312(f312(f314(f860(x97661,x97661)),f312(f312(f239(x97661,x97661),x97662),f594(x97663,x97664,x97665,x97662,x97661))),x97663))
% 155.93/155.62 [9768]~P18(x97681,x97682,f312(f312(f289(f852(x97681)),f312(f312(f312(f100(x97681),f103(x97681,x97683,x97684)),x97685),x97683)),f189(f861(f852(x97681),a846))))+P18(x97681,x97682,f312(f312(f289(f852(x97681)),f312(f312(f312(f100(x97681),x97683),f35(x97684,x97685)),f103(x97681,x97683,f312(f82(a846,a846,a848,a307),x97684)))),f189(f861(f852(x97681),a846))))
% 155.93/155.62 [9769]~P21(x97691,x97692,f312(f312(f289(f852(x97691)),f312(f312(f312(f100(x97691),f103(x97691,x97693,x97694)),x97695),x97693)),f189(f861(f852(x97691),a846))))+P21(x97691,x97692,f312(f312(f289(f852(x97691)),f312(f312(f312(f100(x97691),x97693),f35(x97694,x97695)),f103(x97691,x97693,f312(f82(a846,a846,a848,a307),x97694)))),f189(f861(f852(x97691),a846))))
% 155.93/155.62 [9877]E(f312(f312(f312(a201,f312(f312(a203,f609(x98771,x98772,x98773,x98774,x98775)),f312(a202,x98772))),x98775),f312(f312(a202,f609(x98771,x98772,x98773,x98774,x98775)),a25)),x98771)+~P22(f312(f312(f195(f31(x98775,x98774,x98773)),x98772),x98771))
% 155.93/155.62 [9886]E(f312(f312(f312(a201,f312(f312(a203,f517(x98861,x98862,x98863,x98864,x98865)),f312(a202,x98862))),x98865),f312(f312(a202,f517(x98861,x98862,x98863,x98864,x98865)),a25)),f312(f312(f312(a201,f312(f312(a203,x98861),f312(a202,x98862))),x98865),f312(f312(a202,x98861),a25)))+~P22(f312(f312(f195(f31(x98865,x98864,x98863)),x98862),f312(f312(f312(a201,f312(f312(a203,x98861),f312(a202,x98862))),x98865),f312(f312(a202,x98861),a25))))
% 155.93/155.62 [10040]P18(x100401,x100402,f312(f312(f289(f852(x100401)),f312(f312(f312(f100(x100401),x100403),x100404),x100405)),f189(f861(f852(x100401),a846))))+~P18(x100401,x100402,f312(f312(f289(f852(x100401)),f312(f312(f312(f100(x100401),f312(f16(f861(a848,a846),x100401),f312(f312(f7(a848,a848,a846),a309),f685(x100405,x100404,x100402,x100401,x100403)))),x100404),f312(f16(f861(a848,a846),x100401),f312(x100405,f673(x100405,x100404,x100402,x100401,x100403))))),f189(f861(f852(x100401),a846))))
% 155.93/155.62 [6241]P22(f312(x62412,x62414))+E(f172(x62411,x62412,f312(f312(f129(x62411),x62413),f312(f312(f147(x62411),x62414),x62415))),f172(x62411,x62412,x62413))
% 155.93/155.62 [6291]~P73(x62912)+E(f312(f312(f312(f21(f861(x62911,x62912)),x62913),x62914),x62915),f312(f312(f21(x62912),f312(x62913,x62915)),f312(x62914,x62915)))
% 155.93/155.62 [6293]~P87(x62932)+E(f312(f312(f312(f124(f861(x62931,x62932)),x62933),x62934),x62935),f312(f312(f124(x62932),f312(x62933,x62935)),f312(x62934,x62935)))
% 155.93/155.62 [6295]~P87(x62952)+E(f312(f312(f312(f115(f861(x62951,x62952)),x62953),x62954),x62955),f312(f312(f115(x62952),f312(x62953,x62955)),f312(x62954,x62955)))
% 155.93/155.62 [6308]E(x63081,x63082)+E(f312(f312(f161(x63083),f312(f312(f155(x63083,x63084),x63081),x63085)),x63082),f312(f312(f161(x63083),x63084),x63082))
% 155.93/155.62 [6568]~E(x65684,f189(f861(x65683,a846)))+E(f312(f312(f21(f861(x65681,a846)),x65682),f312(f312(f50(x65683,f861(x65681,a846)),x65684),x65685)),x65682)
% 155.93/155.62 [6569]~E(x65694,f189(f861(x65693,a846)))+E(f312(f312(f124(f861(x65691,a846)),x65692),f312(f312(f50(x65693,f861(x65691,a846)),x65694),x65695)),x65692)
% 155.93/155.62 [6570]~E(x65704,f189(f861(x65703,a846)))+E(f312(f312(f115(f861(x65701,a846)),x65702),f312(f312(f51(x65703,f861(x65701,a846)),x65704),x65705)),x65702)
% 155.93/155.62 [6588]~E(x65884,f189(f861(x65883,a846)))+E(f312(f312(f289(x65881),x65882),f312(f312(f50(x65883,f861(x65881,a846)),x65884),x65885)),f312(f312(f289(x65881),x65882),f189(f861(x65881,a846))))
% 155.93/155.62 [7364]E(f312(f312(f161(x73641),f312(f312(f150(x73642,x73641),x73643),x73644)),x73645),f312(x73643,f312(f312(f161(x73642),x73644),x73645)))+~P22(f312(f312(f228(a853),x73645),f312(f190(f854(x73642)),x73644)))
% 155.93/155.62 [7428]E(f312(f312(f124(f861(x74281,a846)),f312(x74282,x74283)),f312(f312(f50(x74284,f861(x74281,a846)),x74285),x74282)),f312(f312(f50(x74284,f861(x74281,a846)),x74285),x74282))+~P22(f312(f312(f314(x74284),x74283),x74285))
% 155.93/155.62 [7429]E(f312(f312(f115(f861(x74291,a846)),f312(x74292,x74293)),f312(f312(f51(x74294,f861(x74291,a846)),x74295),x74292)),f312(f312(f51(x74294,f861(x74291,a846)),x74295),x74292))+~P22(f312(f312(f314(x74294),x74293),x74295))
% 155.93/155.62 [8030]~E(x80303,f189(f861(x80301,a846)))+E(f312(f312(f50(x80301,f861(x80302,a846)),x80303),f312(f312(f8(f861(x80302,a846),f861(x80302,a846),x80301),f312(f289(x80302),x80304)),x80305)),f189(f861(x80302,a846)))
% 155.93/155.62 [8036]~P22(f312(f312(f314(x80364),x80363),x80365))+P22(f312(f312(f227(f861(x80361,a846)),f312(x80362,x80363)),f312(f312(f50(x80364,f861(x80361,a846)),x80365),x80362)))
% 155.93/155.62 [8096]E(x80961,f312(f312(f312(a201,x80962),x80963),f312(x80964,x80962)))+~P22(f312(f312(f312(f312(a198,f28(x80963,x80964)),x80962),x80965),x80961))
% 155.93/155.62 [8167]~E(f312(x81674,x81672),x81675)+P22(f312(f312(f314(x81671),x81672),f312(f291(x81671,x81673,x81674),f312(f312(f289(x81673),x81675),f189(f861(x81673,a846))))))
% 155.93/155.62 [8214]~P54(x82141,x82142,f312(f265(x82142,x82141),x82143))+E(f312(f312(f115(f861(x82141,a846)),f312(f264(x82142,x82141,x82143),x82144)),f312(f264(x82142,x82141,x82143),x82145)),f312(f264(x82142,x82141,x82143),f312(f312(f115(f861(x82142,a846)),x82144),x82145)))
% 155.93/155.62 [8337]E(x83371,f189(f861(x83372,a846)))+E(f312(f312(f50(x83372,f861(x83373,a846)),x83371),f312(f312(f8(f861(x83373,a846),f861(x83373,a846),x83372),f312(f289(x83373),x83374)),x83375)),f312(f312(f289(x83373),x83374),f312(f312(f50(x83372,f861(x83373,a846)),x83371),x83375)))
% 155.93/155.62 [8396]~P19(x83962,x83961,x83963,f235(f861(x83962,a846)))+E(f312(f312(f21(f861(x83961,a846)),f312(f290(x83962,x83961,x83963),x83964)),f312(f290(x83962,x83961,x83963),x83965)),f312(f290(x83962,x83961,x83963),f312(f312(f21(f861(x83962,a846)),x83964),x83965)))
% 155.93/155.62 [8397]~P19(x83972,x83971,x83973,f235(f861(x83972,a846)))+E(f312(f312(f115(f861(x83971,a846)),f312(f290(x83972,x83971,x83973),x83974)),f312(f290(x83972,x83971,x83973),x83975)),f312(f290(x83972,x83971,x83973),f312(f312(f115(f861(x83972,a846)),x83974),x83975)))
% 155.93/155.62 [8464]~P22(f312(f312(f76(x84641,x84642,x84645),x84643),x84644))+P22(f312(f312(f314(f860(x84641,x84642)),f312(f312(f239(x84641,x84642),x84643),x84644)),x84645))
% 155.93/155.62 [8498]P22(f312(f312(f314(x84981),x84982),f312(f236(x84983,x84981),x84984)))+~P22(f312(f312(f314(f860(x84983,x84981)),f312(f312(f239(x84983,x84981),x84985),x84982)),x84984))
% 155.93/155.62 [8500]P22(f312(f312(f314(x85001),x85002),f312(f238(x85001,x85003),x85004)))+~P22(f312(f312(f314(f860(x85001,x85003)),f312(f312(f239(x85001,x85003),x85002),x85005)),x85004))
% 155.93/155.62 [8626]P22(f312(f312(f76(x86261,x86262,x86263),x86264),x86265))+~P22(f312(f312(f314(f860(x86261,x86262)),f312(f312(f239(x86261,x86262),x86264),x86265)),x86263))
% 155.93/155.62 [8663]E(f312(x86631,x86632),x86633)+~P22(f312(f312(f314(x86634),x86632),f312(f291(x86634,x86635,x86631),f312(f312(f289(x86635),x86633),f189(f861(x86635,a846))))))
% 155.93/155.62 [8895]P22(f312(f312(f314(f860(x88951,x88952)),f312(f312(f239(x88951,x88952),x88953),x88954)),f312(f265(x88952,x88951),x88955)))+~P22(f312(f312(f314(f860(x88952,x88951)),f312(f312(f239(x88952,x88951),x88954),x88953)),x88955))
% 155.93/155.62 [8913]~P22(f312(f312(x89131,x89135),x89134))+P22(f312(f312(x89131,f312(f248(x89132,x89133),f312(f312(f239(x89132,x89133),x89134),x89135))),f312(f246(x89132,x89133),f312(f312(f239(x89132,x89133),x89134),x89135))))
% 155.93/155.62 [8943]~P22(f312(f312(f314(f860(x89432,x89431)),f312(f312(f239(x89432,x89431),x89434),x89433)),f312(f265(x89431,x89432),x89435)))+P22(f312(f312(f314(f860(x89431,x89432)),f312(f312(f239(x89431,x89432),x89433),x89434)),x89435))
% 155.93/155.62 [8971]~P22(f312(f312(f314(f860(x89713,x89711)),f312(f312(f239(x89713,x89711),x89715),x89712)),x89714))+P22(f312(f312(f314(x89711),x89712),f312(f264(x89713,x89711,x89714),f312(f312(f289(x89713),x89715),f189(f861(x89713,a846))))))
% 155.93/155.62 [9016]P22(f312(f312(f314(f860(x90161,x90162)),f312(f312(f239(x90161,x90162),x90163),x90164)),x90165))+~P22(f312(f312(f314(x90162),x90164),f312(f264(x90161,x90162,x90165),f312(f312(f289(x90161),x90163),f189(f861(x90161,a846))))))
% 155.93/155.62 [9037]E(f312(f312(f312(f81(x90371,f857(x90372)),f183(x90371,x90372,x90373,x90374)),x90375),f192(x90372)),f183(x90371,x90372,x90373,f312(f312(f21(f861(x90371,a846)),x90374),f312(f312(f289(x90371),x90375),f189(f861(x90371,a846))))))+~P22(f312(f312(f314(x90371),x90375),x90374))
% 155.93/155.62 [9102]~P26(x91021)+E(f312(f312(f6(a853,x91021),x91022),f283(a853,f312(f312(f89(a853),x91023),x91024),f312(f312(f89(a853),x91025),x91024))),f312(f312(f6(a853,x91021),f312(f312(f8(a853,x91021,a853),x91022),f312(f312(f7(a853,a853,a853),f89(a853)),x91024))),f283(a853,x91023,x91025)))
% 155.93/155.62 [9127]~P26(x91271)+E(f312(f312(f6(a853,x91271),x91272),f312(f282(a853,f312(f312(f89(a853),x91273),x91274)),f312(f312(f89(a853),x91275),x91274))),f312(f312(f6(a853,x91271),f312(f312(f8(a853,x91271,a853),x91272),f312(f312(f7(a853,a853,a853),f89(a853)),x91274))),f312(f282(a853,x91273),x91275)))
% 155.93/155.62 [9182]~P19(x91821,x91822,x91823,f235(f861(x91821,a846)))+E(f312(f312(f150(x91821,x91822),x91823),f312(f132(x91821,f312(f312(f8(a846,a846,x91821),a307),f312(a309,x91824))),x91825)),f312(f132(x91822,f312(f312(f8(a846,a846,x91822),a307),f312(a309,f312(x91823,x91824)))),f312(f312(f150(x91821,x91822),x91823),x91825)))
% 155.93/155.62 [9200]~P19(x92001,x92002,x92003,f312(f312(f289(x92001),x92004),f312(f168(x92001),x92005)))+E(f312(f312(f150(x92001,x92002),x92003),f312(f132(x92001,f312(f312(f8(a846,a846,x92001),a307),f312(a309,x92004))),x92005)),f312(f132(x92002,f312(f312(f8(a846,a846,x92002),a307),f312(a309,f312(x92003,x92004)))),f312(f312(f150(x92001,x92002),x92003),x92005)))
% 155.93/155.62 [9354]P22(f312(f312(f314(f860(f854(x93541),f854(x93541))),f312(f312(f239(f854(x93541),f854(x93541)),f312(f312(f147(x93541),x93542),x93543)),f312(f312(f147(x93541),x93544),x93543))),f153(x93541,x93545)))+~P22(f312(f312(f314(f860(x93541,x93541)),f312(f312(f239(x93541,x93541),x93542),x93544)),x93545))
% 155.93/155.62 [9387]P22(f312(f312(f312(f312(a198,x93871),x93872),x93873),f361(x93874,x93873,x93872,x93875,x93871)))+~P22(f312(f312(f312(f312(a198,f36(x93871,x93875)),x93872),x93873),x93874))
% 155.93/155.62 [9388]P22(f312(f312(f312(f312(a198,x93881),x93882),x93883),f376(x93884,x93883,x93882,x93885,x93881)))+~P22(f312(f312(f312(f312(a198,f36(x93881,x93885)),x93882),x93883),x93884))
% 155.93/155.62 [9458]P18(x94581,x94582,f312(f312(f289(f852(x94581)),f312(f312(f312(f100(x94581),x94583),f312(a27,x94584)),x94585)),f189(f861(f852(x94581),a846))))+~P18(x94581,f312(f312(f289(f852(x94581)),f312(f312(f312(f100(x94581),x94583),f312(a27,x94584)),x94585)),x94582),f312(f312(f289(f852(x94581)),f312(f312(f312(f100(x94581),x94583),f312(f223(a847),f312(a30,x94584))),x94585)),f189(f861(f852(x94581),a846))))
% 155.93/155.62 [9470]E(f312(f312(f289(x94701),f518(x94702,x94703,x94704,x94705,x94701)),f519(x94702,x94703,x94704,x94705,x94701)),f312(f312(f289(x94701),x94704),x94703))+~P22(f312(f71(x94701,x94705,f312(f312(f289(x94701),x94704),x94703)),x94702))
% 155.93/155.62 [9471]E(f312(f312(f289(x94711),f520(x94712,x94713,x94714,x94715,x94711)),f521(x94712,x94713,x94714,x94715,x94711)),f312(f312(f289(x94711),x94714),x94713))+~P22(f312(f71(x94711,x94715,f312(f312(f289(x94711),x94714),x94713)),x94712))
% 155.93/155.62 [9549]P22(f312(f312(f314(x95491),f640(x95492,x95493,x95494,x95495,x95491)),x95494))+P22(f312(f312(f312(f51(x95491,f861(x95495,a846)),x95494),x95493),x95492))
% 155.93/155.62 [9553]P22(f312(f312(f314(x95531),f637(x95532,x95533,x95531,x95534,x95535)),x95533))+P22(f312(f312(f314(x95535),x95534),f312(f312(f51(x95531,f861(x95535,a846)),x95533),x95532)))
% 155.93/155.62 [9562]P22(f312(f312(f314(x95621),f638(x95622,x95623,x95621,x95624,x95625)),x95623))+P22(f312(f312(f227(f861(x95625,a846)),x95624),f312(f312(f51(x95621,f861(x95625,a846)),x95623),x95622)))
% 155.93/155.62 [9565]P22(f312(f312(x95651,f405(x95652,x95651,x95653,x95654,x95655)),x95652))+~P22(f312(f312(f312(f50(x95655,f861(x95654,a846)),x95653),x95651),x95652))
% 155.93/155.62 [9568]P22(f312(f312(f314(x95681),f405(x95682,x95683,x95684,x95685,x95681)),x95684))+~P22(f312(f312(f312(f50(x95681,f861(x95685,a846)),x95684),x95683),x95682))
% 155.93/155.62 [9576]P22(f312(f312(f314(x95761),f411(x95762,x95763,x95761,x95764,x95765)),x95763))+~P22(f312(f312(f314(x95765),x95764),f312(f312(f50(x95761,f861(x95765,a846)),x95763),x95762)))
% 155.93/155.62 [9581]P22(f312(f312(f314(x95811),x95812),f312(x95813,f411(x95813,x95814,x95815,x95812,x95811))))+~P22(f312(f312(f314(x95811),x95812),f312(f312(f50(x95815,f861(x95811,a846)),x95814),x95813)))
% 155.93/155.62 [9675]~P22(f312(f312(x96754,f640(x96755,x96754,x96753,x96752,x96751)),x96755))+P22(f312(f312(f312(f51(x96751,f861(x96752,a846)),x96753),x96754),x96755))
% 155.93/155.62 [9678]~P22(f312(f312(f314(x96781),x96782),f312(x96785,f637(x96785,x96784,x96783,x96782,x96781))))+P22(f312(f312(f314(x96781),x96782),f312(f312(f51(x96783,f861(x96781,a846)),x96784),x96785)))
% 155.93/155.62 [9681]~P22(f312(f312(f227(f861(x96811,a846)),x96812),f312(x96815,f638(x96815,x96814,x96813,x96812,x96811))))+P22(f312(f312(f227(f861(x96811,a846)),x96812),f312(f312(f51(x96813,f861(x96811,a846)),x96814),x96815)))
% 155.93/155.62 [9724]P22(f312(f312(f312(f312(a198,x97241),f361(x97242,x97243,x97244,x97241,x97245)),x97243),x97242))+~P22(f312(f312(f312(f312(a198,f36(x97245,x97241)),x97244),x97243),x97242))
% 155.93/155.62 [9725]P22(f312(f312(f312(f312(a198,x97251),f376(x97252,x97253,x97254,x97251,x97255)),x97253),x97252))+~P22(f312(f312(f312(f312(a198,f36(x97255,x97251)),x97254),x97253),x97252))
% 155.93/155.62 [9752]~P22(f312(f312(f314(x97521),f518(x97525,x97524,x97523,x97522,x97521)),f519(x97525,x97524,x97523,x97522,x97521)))+~P22(f312(f71(x97521,x97522,f312(f312(f289(x97521),x97523),x97524)),x97525))
% 155.93/155.62 [9753]~P22(f312(f312(f314(x97531),f520(x97535,x97534,x97533,x97532,x97531)),f521(x97535,x97534,x97533,x97532,x97531)))+~P22(f312(f71(x97531,x97532,f312(f312(f289(x97531),x97533),x97534)),x97535))
% 155.93/155.62 [9754]~P22(f312(f312(f314(f860(x97541,x97541)),f312(f312(f239(x97541,x97541),x97542),x97545)),f312(f312(f184(f860(x97541,x97541),a846),f312(a126,x97544)),x97543)))+P22(f312(f312(f314(f860(x97541,x97541)),f312(f312(f239(x97541,x97541),x97542),f777(x97543,x97544,x97545,x97542,x97541))),f312(f312(f184(f860(x97541,x97541),a846),x97544),x97543)))
% 155.93/155.62 [9760]P22(f312(f75(x97601,x97601,x97602,f518(x97603,x97604,x97605,x97602,x97601),f519(x97603,x97604,x97605,x97602,x97601)),x97603))+~P22(f312(f71(x97601,x97602,f312(f312(f289(x97601),x97605),x97604)),x97603))
% 155.93/155.62 [9761]P22(f312(f75(x97611,x97611,x97612,f520(x97613,x97614,x97615,x97612,x97611),f521(x97613,x97614,x97615,x97612,x97611)),x97613))+~P22(f312(f71(x97611,x97612,f312(f312(f289(x97611),x97615),x97614)),x97613))
% 155.93/155.62 [9773]~P103(x97731)+P33(x97731,f312(f312(f150(x97732,x97731),x97733),f312(f132(x97732,f312(f312(f7(x97732,x97731,a846),f312(f312(f8(x97731,f861(x97731,a846),x97732),a309),x97733)),f312(x97734,x97735))),x97735)))
% 155.93/155.62 [9818]~P22(f312(f312(f314(x98182),x98185),f312(f264(x98181,x98182,x98184),x98183)))+P22(f312(f312(f314(f860(x98181,x98182)),f312(f312(f239(x98181,x98182),f359(x98183,x98184,x98181,x98185,x98182)),x98185)),x98184))
% 155.93/155.62 [9819]~P22(f312(f312(f314(x98192),x98195),f312(f264(x98191,x98192,x98194),x98193)))+P22(f312(f312(f314(f860(x98191,x98192)),f312(f312(f239(x98191,x98192),f369(x98193,x98194,x98191,x98195,x98192)),x98195)),x98194))
% 155.93/155.62 [9839]~P22(f312(f312(f314(f860(x98391,x98391)),f312(f312(f239(x98391,x98391),x98395),x98394)),f312(f312(f184(f860(x98391,x98391),a846),f312(a126,x98393)),x98392)))+P22(f312(f312(f314(f860(x98391,x98391)),f312(f312(f239(x98391,x98391),f777(x98392,x98393,x98394,x98395,x98391)),x98394)),x98392))
% 155.93/155.62 [9842]~P22(f312(f312(f314(f860(x98421,x98421)),f312(f312(f239(x98421,x98421),x98425),x98424)),f312(f312(f184(f860(x98421,x98421),a846),f312(a126,x98423)),x98422)))+P22(f312(f312(f314(f860(x98421,x98421)),f312(f312(f239(x98421,x98421),f776(x98422,x98423,x98424,x98425,x98421)),x98424)),f312(f312(f184(f860(x98421,x98421),a846),x98423),x98422)))
% 155.93/155.62 [9843]~P22(f312(f312(f314(f860(x98431,x98431)),f312(f312(f239(x98431,x98431),x98435),x98434)),f312(f312(f184(f860(x98431,x98431),a846),f312(a126,x98433)),x98432)))+P22(f312(f312(f314(f860(x98431,x98431)),f312(f312(f239(x98431,x98431),f778(x98432,x98433,x98434,x98435,x98431)),x98434)),f312(f312(f184(f860(x98431,x98431),a846),x98433),x98432)))
% 155.93/155.62 [9844]~P22(f312(f312(f314(f860(f854(x98441),f854(x98441))),f312(f312(f239(f854(x98441),f854(x98441)),x98445),f312(f312(f147(x98441),x98444),x98443))),f154(x98441,x98442)))+P22(f312(f312(f314(f860(x98441,x98441)),f312(f312(f239(x98441,x98441),f592(x98442,x98443,x98444,x98445,x98441)),x98444)),x98442))
% 155.93/155.62 [6967]E(x69671,f192(x69672))+E(f179(x69673,x69672,f312(f312(f312(f81(x69673,f857(x69672)),x69674),x69675),x69671)),f312(f312(f289(x69673),x69675),f179(x69673,x69672,x69674)))
% 155.93/155.62 [7449]~E(x74493,f189(f861(x74492,a846)))+E(f312(f312(f124(f861(x74491,a846)),f312(f312(f50(x74492,f861(x74491,a846)),x74493),x74494)),x74495),x74495)
% 155.93/155.62 [7450]~E(x74503,f189(f861(x74502,a846)))+E(f312(f312(f115(f861(x74501,a846)),f312(f312(f51(x74502,f861(x74501,a846)),x74503),x74504)),x74505),x74505)
% 155.93/155.62 [7805]~E(x78055,f192(x78052))+E(f179(x78051,x78052,f312(f312(f312(f81(x78051,f857(x78052)),x78053),x78054),x78055)),f312(f312(f21(f861(x78051,a846)),f179(x78051,x78052,x78053)),f312(f312(f289(x78051),x78054),f189(f861(x78051,a846)))))
% 155.93/155.62 [7870]~E(x78703,f189(f861(x78702,a846)))+E(f312(f312(f21(f861(x78701,a846)),f312(f312(f51(x78702,f861(x78701,a846)),x78703),x78704)),x78705),f312(f312(f21(f861(x78701,a846)),f235(f861(x78701,a846))),x78705))
% 155.93/155.62 [7998]E(f312(f312(f155(x79981,f312(f312(f129(x79981),x79982),x79983)),x79984),x79985),f312(f312(f129(x79981),f312(f312(f155(x79981,x79982),x79984),x79985)),x79983))+~P22(f312(f312(f228(a853),x79984),f312(f190(f854(x79981)),x79982)))
% 155.93/155.62 [8118]P22(f312(f312(f314(x81181),x81185),f312(f168(x81181),x81183)))+E(f312(f312(f173(x81181,x81182),f312(f312(f177(x81181,x81182),x81183),f312(f312(f150(x81181,x81182),x81184),x81183))),x81185),f192(x81182))
% 155.93/155.62 [8244]~P22(f312(f312(f314(x82441),x82445),f312(f168(x82441),x82443)))+E(f312(f312(f173(x82441,x82442),f312(f312(f177(x82441,x82442),x82443),f312(f312(f150(x82441,x82442),x82444),x82443))),x82445),f312(f219(x82442),f312(x82444,x82445)))
% 155.93/155.62 [8282]E(f312(f312(f161(x82821),f312(f312(f150(a853,x82821),x82822),f135(a853,f312(f282(a853,x82823),x82824)))),x82825),f312(x82822,f312(f312(f89(a853),x82823),x82825)))+~P22(f312(f312(f228(a853),x82825),f312(f312(f21(a853),x82824),x82823)))
% 155.93/155.62 [8324]~E(x83243,f189(f861(x83241,a846)))+E(f312(f312(f50(x83241,f861(x83242,a846)),x83243),f312(f312(f8(f861(x83242,a846),f861(x83242,a846),x83241),f312(f124(f861(x83242,a846)),x83244)),x83245)),f189(f861(x83242,a846)))
% 155.93/155.62 [8325]~E(x83253,f189(f861(x83251,a846)))+E(f312(f312(f51(x83251,f861(x83252,a846)),x83253),f312(f312(f8(f861(x83252,a846),f861(x83252,a846),x83251),f312(f21(f861(x83252,a846)),x83254)),x83255)),f235(f861(x83252,a846)))
% 155.93/155.62 [8326]~E(x83263,f189(f861(x83261,a846)))+E(f312(f312(f51(x83261,f861(x83262,a846)),x83263),f312(f312(f8(f861(x83262,a846),f861(x83262,a846),x83261),f312(f115(f861(x83262,a846)),x83264)),x83265)),f235(f861(x83262,a846)))
% 155.93/155.62 [8331]~P135(x83312)+E(f312(f312(f6(x83311,x83312),f312(f312(f8(x83312,x83312,x83311),f312(f90(x83312),x83313)),x83314)),x83315),f312(f312(f90(x83312),x83313),f312(f312(f6(x83311,x83312),x83314),x83315)))
% 155.93/155.62 [8611]E(x86111,f189(f861(x86112,a846)))+E(f312(f312(f50(x86112,f861(x86113,a846)),x86111),f312(f312(f8(f861(x86113,a846),f861(x86113,a846),x86112),f312(f124(f861(x86113,a846)),x86114)),x86115)),f312(f312(f124(f861(x86113,a846)),x86114),f312(f312(f50(x86112,f861(x86113,a846)),x86111),x86115)))
% 155.93/155.62 [8612]E(x86121,f189(f861(x86122,a846)))+E(f312(f312(f51(x86122,f861(x86123,a846)),x86121),f312(f312(f8(f861(x86123,a846),f861(x86123,a846),x86122),f312(f21(f861(x86123,a846)),x86124)),x86125)),f312(f312(f21(f861(x86123,a846)),x86124),f312(f312(f50(x86122,f861(x86123,a846)),x86121),x86125)))
% 155.93/155.62 [8613]E(x86131,f189(f861(x86132,a846)))+E(f312(f312(f51(x86132,f861(x86133,a846)),x86131),f312(f312(f8(f861(x86133,a846),f861(x86133,a846),x86132),f312(f115(f861(x86133,a846)),x86134)),x86135)),f312(f312(f115(f861(x86133,a846)),x86134),f312(f312(f51(x86132,f861(x86133,a846)),x86131),x86135)))
% 155.93/155.62 [8804]~P22(f312(f312(f228(a853),f312(x88044,x88042)),f312(x88044,x88043)))+P22(f312(f312(f314(f860(x88041,x88041)),f312(f312(f239(x88041,x88041),x88042),x88043)),f149(x88041,f312(f312(f147(f861(x88041,a853)),x88044),x88045))))
% 155.93/155.62 [9055]~P49(f861(x90555,a846),f861(x90551,a846),x90552)+P22(f312(f312(f227(f861(x90551,a846)),f312(f312(f124(f861(x90551,a846)),f312(x90552,x90553)),f312(x90552,x90554))),f312(x90552,f312(f312(f124(f861(x90555,a846)),x90553),x90554))))
% 155.93/155.62 [9069]~P19(x90692,x90691,x90693,f312(f312(f124(f861(x90692,a846)),x90694),x90695))+E(f312(f312(f115(f861(x90691,a846)),f312(f290(x90692,x90691,x90693),f312(f312(f21(f861(x90692,a846)),x90694),x90695))),f312(f290(x90692,x90691,x90693),f312(f312(f21(f861(x90692,a846)),x90695),x90694))),f189(f861(x90691,a846)))
% 155.93/155.62 [9350]~P22(f312(f312(f227(f861(x93503,a846)),f312(f264(x93501,x93503,x93504),x93502)),x93505))+P22(f312(f312(f227(f861(x93501,a846)),x93502),f312(f88(f861(x93501,a846)),f312(f264(x93503,x93501,f312(f265(x93501,x93503),x93504)),f312(f88(f861(x93503,a846)),x93505)))))
% 155.93/155.62 [9372]~P19(x93721,x93722,x93723,f312(f312(f289(x93721),x93724),x93725))+~P22(f312(f312(f314(x93722),f312(x93723,x93724)),f312(f290(x93721,x93722,x93723),f312(f312(f21(f861(x93721,a846)),x93725),f312(f312(f289(x93721),x93724),f189(f861(x93721,a846)))))))
% 155.93/155.62 [9425]P22(f312(f312(f227(f861(x94251,a846)),f312(f264(x94252,x94251,x94253),x94254)),x94255))+~P22(f312(f312(f227(f861(x94252,a846)),x94254),f312(f88(f861(x94252,a846)),f312(f264(x94251,x94252,f312(f265(x94252,x94251),x94253)),f312(f88(f861(x94251,a846)),x94255)))))
% 155.93/155.62 [9500]~P83(x95001)+P22(f312(f312(f227(x95001),f312(f84(x95001),f312(f312(f21(x95001),f312(f312(f89(x95001),x95002),x95003)),f312(f312(f89(x95001),x95004),x95005)))),f312(f312(f89(x95001),f312(f84(x95001),f312(f312(f21(x95001),x95002),x95004))),f312(f84(x95001),f312(f312(f21(x95001),x95003),x95005)))))
% 155.93/155.62 [9595]P22(f312(f312(f314(x95951),f414(x95952,x95953,x95954,x95951,x95955)),x95954))+P22(f312(f312(f227(f861(x95955,a846)),f312(f312(f50(x95951,f861(x95955,a846)),x95954),x95953)),x95952))
% 155.93/155.62 [9795]~P22(f312(f312(f227(f861(x97951,a846)),f312(x97954,f414(x97955,x97954,x97953,x97952,x97951))),x97955))+P22(f312(f312(f227(f861(x97951,a846)),f312(f312(f50(x97952,f861(x97951,a846)),x97953),x97954)),x97955))
% 155.93/155.62 [8442]E(f312(f312(f129(x84421),x84422),f312(f312(f155(x84421,x84423),f312(f312(f21(a853),x84424),f312(f190(f854(x84421)),x84422))),x84425)),f312(f312(f155(x84421,f312(f312(f129(x84421),x84422),x84423)),x84424),x84425))+P22(f312(f312(f228(a853),x84424),f312(f190(f854(x84421)),x84422)))
% 155.93/155.62 [8472]~P132(x84721)+E(f312(f312(f89(x84721),f312(f312(f90(x84721),x84722),x84723)),f312(f312(f89(x84721),f312(f312(f90(x84721),x84724),x84723)),x84725)),f312(f312(f89(x84721),f312(f312(f90(x84721),f312(f312(f89(x84721),x84722),x84724)),x84723)),x84725))
% 155.93/155.62 [9026]~P135(x90261)+E(f312(f162(x90261),f312(f312(f150(x90262,x90261),f312(f312(f8(x90261,x90261,x90262),f312(f90(x90261),x90263)),x90264)),x90265)),f312(f312(f90(x90261),x90263),f312(f162(x90261),f312(f312(f150(x90262,x90261),x90264),x90265))))
% 155.93/155.62 [9199]E(f312(f190(f854(x91991)),f312(f312(f169(x91991),f312(f312(f225(a853),f312(f190(f854(x91991)),x91992)),f312(f190(f854(x91993)),x91994))),x91992)),f312(f190(f854(x91993)),f312(f312(f169(x91993),f312(f312(f225(a853),f312(f190(f854(x91991)),x91992)),f312(f190(f854(x91993)),x91994))),x91994)))+P22(f312(x91995,f312(f312(f177(x91991,x91993),x91992),x91994)))
% 155.93/155.62 [9437]~P135(x94372)+E(f312(f312(f6(x94371,x94372),f312(f312(f7(x94371,x94372,x94372),f312(f312(f8(x94372,f861(x94372,x94372),x94371),f90(x94372)),x94373)),x94374)),x94375),f312(f312(f90(x94372),f312(f312(f6(x94371,x94372),x94373),x94375)),x94374))
% 155.93/155.62 [9438]~P65(x94382)+E(f312(f312(f6(x94381,x94382),f312(f312(f7(x94381,x94382,x94382),f312(f312(f8(x94382,f861(x94382,x94382),x94381),f268(x94382)),x94383)),x94384)),x94385),f312(f312(f268(x94382),f312(f312(f6(x94381,x94382),x94383),x94385)),x94384))
% 155.93/155.62 [9444]~P72(x94442)+E(f312(f312(f9(x94441,x94442),f312(f312(f18(x94441,x94442,x94442),f312(f312(f8(x94442,f861(x94442,x94442),x94441),f90(x94442)),x94443)),x94444)),x94445),f312(f312(f90(x94442),f312(f312(f9(x94441,x94442),x94443),x94445)),f312(f312(f9(x94441,x94442),x94444),x94445)))
% 155.93/155.62 [9445]~P26(x94452)+E(f312(f312(f6(x94451,x94452),f312(f312(f18(x94451,x94452,x94452),f312(f312(f8(x94452,f861(x94452,x94452),x94451),f89(x94452)),x94453)),x94454)),x94455),f312(f312(f89(x94452),f312(f312(f6(x94451,x94452),x94453),x94455)),f312(f312(f6(x94451,x94452),x94454),x94455)))
% 155.93/155.62 [9446]~P30(x94462)+E(f312(f312(f6(x94461,x94462),f312(f312(f18(x94461,x94462,x94462),f312(f312(f8(x94462,f861(x94462,x94462),x94461),f21(x94462)),x94463)),x94464)),x94465),f312(f312(f21(x94462),f312(f312(f6(x94461,x94462),x94463),x94465)),f312(f312(f6(x94461,x94462),x94464),x94465)))
% 155.93/155.62 [9483]~E(x94833,f189(f861(x94831,a846)))+E(f312(f312(f50(x94831,f861(x94832,a846)),x94833),f312(f312(f7(x94831,f861(x94832,a846),f861(x94832,a846)),f312(f312(f8(f861(x94832,a846),f861(f861(x94832,a846),f861(x94832,a846)),x94831),f124(f861(x94832,a846))),x94834)),x94835)),f189(f861(x94832,a846)))
% 155.93/155.62 [9484]~E(x94843,f189(f861(x94841,a846)))+E(f312(f312(f51(x94841,f861(x94842,a846)),x94843),f312(f312(f7(x94841,f861(x94842,a846),f861(x94842,a846)),f312(f312(f8(f861(x94842,a846),f861(f861(x94842,a846),f861(x94842,a846)),x94841),f21(f861(x94842,a846))),x94844)),x94845)),f235(f861(x94842,a846)))
% 155.93/155.62 [9485]~E(x94853,f189(f861(x94851,a846)))+E(f312(f312(f51(x94851,f861(x94852,a846)),x94853),f312(f312(f7(x94851,f861(x94852,a846),f861(x94852,a846)),f312(f312(f8(f861(x94852,a846),f861(f861(x94852,a846),f861(x94852,a846)),x94851),f115(f861(x94852,a846))),x94854)),x94855)),f235(f861(x94852,a846)))
% 155.93/155.62 [9508]E(x95081,f189(f861(x95082,a846)))+E(f312(f312(f50(x95082,f861(x95083,a846)),x95081),f312(f312(f7(x95082,f861(x95083,a846),f861(x95083,a846)),f312(f312(f8(f861(x95083,a846),f861(f861(x95083,a846),f861(x95083,a846)),x95082),f124(f861(x95083,a846))),x95084)),x95085)),f312(f312(f124(f861(x95083,a846)),f312(f312(f50(x95082,f861(x95083,a846)),x95081),x95084)),x95085))
% 155.93/155.62 [9509]E(x95091,f189(f861(x95092,a846)))+E(f312(f312(f51(x95092,f861(x95093,a846)),x95091),f312(f312(f7(x95092,f861(x95093,a846),f861(x95093,a846)),f312(f312(f8(f861(x95093,a846),f861(f861(x95093,a846),f861(x95093,a846)),x95092),f21(f861(x95093,a846))),x95094)),x95095)),f312(f312(f21(f861(x95093,a846)),f312(f312(f51(x95092,f861(x95093,a846)),x95091),x95094)),x95095))
% 155.93/155.62 [9510]E(x95101,f189(f861(x95102,a846)))+E(f312(f312(f51(x95102,f861(x95103,a846)),x95101),f312(f312(f7(x95102,f861(x95103,a846),f861(x95103,a846)),f312(f312(f8(f861(x95103,a846),f861(f861(x95103,a846),f861(x95103,a846)),x95102),f115(f861(x95103,a846))),x95104)),x95105)),f312(f312(f115(f861(x95103,a846)),f312(f312(f51(x95102,f861(x95103,a846)),x95101),x95104)),x95105))
% 155.93/155.62 [9076]~P22(f312(f312(f227(a853),x90761),x90764))+E(f312(f312(f21(a853),f312(f312(f89(a853),f312(f312(f90(a853),x90761),x90762)),x90763)),f312(f312(f89(a853),f312(f312(f90(a853),x90764),x90762)),x90765)),f312(f312(f21(a853),x90763),f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x90764),x90761)),x90762)),x90765)))
% 155.93/155.62 [9656]~P135(x96561)+E(f312(f162(x96561),f312(f312(f150(x96562,x96561),f312(f312(f7(x96562,x96561,x96561),f312(f312(f8(x96561,f861(x96561,x96561),x96562),f90(x96561)),x96563)),x96564)),x96565)),f312(f312(f90(x96561),f312(f162(x96561),f312(f312(f150(x96562,x96561),x96563),x96565))),x96564))
% 155.93/155.62 [9662]~P26(x96621)+E(f312(f162(x96621),f312(f312(f150(x96622,x96621),f312(f312(f18(x96622,x96621,x96621),f312(f312(f8(x96621,f861(x96621,x96621),x96622),f89(x96621)),x96623)),x96624)),x96625)),f312(f312(f89(x96621),f312(f162(x96621),f312(f312(f150(x96622,x96621),x96623),x96625))),f312(f162(x96621),f312(f312(f150(x96622,x96621),x96624),x96625))))
% 155.93/155.62 [9663]~P30(x96631)+E(f312(f162(x96631),f312(f312(f150(x96632,x96631),f312(f312(f18(x96632,x96631,x96631),f312(f312(f8(x96631,f861(x96631,x96631),x96632),f21(x96631)),x96633)),x96634)),x96635)),f312(f312(f21(x96631),f312(f162(x96631),f312(f312(f150(x96632,x96631),x96633),x96635))),f312(f162(x96631),f312(f312(f150(x96632,x96631),x96634),x96635))))
% 155.93/155.62 [9808]P22(f312(x98081,f312(f312(f177(x98082,x98083),x98084),x98085)))+~P22(f312(x98081,f312(f312(f177(x98082,x98083),f312(f312(f169(x98082),f312(f312(f225(a853),f312(f190(f854(x98082)),x98084)),f312(f190(f854(x98083)),x98085))),x98084)),f312(f312(f169(x98083),f312(f312(f225(a853),f312(f190(f854(x98082)),x98084)),f312(f190(f854(x98083)),x98085))),x98085))))
% 155.93/155.62 [9317]~P22(f312(f312(f227(a853),x93174),x93171))+E(f312(f312(f21(a853),f312(f312(f89(a853),f312(f312(f90(a853),x93171),x93172)),x93173)),f312(f312(f89(a853),f312(f312(f90(a853),x93174),x93172)),x93175)),f312(f312(f21(a853),f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x93171),x93174)),x93172)),x93173)),x93175))
% 155.93/155.62 [10069]P18(x100691,x100692,f312(f290(a849,f852(x100691),f312(f312(f18(a849,f861(x100691,f861(a848,a846)),f852(x100691)),f312(f312(f18(a849,a847,f861(f861(x100691,f861(a848,a846)),f852(x100691))),f312(f312(f8(f861(x100691,f861(a848,a846)),f861(a847,f861(f861(x100691,f861(a848,a846)),f852(x100691))),a849),f100(x100691)),x100693)),a27)),x100694)),x100695))+~P18(x100691,f312(f312(f124(f861(f852(x100691),a846)),x100692),f312(f290(a849,f852(x100691),f312(f312(f18(a849,f861(x100691,f861(a848,a846)),f852(x100691)),f312(f312(f18(a849,a847,f861(f861(x100691,f861(a848,a846)),f852(x100691))),f312(f312(f8(f861(x100691,f861(a848,a846)),f861(a847,f861(f861(x100691,f861(a848,a846)),f852(x100691))),a849),f100(x100691)),x100693)),a27)),x100694)),x100695)),f312(f290(a849,f852(x100691),f312(f312(f18(a849,f861(x100691,f861(a848,a846)),f852(x100691)),f312(f312(f18(a849,a847,f861(f861(x100691,f861(a848,a846)),f852(x100691))),f312(f312(f8(f861(x100691,f861(a848,a846)),f861(a847,f861(f861(x100691,f861(a848,a846)),f852(x100691))),a849),f100(x100691)),x100693)),f312(f312(f8(f857(a847),a847,a849),f223(a847)),a30))),x100694)),x100695))
% 155.93/155.62 [10070]P21(x100701,x100702,f312(f290(a849,f852(x100701),f312(f312(f18(a849,f861(x100701,f861(a848,a846)),f852(x100701)),f312(f312(f18(a849,a847,f861(f861(x100701,f861(a848,a846)),f852(x100701))),f312(f312(f8(f861(x100701,f861(a848,a846)),f861(a847,f861(f861(x100701,f861(a848,a846)),f852(x100701))),a849),f100(x100701)),x100703)),a27)),x100704)),x100705))+~P21(x100701,f312(f312(f124(f861(f852(x100701),a846)),x100702),f312(f290(a849,f852(x100701),f312(f312(f18(a849,f861(x100701,f861(a848,a846)),f852(x100701)),f312(f312(f18(a849,a847,f861(f861(x100701,f861(a848,a846)),f852(x100701))),f312(f312(f8(f861(x100701,f861(a848,a846)),f861(a847,f861(f861(x100701,f861(a848,a846)),f852(x100701))),a849),f100(x100701)),x100703)),a27)),x100704)),x100705)),f312(f290(a849,f852(x100701),f312(f312(f18(a849,f861(x100701,f861(a848,a846)),f852(x100701)),f312(f312(f18(a849,a847,f861(f861(x100701,f861(a848,a846)),f852(x100701))),f312(f312(f8(f861(x100701,f861(a848,a846)),f861(a847,f861(f861(x100701,f861(a848,a846)),f852(x100701))),a849),f100(x100701)),x100703)),f312(f312(f8(f857(a847),a847,a849),f223(a847)),a30))),x100704)),x100705))
% 155.93/155.62 [5194]E(x51941,x51942)+~E(f33(x51943,x51944,x51941),f33(x51945,x51946,x51942))
% 155.93/155.62 [5195]E(x51951,x51952)+~E(f33(x51953,x51951,x51954),f33(x51955,x51952,x51956))
% 155.93/155.62 [5196]E(x51961,x51962)+~E(f33(x51961,x51963,x51964),f33(x51962,x51965,x51966))
% 155.93/155.62 [5197]E(x51971,x51972)+~E(f32(x51973,x51974,x51971),f32(x51975,x51976,x51972))
% 155.93/155.62 [5198]E(x51981,x51982)+~E(f32(x51983,x51981,x51984),f32(x51985,x51982,x51986))
% 155.93/155.62 [5199]E(x51991,x51992)+~E(f32(x51991,x51993,x51994),f32(x51992,x51995,x51996))
% 155.93/155.62 [5200]E(x52001,x52002)+~E(f31(x52003,x52004,x52001),f31(x52005,x52006,x52002))
% 155.93/155.62 [5201]E(x52011,x52012)+~E(f31(x52013,x52011,x52014),f31(x52015,x52012,x52016))
% 155.93/155.62 [5202]E(x52021,x52022)+~E(f31(x52021,x52023,x52024),f31(x52022,x52025,x52026))
% 155.93/155.62 [7148]E(x71481,x71482)+~E(f209(x71483,x71484,x71485,x71481),f209(x71483,x71484,x71486,x71482))
% 155.93/155.62 [7149]E(x71491,x71492)+~E(f209(x71493,x71494,x71491,x71495),f209(x71493,x71494,x71492,x71496))
% 155.93/155.62 [9323]~P36(x93231,x93232,x93233,x93236)+P36(x93231,x93232,f182(x93231,x93232,x93233,x93234,x93235),f182(x93231,x93232,x93236,x93234,x93235))
% 155.93/155.62 [6612]E(f312(f180(x66121,x66122,x66123,x66124),x66125),f312(f219(x66122),x66126))+~E(f312(x66124,x66125),f312(f219(x66122),x66126))
% 155.93/155.62 [6750]E(f312(f221(f857(x67501),x67502,f192(x67501),x67503),f312(x67504,x67505)),f312(x67503,x67506))+~E(f312(x67504,x67505),f312(f219(x67502),x67506))
% 155.93/155.62 [8266]~P14(x82665,x82661,x82662,x82666)+E(f312(f82(x82661,x82661,x82661,f312(x82662,x82663)),f312(x82662,x82664)),f312(f82(x82661,x82661,x82661,f312(x82662,x82664)),f312(x82662,x82663)))
% 155.93/155.62 [8513]~P56(x85134,x85135,x85132,x85131,x85136)+E(f312(x85131,f312(x85132,x85133)),x85133)
% 155.93/155.62 [8661]P19(x86611,x86612,x86613,x86614)+~P19(x86611,x86615,f312(f82(x86612,x86615,x86611,x86616),x86613),x86614)
% 155.93/155.62 [8742]~P19(x87424,x87422,f312(f82(x87421,x87422,x87424,x87423),x87425),x87426)+P19(x87421,x87422,x87423,f312(f290(x87424,x87421,x87425),x87426))
% 155.93/155.62 [9447]P22(f312(f70(x94471),x94472))+~P22(f312(f75(x94471,x94473,x94474,x94475,x94472),x94476))
% 155.93/155.62 [9454]~P22(f312(f312(f314(x94544),x94543),f278(x94544,x94545,x94541,x94542,x94546)))+P22(f312(f312(x94541,x94542),x94543))
% 155.93/155.62 [9455]~P22(f312(f312(f314(x94554),x94553),f275(x94554,x94551,x94555,x94552,x94556)))+P22(f312(f312(x94551,x94552),x94553))
% 155.93/155.62 [9456]~P22(f312(f312(f314(x94564),x94562),f278(x94564,x94561,x94565,x94566,x94563)))+P22(f312(f312(x94561,x94562),x94563))
% 155.93/155.62 [9457]~P22(f312(f312(f314(x94574),x94572),f275(x94574,x94575,x94571,x94576,x94573)))+P22(f312(f312(x94571,x94572),x94573))
% 155.93/155.62 [5689]E(x56891,x56892)+~E(f312(f312(f239(x56893,x56894),x56895),x56891),f312(f312(f239(x56893,x56894),x56896),x56892))
% 155.93/155.62 [5691]E(x56911,x56912)+~E(f312(f312(f239(x56913,x56914),x56911),x56915),f312(f312(f239(x56913,x56914),x56912),x56916))
% 155.93/155.62 [7198]~P37(x71984,x71981,f312(f312(f147(x71984),x71982),x71985),f312(f312(f147(x71984),x71983),x71986))+P22(f312(f312(x71981,x71982),x71983))
% 155.93/155.62 [7563]P37(x75631,x75632,x75633,x75634)+~P37(x75631,x75632,f312(f312(f147(x75631),x75635),x75633),f312(f312(f147(x75631),x75636),x75634))
% 155.93/155.62 [8376]~P36(x83761,x83762,x83763,x83765)+P36(x83761,x83762,f312(f312(f312(f81(x83761,f857(x83762)),x83763),x83764),f192(x83762)),f312(f312(f312(f81(x83761,f857(x83762)),x83765),x83764),f312(f219(x83762),x83766)))
% 155.93/155.62 [8602]~P56(x86025,x86021,x86022,x86026,x86024)+P22(f312(f312(f314(x86021),f312(x86022,x86023)),x86024))
% 155.93/155.62 [8769]E(f312(f85(x87691,x87692,x87693,x87694,x87695),x87696),f312(x87693,x87696))+P22(f312(f312(f314(x87691),x87696),x87695))
% 155.93/155.62 [8789]~E(x87893,f312(f312(f147(x87891),x87895),x87896))+P22(f312(f312(f314(f860(f854(x87891),f854(x87891))),f312(f312(f239(f854(x87891),f854(x87891)),x87892),f312(f312(f129(x87891),x87892),x87893))),f143(x87891,x87894)))
% 155.93/155.62 [8795]E(f312(f85(x87951,x87952,x87953,x87954,x87955),x87956),f312(x87954,x87956))+~P22(f312(f312(f314(x87951),x87956),x87955))
% 155.93/155.62 [8800]E(f312(f182(x88001,x88002,x88003,x88004,x88005),x88006),f312(x88003,x88006))+P22(f312(f312(f314(x88001),x88006),f312(f168(x88001),x88004)))
% 155.93/155.62 [9030]~P39(x90301,x90302,x90303,x90305,x90306)+P39(x90301,x90302,x90303,f312(f312(f169(x90301),x90304),x90305),f312(f312(f169(x90302),x90304),x90306))
% 155.93/155.62 [9031]~P39(x90311,x90312,x90313,x90315,x90316)+P39(x90311,x90312,x90313,f312(f312(f134(x90311),x90314),x90315),f312(f312(f134(x90312),x90314),x90316))
% 155.93/155.62 [9519]~P17(x95194,x95192,x95195,x95193,x95196,x95191)+E(f312(x95191,f189(f861(x95192,a846))),x95193)
% 155.93/155.62 [9755]~E(f312(x97554,f312(f246(x97551,x97553),x97555)),f312(x97556,f312(f246(x97551,x97553),x97555)))+E(f312(f250(x97551,x97552,x97553,x97553,x97554,f39(x97553)),x97555),f312(f250(x97551,x97552,x97553,x97553,x97556,f39(x97553)),x97555))
% 155.93/155.62 [9756]~E(f312(x97564,f312(f248(x97561,x97562),x97565)),f312(x97566,f312(f248(x97561,x97562),x97565)))+E(f312(f250(x97561,x97561,x97562,x97563,f39(x97561),x97564),x97565),f312(f250(x97561,x97561,x97562,x97563,f39(x97561),x97566),x97565))
% 155.93/155.62 [9805]~E(f312(f250(x98052,x98056,x98053,x98053,x98051,f39(x98053)),x98054),f312(f250(x98052,x98056,x98053,x98053,x98055,f39(x98053)),x98054))+E(f312(x98051,f312(f246(x98052,x98053),x98054)),f312(x98055,f312(f246(x98052,x98053),x98054)))
% 155.93/155.62 [9806]~E(f312(f250(x98062,x98062,x98063,x98066,f39(x98062),x98061),x98064),f312(f250(x98062,x98062,x98063,x98066,f39(x98062),x98065),x98064))+E(f312(x98061,f312(f248(x98062,x98063),x98064)),f312(x98065,f312(f248(x98062,x98063),x98064)))
% 155.93/155.62 [8698]P22(f312(f312(f314(x86981),x86982),x86983))+~P22(f312(f312(f314(f860(x86981,x86984)),f312(f312(f239(x86981,x86984),x86982),x86985)),f312(f312(f247(x86981,x86984),x86983),x86986)))
% 155.93/155.62 [8712]P22(f312(f312(f314(x87121),x87122),f312(x87123,x87124)))+~P22(f312(f312(f314(f860(x87125,x87121)),f312(f312(f239(x87125,x87121),x87124),x87122)),f312(f312(f247(x87125,x87121),x87126),x87123)))
% 155.93/155.62 [8797]~E(f312(f190(f854(x87971)),x87974),f312(f190(f854(x87972)),x87975))+E(f182(x87971,x87972,x87973,x87974,f312(f312(f129(x87972),x87975),x87976)),f182(x87971,x87972,x87973,x87974,x87975))
% 155.93/155.62 [8798]~E(f312(f190(f854(x87981)),x87984),f312(f190(f854(x87982)),x87986))+E(f182(x87981,x87982,x87983,f312(f312(f129(x87981),x87984),x87985),x87986),f182(x87981,x87982,x87983,x87984,x87986))
% 155.93/155.62 [9049]P22(f312(f312(f314(x90491),x90494),f179(x90491,x90492,x90496)))+E(f180(x90491,x90492,f312(f312(f312(f81(x90491,f857(x90492)),x90493),x90494),f312(f219(x90492),x90495)),x90496),f312(f312(f312(f81(x90491,f857(x90492)),f180(x90491,x90492,x90493,x90496)),x90494),f312(f219(x90492),x90495)))
% 155.93/155.62 [9149]P22(f312(f312(f314(f860(x91491,x91491)),f312(f312(f239(x91491,x91491),f312(x91492,x91493)),f312(x91492,x91494))),x91495))+~P22(f312(f312(f314(f860(x91496,x91496)),f312(f312(f239(x91496,x91496),x91493),x91494)),f312(f312(f266(x91491,x91496),x91495),x91492)))
% 155.93/155.62 [9168]~P22(f312(f312(f314(f860(x91684,x91684)),f312(f312(f239(x91684,x91684),f312(x91686,x91682)),f312(x91686,x91683))),x91685))+P22(f312(f312(f314(f860(x91681,x91681)),f312(f312(f239(x91681,x91681),x91682),x91683)),f312(f312(f266(x91684,x91681),x91685),x91686)))
% 155.93/155.62 [9790]P22(f312(f312(f312(f312(a198,x97901),f312(f312(f312(a201,x97902),f40(x97903)),f312(x97904,x97902))),x97905),f453(x97906,x97905,x97902,x97901,x97904,x97903)))+~P22(f312(f312(f312(f312(a198,f32(x97903,x97904,x97901)),x97902),x97905),f312(f312(f312(a201,x97906),f40(x97903)),f312(f312(a202,x97902),x97903))))
% 155.93/155.62 [9809]P22(f312(f312(f312(f312(a198,f312(a27,x98091)),f312(f312(f312(a201,f312(f312(a203,x98092),a204)),f40(a26)),f312(x98093,x98092))),x98094),f528(x98095,x98094,x98092,x98093,x98091,x98096)))+~P22(f312(f312(f312(f312(a198,f31(x98096,x98091,x98093)),x98092),x98094),f312(f312(f312(a201,f312(f312(a203,x98095),f312(a202,x98092))),x98096),f312(f312(a202,x98095),a25))))
% 155.93/155.62 [9885]E(f312(f312(f312(a201,f453(x98851,x98852,x98853,x98854,x98855,x98856)),f40(x98856)),f312(f312(a202,x98853),x98856)),f312(f312(f312(a201,x98851),f40(x98856)),f312(f312(a202,x98853),x98856)))+~P22(f312(f312(f312(f312(a198,f32(x98856,x98855,x98854)),x98853),x98852),f312(f312(f312(a201,x98851),f40(x98856)),f312(f312(a202,x98853),x98856))))
% 155.93/155.62 [10005]E(f312(f312(f312(a201,f312(f312(a203,f528(x100051,x100052,x100053,x100054,x100055,x100056)),f312(a202,x100053))),x100056),f312(f312(a202,f528(x100051,x100052,x100053,x100054,x100055,x100056)),a25)),f312(f312(f312(a201,f312(f312(a203,x100051),f312(a202,x100053))),x100056),f312(f312(a202,x100051),a25)))+~P22(f312(f312(f312(f312(a198,f31(x100056,x100055,x100054)),x100053),x100052),f312(f312(f312(a201,f312(f312(a203,x100051),f312(a202,x100053))),x100056),f312(f312(a202,x100051),a25))))
% 155.93/155.62 [6082]~E(x60826,x60824)+E(f312(f312(f312(f312(f81(x60821,x60822),x60823),x60824),x60825),x60826),x60825)
% 155.93/155.62 [6131]E(x61311,x61312)+E(f312(f312(f312(f312(f81(x61313,x61314),x61315),x61312),x61316),x61311),f312(x61315,x61311))
% 155.93/155.62 [7634]~P31(x76342)+E(f312(f312(f50(x76341,x76342),x76343),f312(f312(f7(x76341,x76344,x76342),x76345),x76346)),f312(f312(f312(f50(x76341,f861(x76344,x76342)),x76343),x76345),x76346))
% 155.93/155.62 [7635]~P31(x76352)+E(f312(f312(f51(x76351,x76352),x76353),f312(f312(f7(x76351,x76354,x76352),x76355),x76356)),f312(f312(f312(f51(x76351,f861(x76354,x76352)),x76353),x76355),x76356))
% 155.93/155.62 [8294]~P36(x82941,x82942,x82943,x82946)+P36(x82941,x82942,f312(f312(f312(f81(x82941,f857(x82942)),x82943),x82944),x82945),f312(f312(f312(f81(x82941,f857(x82942)),x82946),x82944),x82945))
% 155.93/155.62 [8423]E(f312(f312(f50(x84231,f861(x84232,a846)),x84233),f312(f312(f8(f861(x84232,a846),f861(x84232,a846),x84231),f312(f289(x84232),x84234)),x84235)),f312(f312(f289(x84232),x84234),f312(f312(f50(x84231,f861(x84232,a846)),x84233),x84235)))+~P22(f312(f312(f314(x84231),x84236),x84233))
% 155.93/155.62 [8851]~P31(x88512)+E(f312(f312(f50(x88511,x88512),x88513),f312(f312(f8(f861(x88514,x88512),x88512,x88511),f312(f50(x88514,x88512),x88515)),f312(f7(x88514,x88511,x88512),x88516))),f312(f312(f50(x88514,x88512),x88515),f312(f312(f8(f861(x88511,x88512),x88512,x88514),f312(f50(x88511,x88512),x88513)),x88516)))
% 155.93/155.62 [8852]~P31(x88522)+E(f312(f312(f51(x88521,x88522),x88523),f312(f312(f8(f861(x88524,x88522),x88522,x88521),f312(f51(x88524,x88522),x88525)),f312(f7(x88524,x88521,x88522),x88526))),f312(f312(f51(x88524,x88522),x88525),f312(f312(f8(f861(x88521,x88522),x88522,x88524),f312(f51(x88521,x88522),x88523)),x88526)))
% 155.93/155.62 [9059]P22(f312(f312(f314(x90591),x90592),f312(f168(x90591),x90593)))+~P22(f312(f312(f314(f860(x90594,x90591)),f312(f312(f239(x90594,x90591),x90595),x90592)),f312(f168(f860(x90594,x90591)),f312(f312(f177(x90594,x90591),x90596),x90593))))
% 155.93/155.62 [9060]P22(f312(f312(f314(x90601),x90602),f312(f168(x90601),x90603)))+~P22(f312(f312(f314(f860(x90601,x90604)),f312(f312(f239(x90601,x90604),x90602),x90605)),f312(f168(f860(x90601,x90604)),f312(f312(f177(x90601,x90604),x90603),x90606))))
% 155.93/155.62 [9162]P22(f312(f312(f227(f861(x91621,a846)),f312(f264(x91622,x91621,x91623),x91624)),x91625))+~P22(f312(f312(f227(f861(f860(x91622,x91621),a846)),x91623),f312(f312(f247(x91622,x91621),x91626),f312(f16(f861(x91621,a846),x91622),x91625))))
% 155.93/155.62 [9353]P22(f312(f312(f314(f860(f854(x93531),f854(x93531))),f312(f312(f239(f854(x93531),f854(x93531)),f312(f312(f147(x93531),x93532),x93533)),f312(f312(f147(x93531),x93534),x93535))),f143(x93531,x93536)))+~P22(f312(f312(f314(f860(x93531,x93531)),f312(f312(f239(x93531,x93531),x93532),x93534)),x93536))
% 155.93/155.62 [9391]P22(f312(f312(f312(f312(a198,f32(x93911,x93912,x93913)),x93914),x93915),f312(f312(f312(a201,x93916),f40(x93911)),f312(f312(a202,x93914),x93911))))+~P22(f312(f312(f312(f312(a198,x93913),f312(f312(f312(a201,x93914),f40(x93911)),f312(x93912,x93914))),x93915),x93916))
% 155.93/155.62 [9665]P22(f312(f312(f312(f312(a198,f31(x96651,x96652,x96653)),x96654),x96655),f312(f312(f312(a201,f312(f312(a203,x96656),f312(a202,x96654))),x96651),f312(f312(a202,x96656),a25))))+~P22(f312(f312(f312(f312(a198,f312(a27,x96652)),f312(f312(f312(a201,f312(f312(a203,x96654),a204)),f40(a26)),f312(x96653,x96654))),x96655),x96656))
% 155.93/155.62 [9785]P22(f312(f312(f312(f312(a198,x97851),f312(f312(f312(a201,x97852),f40(x97853)),f312(x97854,x97852))),x97855),f485(x97856,x97855,x97852,x97851,x97854,x97853)))+~P22(f312(f312(f312(f312(a198,f32(x97853,x97854,x97851)),x97852),x97855),x97856))
% 155.93/155.62 [9801]P22(f312(f312(f312(f312(a198,f312(a27,x98011)),f312(f312(f312(a201,f312(f312(a203,x98012),a204)),f40(a26)),f312(x98013,x98012))),x98014),f620(x98015,x98014,x98012,x98013,x98011,x98016)))+~P22(f312(f312(f312(f312(a198,f31(x98016,x98011,x98013)),x98012),x98014),x98015))
% 155.93/155.62 [9804]E(f312(f312(f239(x98041,x98042),f714(x98043,x98044,x98045,x98042,x98041,x98046)),f715(x98043,x98044,x98045,x98042,x98041,x98046)),x98046)+P22(f312(f312(f314(x98045),x98044),f312(f312(f249(x98041,x98042,f861(x98045,a846)),x98043),x98046)))
% 155.93/155.62 [9810]E(f312(f312(f239(x98101,x98102),f716(x98103,x98104,x98102,x98101,x98105,x98106)),f717(x98103,x98104,x98102,x98101,x98105,x98106)),x98103)+~P22(f312(f312(f314(x98106),x98105),f312(f312(f249(x98101,x98102,f861(x98106,a846)),x98104),x98103)))
% 155.93/155.62 [9881]E(f312(f312(f312(a201,f485(x98811,x98812,x98813,x98814,x98815,x98816)),f40(x98816)),f312(f312(a202,x98813),x98816)),x98811)+~P22(f312(f312(f312(f312(a198,f32(x98816,x98815,x98814)),x98813),x98812),x98811))
% 155.93/155.62 [9971]P22(f312(f312(f314(x99711),x99712),f312(f312(x99713,f716(x99714,x99713,x99715,x99716,x99712,x99711)),f717(x99714,x99713,x99715,x99716,x99712,x99711))))+~P22(f312(f312(f314(x99711),x99712),f312(f312(f249(x99716,x99715,f861(x99711,a846)),x99713),x99714)))
% 155.93/155.62 [9991]~P22(f312(f312(f314(x99911),x99912),f312(f312(x99915,f714(x99915,x99912,x99911,x99914,x99913,x99916)),f715(x99915,x99912,x99911,x99914,x99913,x99916))))+P22(f312(f312(f314(x99911),x99912),f312(f312(f249(x99913,x99914,f861(x99911,a846)),x99915),x99916)))
% 155.93/155.62 [10003]E(f312(f312(f312(a201,f312(f312(a203,f620(x100031,x100032,x100033,x100034,x100035,x100036)),f312(a202,x100033))),x100036),f312(f312(a202,f620(x100031,x100032,x100033,x100034,x100035,x100036)),a25)),x100031)+~P22(f312(f312(f312(f312(a198,f31(x100036,x100035,x100034)),x100033),x100032),x100031))
% 155.93/155.62 [7757]P22(f312(f312(f314(x77571),x77574),x77576))+E(f183(x77571,x77572,f312(f312(f312(f81(x77571,f857(x77572)),x77573),x77574),x77575),x77576),f183(x77571,x77572,x77573,x77576))
% 155.93/155.62 [7826]P22(f312(f312(f314(x78261),x78264),x78266))+E(f312(f290(x78261,x78262,f312(f312(f312(f81(x78261,x78262),x78263),x78264),x78265)),x78266),f312(f290(x78261,x78262,x78263),x78266))
% 155.93/155.62 [7852]P22(f312(f312(f314(x78521),x78524),f312(f168(x78521),x78526)))+E(f312(f312(f150(x78521,x78522),f312(f312(f312(f81(x78521,x78522),x78523),x78524),x78525)),x78526),f312(f312(f150(x78521,x78522),x78523),x78526))
% 155.93/155.62 [8315]E(x83151,x83152)+E(f312(f312(f155(x83153,f312(f312(f155(x83153,x83154),x83151),x83155)),x83152),x83156),f312(f312(f155(x83153,f312(f312(f155(x83153,x83154),x83152),x83156)),x83151),x83155))
% 155.93/155.62 [8857]~P22(f312(f312(f314(x88573),x88576),x88575))+E(f312(f312(f289(x88571),x88572),f312(f290(x88573,x88571,x88574),f312(f312(f21(f861(x88573,a846)),x88575),f312(f312(f289(x88573),x88576),f189(f861(x88573,a846)))))),f312(f290(x88573,x88571,f312(f312(f312(f81(x88573,x88571),x88574),x88576),x88572)),x88575))
% 155.93/155.62 [9620]E(f182(x96201,x96202,x96203,f312(f312(f129(x96201),x96204),f312(f312(f147(x96201),x96205),f127(x96201))),x96206),f312(f312(f312(f81(x96201,f857(x96202)),f182(x96201,x96202,x96203,x96204,x96206)),x96205),f312(f219(x96202),f312(f312(f161(x96202),x96206),f312(f190(f854(x96201)),x96204)))))+~P22(f312(f312(f228(a853),f312(f190(f854(x96201)),x96204)),f312(f190(f854(x96202)),x96206)))
% 155.93/155.62 [8642]~E(x86423,x86426)+E(f312(f312(f173(x86421,x86422),f312(f312(f147(f860(x86421,x86422)),f312(f312(f239(x86421,x86422),x86423),x86424)),x86425)),x86426),f312(f219(x86422),x86424))
% 155.93/155.62 [8670]E(x86701,x86702)+E(f312(f312(f173(x86703,x86704),f312(f312(f147(f860(x86703,x86704)),f312(f312(f239(x86703,x86704),x86701),x86705)),x86706)),x86702),f312(f312(f173(x86703,x86704),x86706),x86702))
% 155.93/155.62 [8937]~P22(f312(f312(x89374,x89375),x89376))+P22(f312(f312(f312(f312(f124(f861(x89371,f861(x89372,a846))),x89373),x89374),x89375),x89376))
% 155.93/155.62 [8939]~P22(f312(f312(x89393,x89395),x89396))+P22(f312(f312(f312(f312(f124(f861(x89391,f861(x89392,a846))),x89393),x89394),x89395),x89396))
% 155.93/155.62 [9220]P22(f312(f312(x92201,x92202),x92203))+~P22(f312(f312(f312(f312(f115(f861(x92204,f861(x92205,a846))),x92206),x92201),x92202),x92203))
% 155.93/155.62 [9221]P22(f312(f312(x92211,x92212),x92213))+~P22(f312(f312(f312(f312(f115(f861(x92214,f861(x92215,a846))),x92211),x92216),x92212),x92213))
% 155.93/155.62 [9643]~P72(x96432)+E(f312(f312(f9(x96431,x96432),f312(f312(f7(x96431,f861(x96433,a846),x96432),f312(f312(f8(f861(x96433,x96432),f861(f861(x96433,a846),x96432),x96431),f9(x96433,x96432)),x96434)),x96435)),x96436),f312(f312(f9(f860(x96431,x96433),x96432),f312(f249(x96431,x96433,x96432),x96434)),f312(f312(f247(x96431,x96433),x96436),f312(f16(f861(x96433,a846),x96431),x96435))))
% 155.93/155.62 [9644]~P26(x96442)+E(f312(f312(f6(x96441,x96442),f312(f312(f7(x96441,f861(x96443,a846),x96442),f312(f312(f8(f861(x96443,x96442),f861(f861(x96443,a846),x96442),x96441),f6(x96443,x96442)),x96444)),x96445)),x96446),f312(f312(f6(f860(x96441,x96443),x96442),f312(f249(x96441,x96443,x96442),x96444)),f312(f312(f247(x96441,x96443),x96446),f312(f16(f861(x96443,a846),x96441),x96445))))
% 155.93/155.62 [9782]~P26(x97822)+E(f312(f312(f6(x97821,x97822),f312(f312(f7(x97821,f861(x97823,a846),x97822),f312(f312(f8(f861(x97823,x97822),f861(f861(x97823,a846),x97822),x97821),f6(x97823,x97822)),f312(f7(x97823,x97821,x97822),x97824))),x97825)),x97826),f312(f312(f6(x97823,x97822),f312(f312(f7(x97823,f861(x97821,a846),x97822),f312(f312(f8(f861(x97821,x97822),f861(f861(x97821,a846),x97822),x97823),f6(x97821,x97822)),x97824)),x97826)),x97825))
% 155.93/155.62 [9488]~P22(f312(f312(f314(x94881),x94885),x94884))+E(f312(f312(f312(f81(x94881,f857(x94882)),f183(x94881,x94882,x94883,f312(f312(f21(f861(x94881,a846)),x94884),f312(f312(f289(x94881),x94885),f189(f861(x94881,a846)))))),x94885),x94886),f183(x94881,x94882,f312(f312(f312(f81(x94881,f857(x94882)),x94883),x94885),x94886),x94884))
% 155.93/155.62 [10073]~P22(f312(f312(f314(f860(x100731,x100732)),f312(f312(f239(x100731,x100732),x100735),x100736)),f312(f312(f124(f861(f860(x100731,x100732),a846)),x100733),x100734)))+P22(f312(f312(f312(f312(f124(f861(x100731,f861(x100732,a846))),f312(f312(f7(x100731,f861(f860(x100731,x100732),a846),f861(x100732,a846)),f312(f312(f8(f861(x100732,f861(f861(f860(x100731,x100732),a846),a846)),f861(f861(f860(x100731,x100732),a846),f861(x100732,a846)),x100731),f7(x100732,f861(f860(x100731,x100732),a846),a846)),f312(f312(f8(f861(x100732,f860(x100731,x100732)),f861(x100732,f861(f861(f860(x100731,x100732),a846),a846)),x100731),f312(f8(f860(x100731,x100732),f861(f861(f860(x100731,x100732),a846),a846),x100732),f314(f860(x100731,x100732)))),f239(x100731,x100732)))),x100733)),f312(f312(f7(x100731,f861(f860(x100731,x100732),a846),f861(x100732,a846)),f312(f312(f8(f861(x100732,f861(f861(f860(x100731,x100732),a846),a846)),f861(f861(f860(x100731,x100732),a846),f861(x100732,a846)),x100731),f7(x100732,f861(f860(x100731,x100732),a846),a846)),f312(f312(f8(f861(x100732,f860(x100731,x100732)),f861(x100732,f861(f861(f860(x100731,x100732),a846),a846)),x100731),f312(f8(f860(x100731,x100732),f861(f861(f860(x100731,x100732),a846),a846),x100732),f314(f860(x100731,x100732)))),f239(x100731,x100732)))),x100734)),x100735),x100736))
% 155.93/155.62 [10074]~P22(f312(f312(f314(f860(x100741,x100742)),f312(f312(f239(x100741,x100742),x100745),x100746)),f312(f312(f115(f861(f860(x100741,x100742),a846)),x100743),x100744)))+P22(f312(f312(f312(f312(f115(f861(x100741,f861(x100742,a846))),f312(f312(f7(x100741,f861(f860(x100741,x100742),a846),f861(x100742,a846)),f312(f312(f8(f861(x100742,f861(f861(f860(x100741,x100742),a846),a846)),f861(f861(f860(x100741,x100742),a846),f861(x100742,a846)),x100741),f7(x100742,f861(f860(x100741,x100742),a846),a846)),f312(f312(f8(f861(x100742,f860(x100741,x100742)),f861(x100742,f861(f861(f860(x100741,x100742),a846),a846)),x100741),f312(f8(f860(x100741,x100742),f861(f861(f860(x100741,x100742),a846),a846),x100742),f314(f860(x100741,x100742)))),f239(x100741,x100742)))),x100743)),f312(f312(f7(x100741,f861(f860(x100741,x100742),a846),f861(x100742,a846)),f312(f312(f8(f861(x100742,f861(f861(f860(x100741,x100742),a846),a846)),f861(f861(f860(x100741,x100742),a846),f861(x100742,a846)),x100741),f7(x100742,f861(f860(x100741,x100742),a846),a846)),f312(f312(f8(f861(x100742,f860(x100741,x100742)),f861(x100742,f861(f861(f860(x100741,x100742),a846),a846)),x100741),f312(f8(f860(x100741,x100742),f861(f861(f860(x100741,x100742),a846),a846),x100742),f314(f860(x100741,x100742)))),f239(x100741,x100742)))),x100744)),x100745),x100746))
% 155.93/155.62 [10080]P22(f312(f312(f314(f860(x100801,x100802)),f312(f312(f239(x100801,x100802),x100803),x100804)),f312(f312(f124(f861(f860(x100801,x100802),a846)),x100805),x100806)))+~P22(f312(f312(f312(f312(f124(f861(x100801,f861(x100802,a846))),f312(f312(f7(x100801,f861(f860(x100801,x100802),a846),f861(x100802,a846)),f312(f312(f8(f861(x100802,f861(f861(f860(x100801,x100802),a846),a846)),f861(f861(f860(x100801,x100802),a846),f861(x100802,a846)),x100801),f7(x100802,f861(f860(x100801,x100802),a846),a846)),f312(f312(f8(f861(x100802,f860(x100801,x100802)),f861(x100802,f861(f861(f860(x100801,x100802),a846),a846)),x100801),f312(f8(f860(x100801,x100802),f861(f861(f860(x100801,x100802),a846),a846),x100802),f314(f860(x100801,x100802)))),f239(x100801,x100802)))),x100805)),f312(f312(f7(x100801,f861(f860(x100801,x100802),a846),f861(x100802,a846)),f312(f312(f8(f861(x100802,f861(f861(f860(x100801,x100802),a846),a846)),f861(f861(f860(x100801,x100802),a846),f861(x100802,a846)),x100801),f7(x100802,f861(f860(x100801,x100802),a846),a846)),f312(f312(f8(f861(x100802,f860(x100801,x100802)),f861(x100802,f861(f861(f860(x100801,x100802),a846),a846)),x100801),f312(f8(f860(x100801,x100802),f861(f861(f860(x100801,x100802),a846),a846),x100802),f314(f860(x100801,x100802)))),f239(x100801,x100802)))),x100806)),x100803),x100804))
% 155.93/155.62 [10081]P22(f312(f312(f314(f860(x100811,x100812)),f312(f312(f239(x100811,x100812),x100813),x100814)),f312(f312(f115(f861(f860(x100811,x100812),a846)),x100815),x100816)))+~P22(f312(f312(f312(f312(f115(f861(x100811,f861(x100812,a846))),f312(f312(f7(x100811,f861(f860(x100811,x100812),a846),f861(x100812,a846)),f312(f312(f8(f861(x100812,f861(f861(f860(x100811,x100812),a846),a846)),f861(f861(f860(x100811,x100812),a846),f861(x100812,a846)),x100811),f7(x100812,f861(f860(x100811,x100812),a846),a846)),f312(f312(f8(f861(x100812,f860(x100811,x100812)),f861(x100812,f861(f861(f860(x100811,x100812),a846),a846)),x100811),f312(f8(f860(x100811,x100812),f861(f861(f860(x100811,x100812),a846),a846),x100812),f314(f860(x100811,x100812)))),f239(x100811,x100812)))),x100815)),f312(f312(f7(x100811,f861(f860(x100811,x100812),a846),f861(x100812,a846)),f312(f312(f8(f861(x100812,f861(f861(f860(x100811,x100812),a846),a846)),f861(f861(f860(x100811,x100812),a846),f861(x100812,a846)),x100811),f7(x100812,f861(f860(x100811,x100812),a846),a846)),f312(f312(f8(f861(x100812,f860(x100811,x100812)),f861(x100812,f861(f861(f860(x100811,x100812),a846),a846)),x100811),f312(f8(f860(x100811,x100812),f861(f861(f860(x100811,x100812),a846),a846),x100812),f314(f860(x100811,x100812)))),f239(x100811,x100812)))),x100816)),x100813),x100814))
% 155.93/155.62 [10067]~P22(f312(f312(f314(f860(x100672,x100673)),f312(f312(f239(x100672,x100673),x100675),x100676)),f312(f312(f50(x100671,f861(f860(x100672,x100673),a846)),f235(f861(x100671,a846))),x100674)))+P22(f312(f312(f312(f312(f50(x100671,f861(x100672,f861(x100673,a846))),f235(f861(x100671,a846))),f312(f312(f8(f861(f860(x100672,x100673),a846),f861(x100672,f861(x100673,a846)),x100671),f312(f7(x100672,f861(f860(x100672,x100673),a846),f861(x100673,a846)),f312(f312(f8(f861(x100673,f861(f861(f860(x100672,x100673),a846),a846)),f861(f861(f860(x100672,x100673),a846),f861(x100673,a846)),x100672),f7(x100673,f861(f860(x100672,x100673),a846),a846)),f312(f312(f8(f861(x100673,f860(x100672,x100673)),f861(x100673,f861(f861(f860(x100672,x100673),a846),a846)),x100672),f312(f8(f860(x100672,x100673),f861(f861(f860(x100672,x100673),a846),a846),x100673),f314(f860(x100672,x100673)))),f239(x100672,x100673))))),x100674)),x100675),x100676))
% 155.93/155.62 [10068]~P22(f312(f312(f314(f860(x100682,x100683)),f312(f312(f239(x100682,x100683),x100685),x100686)),f312(f312(f51(x100681,f861(f860(x100682,x100683),a846)),f235(f861(x100681,a846))),x100684)))+P22(f312(f312(f312(f312(f51(x100681,f861(x100682,f861(x100683,a846))),f235(f861(x100681,a846))),f312(f312(f8(f861(f860(x100682,x100683),a846),f861(x100682,f861(x100683,a846)),x100681),f312(f7(x100682,f861(f860(x100682,x100683),a846),f861(x100683,a846)),f312(f312(f8(f861(x100683,f861(f861(f860(x100682,x100683),a846),a846)),f861(f861(f860(x100682,x100683),a846),f861(x100683,a846)),x100682),f7(x100683,f861(f860(x100682,x100683),a846),a846)),f312(f312(f8(f861(x100683,f860(x100682,x100683)),f861(x100683,f861(f861(f860(x100682,x100683),a846),a846)),x100682),f312(f8(f860(x100682,x100683),f861(f861(f860(x100682,x100683),a846),a846),x100683),f314(f860(x100682,x100683)))),f239(x100682,x100683))))),x100684)),x100685),x100686))
% 155.93/155.62 [10077]P22(f312(f312(f314(f860(x100771,x100772)),f312(f312(f239(x100771,x100772),x100773),x100774)),f312(f312(f50(x100775,f861(f860(x100771,x100772),a846)),f235(f861(x100775,a846))),x100776)))+~P22(f312(f312(f312(f312(f50(x100775,f861(x100771,f861(x100772,a846))),f235(f861(x100775,a846))),f312(f312(f8(f861(f860(x100771,x100772),a846),f861(x100771,f861(x100772,a846)),x100775),f312(f7(x100771,f861(f860(x100771,x100772),a846),f861(x100772,a846)),f312(f312(f8(f861(x100772,f861(f861(f860(x100771,x100772),a846),a846)),f861(f861(f860(x100771,x100772),a846),f861(x100772,a846)),x100771),f7(x100772,f861(f860(x100771,x100772),a846),a846)),f312(f312(f8(f861(x100772,f860(x100771,x100772)),f861(x100772,f861(f861(f860(x100771,x100772),a846),a846)),x100771),f312(f8(f860(x100771,x100772),f861(f861(f860(x100771,x100772),a846),a846),x100772),f314(f860(x100771,x100772)))),f239(x100771,x100772))))),x100776)),x100773),x100774))
% 155.93/155.62 [10078]P22(f312(f312(f314(f860(x100781,x100782)),f312(f312(f239(x100781,x100782),x100783),x100784)),f312(f312(f51(x100785,f861(f860(x100781,x100782),a846)),f235(f861(x100785,a846))),x100786)))+~P22(f312(f312(f312(f312(f51(x100785,f861(x100781,f861(x100782,a846))),f235(f861(x100785,a846))),f312(f312(f8(f861(f860(x100781,x100782),a846),f861(x100781,f861(x100782,a846)),x100785),f312(f7(x100781,f861(f860(x100781,x100782),a846),f861(x100782,a846)),f312(f312(f8(f861(x100782,f861(f861(f860(x100781,x100782),a846),a846)),f861(f861(f860(x100781,x100782),a846),f861(x100782,a846)),x100781),f7(x100782,f861(f860(x100781,x100782),a846),a846)),f312(f312(f8(f861(x100782,f860(x100781,x100782)),f861(x100782,f861(f861(f860(x100781,x100782),a846),a846)),x100781),f312(f8(f860(x100781,x100782),f861(f861(f860(x100781,x100782),a846),a846),x100782),f314(f860(x100781,x100782)))),f239(x100781,x100782))))),x100786)),x100783),x100784))
% 155.93/155.62 [9129]E(x91291,x91292)+~E(f299(x91293,x91294,x91295,x91296,x91291),f299(x91293,x91294,x91295,x91297,x91292))
% 155.93/155.62 [9130]E(x91301,x91302)+~E(f299(x91303,x91304,x91305,x91301,x91306),f299(x91303,x91304,x91305,x91302,x91307))
% 155.93/155.62 [7313]E(f312(x73131,f312(x73132,x73133)),f312(x73134,x73133))+~E(f312(f82(x73135,x73136,x73137,x73131),x73132),x73134)
% 155.93/155.62 [9867]~P53(x98675,x98676,x98677,x98671,x98674,x98672,x98673)+P22(f312(f312(x98671,x98672),f569(x98673,x98672,x98674,x98671)))
% 155.93/155.62 [9890]~E(f312(f221(f857(x98907),x98901,f192(x98907),x98905),f312(x98904,x98903)),f312(f219(x98907),x98902))+E(f312(f219(x98901),f596(x98902,x98903,x98904,x98905,x98906,x98907,x98901)),f312(x98904,x98903))
% 155.93/155.62 [9891]~E(f312(f221(f857(x98916),x98917,f192(x98916),x98911),f312(x98914,x98913)),f312(f219(x98916),x98912))+E(f312(x98911,f596(x98912,x98913,x98914,x98911,x98915,x98916,x98917)),f312(f219(x98916),x98912))
% 155.93/155.62 [5915]~E(f312(f312(f150(x59151,x59155),x59156),x59152),f312(f312(f150(x59153,x59155),x59157),x59154))+E(f312(f190(f854(x59151)),x59152),f312(f190(f854(x59153)),x59154))
% 155.93/155.62 [7388]E(x73881,x73882)+~E(f312(f312(f312(f81(x73883,f857(x73884)),x73885),x73886),f312(f219(x73884),x73881)),f312(f312(f312(f81(x73883,f857(x73884)),x73887),x73886),f312(f219(x73884),x73882)))
% 155.93/155.62 [8357]E(f312(x83571,f312(x83572,x83573)),f312(x83574,x83573))+~E(f312(f82(x83575,x83576,x83577,x83571),x83572),f312(f82(x83576,x83576,x83577,f39(x83576)),x83574))
% 155.93/155.62 [8688]~P39(x86884,x86885,x86881,f312(f312(f147(x86884),x86882),x86886),f312(f312(f147(x86885),x86883),x86887))+P22(f312(f312(x86881,x86882),x86883))
% 155.93/155.62 [9064]P39(x90641,x90642,x90643,x90644,x90645)+~P39(x90641,x90642,x90643,f312(f312(f147(x90641),x90646),x90644),f312(f312(f147(x90642),x90647),x90645))
% 155.93/155.62 [9872]~P53(x98725,x98726,x98727,x98724,x98721,x98723,x98722)+P22(f312(f312(x98721,f569(x98722,x98723,x98721,x98724)),x98722))
% 155.93/155.62 [5957]E(x59571,x59572)+~E(f312(f312(f312(f100(x59573),x59574),x59575),x59571),f312(f312(f312(f100(x59573),x59576),x59577),x59572))
% 155.93/155.62 [5958]E(x59581,x59582)+~E(f312(f312(f312(f100(x59583),x59584),x59581),x59585),f312(f312(f312(f100(x59583),x59586),x59582),x59587))
% 155.93/155.62 [5959]E(x59591,x59592)+~E(f312(f312(f312(f100(x59593),x59591),x59594),x59595),f312(f312(f312(f100(x59593),x59592),x59596),x59597))
% 155.93/155.62 [8802]~P15(x88026,x88021,x88023,x88027)+E(f312(f82(x88021,x88021,x88022,f312(x88023,x88024)),f312(f82(x88021,x88021,x88022,f312(x88023,x88024)),x88025)),f312(f82(x88021,x88021,x88022,f312(x88023,x88024)),x88025))
% 155.93/155.62 [9172]~P39(x91723,x91722,x91724,f312(f312(f150(x91721,x91723),x91725),x91726),x91727)+P39(x91721,x91722,f312(f312(f8(x91723,f861(x91722,a846),x91721),x91724),x91725),x91726,x91727)
% 155.93/155.62 [9196]P39(x91961,x91962,x91963,f312(f312(f150(x91964,x91961),x91965),x91966),x91967)+~P39(x91964,x91962,f312(f312(f8(x91961,f861(x91962,a846),x91964),x91963),x91965),x91966,x91967)
% 155.93/155.62 [9598]E(f182(x95981,x95982,f312(f312(f312(f81(x95981,f857(x95982)),x95983),x95984),f312(f219(x95982),x95985)),x95986,x95987),f312(f312(f312(f81(x95981,f857(x95982)),f182(x95981,x95982,x95983,x95986,x95987)),x95984),f312(f219(x95982),x95985)))+P22(f312(f312(f314(x95981),x95984),f312(f168(x95981),x95986)))
% 155.93/155.62 [8801]~P22(f312(f312(f314(x88011),x88012),f312(f312(x88015,x88016),x88017)))+P22(f312(f312(f314(x88011),x88012),f312(f312(f249(x88013,x88014,f861(x88011,a846)),x88015),f312(f312(f239(x88013,x88014),x88016),x88017))))
% 155.93/155.62 [9090]P22(f312(f312(f312(x90901,x90902),x90903),x90904))+~P22(f312(f312(f312(f249(x90905,x90906,f861(x90907,a846)),x90901),f312(f312(f239(x90905,x90906),x90902),x90903)),x90904))
% 155.93/155.62 [9234]P22(f312(f312(f314(x92341),f312(f312(x92342,x92343),x92344)),f312(f290(f860(x92345,x92346),x92341,f312(f249(x92345,x92346,x92341),x92342)),x92347)))+~P22(f312(f312(f314(f860(x92345,x92346)),f312(f312(f239(x92345,x92346),x92343),x92344)),x92347))
% 155.93/155.62 [9560]P22(f312(f312(f314(f860(f854(x95601),f854(x95601))),f312(f312(f239(f854(x95601),f854(x95601)),f312(f312(f129(x95601),x95602),f312(f312(f147(x95601),x95603),x95604))),f312(f312(f129(x95601),x95602),f312(f312(f147(x95601),x95605),x95606)))),f143(x95601,x95607)))+~P22(f312(f312(f314(f860(x95601,x95601)),f312(f312(f239(x95601,x95601),x95603),x95605)),x95607))
% 155.93/155.62 [9621]~P39(x96211,x96213,x96214,x96216,f312(f312(f150(x96212,x96213),x96215),x96217))+P39(x96211,x96212,f312(f312(f7(x96211,f861(x96212,x96213),f861(x96212,a846)),f312(f312(f8(f861(x96213,a846),f861(f861(x96212,x96213),f861(x96212,a846)),x96211),f8(x96213,a846,x96212)),x96214)),x96215),x96216,x96217)
% 155.93/155.62 [9701]P39(x97011,x97012,x97013,x97014,f312(f312(f150(x97015,x97012),x97016),x97017))+~P39(x97011,x97015,f312(f312(f7(x97011,f861(x97015,x97012),f861(x97015,a846)),f312(f312(f8(f861(x97012,a846),f861(f861(x97015,x97012),f861(x97015,a846)),x97011),f8(x97012,a846,x97015)),x97013)),x97016),x97014,x97017)
% 155.93/155.62 [9990]P53(x99901,x99902,x99903,f312(f312(f7(x99901,f861(f860(x99901,x99902),a846),f861(x99902,a846)),f312(f312(f8(f861(x99902,f861(f861(f860(x99901,x99902),a846),a846)),f861(f861(f860(x99901,x99902),a846),f861(x99902,a846)),x99901),f7(x99902,f861(f860(x99901,x99902),a846),a846)),f312(f312(f8(f861(x99902,f860(x99901,x99902)),f861(x99902,f861(f861(f860(x99901,x99902),a846),a846)),x99901),f312(f8(f860(x99901,x99902),f861(f861(f860(x99901,x99902),a846),a846),x99902),f314(f860(x99901,x99902)))),f239(x99901,x99902)))),x99904),f312(f312(f7(x99902,f861(f860(x99902,x99903),a846),f861(x99903,a846)),f312(f312(f8(f861(x99903,f861(f861(f860(x99902,x99903),a846),a846)),f861(f861(f860(x99902,x99903),a846),f861(x99903,a846)),x99902),f7(x99903,f861(f860(x99902,x99903),a846),a846)),f312(f312(f8(f861(x99903,f860(x99902,x99903)),f861(x99903,f861(f861(f860(x99902,x99903),a846),a846)),x99902),f312(f8(f860(x99902,x99903),f861(f861(f860(x99902,x99903),a846),a846),x99903),f314(f860(x99902,x99903)))),f239(x99902,x99903)))),x99905),x99906,x99907)+~P22(f312(f312(f314(f860(x99901,x99903)),f312(f312(f239(x99901,x99903),x99906),x99907)),f312(f312(f267(x99901,x99902,x99903),x99904),x99905)))
% 155.93/155.62 [10021]~P53(x100211,x100215,x100212,f312(f312(f7(x100211,f861(f860(x100211,x100215),a846),f861(x100215,a846)),f312(f312(f8(f861(x100215,f861(f861(f860(x100211,x100215),a846),a846)),f861(f861(f860(x100211,x100215),a846),f861(x100215,a846)),x100211),f7(x100215,f861(f860(x100211,x100215),a846),a846)),f312(f312(f8(f861(x100215,f860(x100211,x100215)),f861(x100215,f861(f861(f860(x100211,x100215),a846),a846)),x100211),f312(f8(f860(x100211,x100215),f861(f861(f860(x100211,x100215),a846),a846),x100215),f314(f860(x100211,x100215)))),f239(x100211,x100215)))),x100216),f312(f312(f7(x100215,f861(f860(x100215,x100212),a846),f861(x100212,a846)),f312(f312(f8(f861(x100212,f861(f861(f860(x100215,x100212),a846),a846)),f861(f861(f860(x100215,x100212),a846),f861(x100212,a846)),x100215),f7(x100212,f861(f860(x100215,x100212),a846),a846)),f312(f312(f8(f861(x100212,f860(x100215,x100212)),f861(x100212,f861(f861(f860(x100215,x100212),a846),a846)),x100215),f312(f8(f860(x100215,x100212),f861(f861(f860(x100215,x100212),a846),a846),x100212),f314(f860(x100215,x100212)))),f239(x100215,x100212)))),x100217),x100213,x100214)+P22(f312(f312(f314(f860(x100211,x100212)),f312(f312(f239(x100211,x100212),x100213),x100214)),f312(f312(f267(x100211,x100215,x100212),x100216),x100217)))
% 155.93/155.62 [9082]E(x90821,x90822)+E(f312(f312(f312(f81(x90823,x90824),f312(f312(f312(f81(x90823,x90824),x90825),x90821),x90826)),x90822),x90827),f312(f312(f312(f81(x90823,x90824),f312(f312(f312(f81(x90823,x90824),x90825),x90822),x90827)),x90821),x90826))
% 155.93/155.62 [9327]E(f182(x93271,x93272,f312(f312(f312(f81(x93271,f857(x93272)),x93273),x93274),f312(f219(x93272),x93275)),x93276,x93277),f182(x93271,x93272,x93273,x93276,x93277))+~P22(f312(f312(f314(x93271),x93274),f312(f168(x93271),f312(f312(f169(x93271),f312(f190(f854(x93272)),x93277)),x93276))))
% 155.93/155.62 [9633]E(f182(x96331,x96332,f312(f312(f312(f81(x96331,f857(x96332)),x96333),x96334),f312(f219(x96332),x96335)),x96336,x96337),f312(f312(f312(f81(x96331,f857(x96332)),f182(x96331,x96332,x96333,x96336,x96337)),x96334),f312(f219(x96332),x96335)))+P22(f312(f312(f314(x96331),x96334),f312(f168(x96331),f312(f312(f169(x96331),f312(f190(f854(x96332)),x96337)),x96336))))
% 155.93/155.62 [10002]P22(f312(f312(f314(x100021),f642(x100022,x100023,x100024,x100025,x100026,x100027,x100021)),x100025))+P22(f312(f312(f312(f312(f51(x100021,f861(x100027,f861(x100026,a846))),x100025),x100024),x100023),x100022))
% 155.93/155.62 [10004]P22(f312(f312(f314(x100041),f424(x100042,x100043,x100044,x100045,x100046,x100047,x100041)),x100045))+~P22(f312(f312(f312(f312(f50(x100041,f861(x100047,f861(x100046,a846))),x100045),x100044),x100043),x100042))
% 155.93/155.62 [10030]P22(f312(f312(f312(x100301,f424(x100302,x100303,x100301,x100304,x100305,x100306,x100307)),x100303),x100302))+~P22(f312(f312(f312(f312(f50(x100307,f861(x100306,f861(x100305,a846))),x100304),x100301),x100303),x100302))
% 155.93/155.62 [10047]~P22(f312(f312(f312(x100475,f642(x100477,x100476,x100475,x100474,x100473,x100472,x100471)),x100476),x100477))+P22(f312(f312(f312(f312(f51(x100471,f861(x100472,f861(x100473,a846))),x100474),x100475),x100476),x100477))
% 155.93/155.62 [10014]~P135(x100142)+E(f312(f312(f6(x100141,x100142),f312(f312(f7(x100141,f861(x100143,a846),x100142),f312(f312(f8(f861(x100143,x100142),f861(f861(x100143,a846),x100142),x100141),f6(x100143,x100142)),f312(f312(f7(x100141,f861(x100143,x100142),f861(x100143,x100142)),f312(f312(f8(f861(x100142,x100142),f861(f861(x100143,x100142),f861(x100143,x100142)),x100141),f8(x100142,x100142,x100143)),f312(f312(f8(x100142,f861(x100142,x100142),x100141),f90(x100142)),x100144))),x100145))),x100146)),x100147),f312(f312(f90(x100142),f312(f312(f6(x100141,x100142),x100144),x100147)),f312(f312(f6(x100143,x100142),x100145),x100146)))
% 155.93/155.62 [9124]~P14(x91247,x91241,x91243,x91248)+E(f312(f82(x91241,x91241,x91242,f312(x91243,x91244)),f312(f82(x91241,x91241,x91242,f312(x91243,x91245)),x91246)),f312(f82(x91241,x91241,x91242,f312(x91243,x91245)),f312(f82(x91241,x91241,x91242,f312(x91243,x91244)),x91246)))
% 155.93/155.62 [10062]P18(x100621,x100622,f312(f312(f289(f852(x100621)),f312(f312(f312(f100(x100621),f312(f312(f8(f861(a848,a846),f861(a848,a846),x100621),f312(f18(a848,a846,a846),f312(f312(f8(a846,f861(a846,a846),a848),a310),f312(a309,x100623)))),f312(f312(f7(x100621,f861(a848,a848),f861(a848,a846)),f312(f312(f8(f861(a848,a846),f861(f861(a848,a848),f861(a848,a846)),x100621),f8(a848,a846,a848)),x100624)),f312(f312(f18(a848,a853,a848),f312(f312(f7(a848,a851,f861(a853,a848)),a201),f40(x100625))),x100626)))),f32(x100625,x100626,x100627)),x100628)),f189(f861(f852(x100621),a846))))+~P18(x100621,x100622,f312(f312(f289(f852(x100621)),f312(f312(f312(f100(x100621),x100624),x100627),f312(f312(f7(x100621,f861(a848,a848),f861(a848,a846)),f312(f312(f8(f861(a848,a846),f861(f861(a848,a848),f861(a848,a846)),x100621),f8(a848,a846,a848)),x100628)),f312(f312(f7(a848,a853,a848),f312(f312(f7(a848,a851,f861(a853,a848)),a201),f40(x100625))),f312(f312(a202,x100623),x100625))))),f189(f861(f852(x100621),a846))))
% 155.93/155.62 [10071]E(f312(f312(f239(x100711,x100712),f312(x100713,f534(x100714,x100715,x100713,x100716,x100717,x100718,x100712,x100711))),f312(x100715,f535(x100714,x100715,x100713,x100716,x100717,x100718,x100712,x100711))),x100718)+~P22(f312(f312(f314(f860(x100711,x100712)),x100718),f312(f290(f860(x100717,x100716),f860(x100711,x100712),f250(x100717,x100711,x100716,x100712,x100713,x100715)),x100714)))
% 155.93/155.62 [10086]P18(x100861,x100862,f312(f312(f289(f852(x100861)),f312(f312(f312(f100(x100861),f312(f312(f8(f861(a848,a846),f861(a848,a846),x100861),f312(f18(a848,a846,a846),f312(f312(f8(a846,f861(a846,a846),a848),a310),f312(a309,x100863)))),f312(f312(f7(x100861,f861(a848,a848),f861(a848,a846)),f312(f312(f8(f861(a848,a846),f861(f861(a848,a848),f861(a848,a846)),x100861),f8(a848,a846,a848)),x100864)),f312(f312(f18(a848,a853,a848),f312(f312(f7(a848,a851,f861(a853,a848)),f312(f312(f8(a848,f861(a851,f861(a853,a848)),a848),a201),f312(f312(f7(a848,f861(a850,a853),a848),a203),a204))),f40(a26))),x100865)))),f31(x100866,x100867,x100865)),x100868)),f189(f861(f852(x100861),a846))))+~P18(x100861,x100862,f312(f312(f289(f852(x100861)),f312(f312(f312(f100(x100861),x100864),f312(a27,x100867)),f312(f312(f7(x100861,f861(a848,a848),f861(a848,a846)),f312(f312(f8(f861(a848,a846),f861(f861(a848,a848),f861(a848,a846)),x100861),f8(a848,a846,a848)),x100868)),f312(f312(f18(a848,a853,a848),f312(f312(f7(a848,a851,f861(a853,a848)),f312(f312(f8(a848,f861(a851,f861(a853,a848)),a848),a201),f312(f312(f7(a848,f861(a850,a853),a848),a203),f312(a202,x100863)))),x100866)),f312(f312(f7(a848,a850,a853),a202),a25))))),f189(f861(f852(x100861),a846))))
% 155.93/155.62 [10087]~P22(f312(f312(f314(f860(x100878,x100877)),x100876),f312(f290(f860(x100871,x100872),f860(x100878,x100877),f250(x100871,x100878,x100872,x100877,x100875,x100874)),x100873)))+P22(f312(f312(f314(f860(x100871,x100872)),f312(f312(f239(x100871,x100872),f534(x100873,x100874,x100875,x100872,x100871,x100876,x100877,x100878)),f535(x100873,x100874,x100875,x100872,x100871,x100876,x100877,x100878))),x100873))
% 155.93/155.62 [9550]P22(f312(f312(f314(f860(f860(x95501,x95502),f860(x95501,x95502))),f312(f312(f239(f860(x95501,x95502),f860(x95501,x95502)),f312(f312(f239(x95501,x95502),x95503),x95504)),f312(f312(f239(x95501,x95502),x95505),x95506))),f304(x95501,x95502,x95507,x95508)))+~P22(f312(f312(f314(f860(x95501,x95501)),f312(f312(f239(x95501,x95501),x95503),x95505)),x95507))
% 155.93/155.62 [10060]E(f312(f138(x100601,x100602,f312(f7(x100602,x100601,x100601),x100603),f312(x100604,x100605)),x100606),f312(x100604,f312(f138(x100607,x100602,f312(f7(x100602,x100607,x100607),x100608),x100605),x100606)))+P22(f312(f312(f314(x100602),f709(x100605,x100608,x100604,x100603,x100607,x100601,x100606,x100602)),f312(f168(x100602),x100606)))
% 155.93/155.62 [10079]~E(f312(f82(x100791,x100791,x100797,f312(x100793,f709(x100795,x100798,x100794,x100793,x100797,x100791,x100796,x100792))),x100794),f312(f82(x100797,x100791,x100797,x100794),f312(x100798,f709(x100795,x100798,x100794,x100793,x100797,x100791,x100796,x100792))))+E(f312(f138(x100791,x100792,f312(f7(x100792,x100791,x100791),x100793),f312(x100794,x100795)),x100796),f312(x100794,f312(f138(x100797,x100792,f312(f7(x100792,x100797,x100797),x100798),x100795),x100796)))
% 155.93/155.62 [8363]E(f312(x83631,f312(x83632,x83633)),f312(x83634,f312(x83635,x83633)))+~E(f312(f82(x83636,x83637,x83638,x83631),x83632),f312(f82(x83639,x83637,x83638,x83634),x83635))
% 155.93/155.62 [9941]P22(f312(f312(f314(f860(x99411,x99412)),f312(f312(f239(x99411,x99412),f312(x99413,x99414)),f312(x99415,x99416))),f312(f290(f860(x99417,x99418),f860(x99411,x99412),f250(x99417,x99411,x99418,x99412,x99413,x99415)),x99419)))+~P22(f312(f312(f314(f860(x99417,x99418)),f312(f312(f239(x99417,x99418),x99414),x99416)),x99419))
% 155.93/155.62 [8635]~E(f312(x86354,f312(x86355,x86356)),f312(x86359,f312(x863510,x863511)))+E(f312(f312(f82(x86351,x86352,x86353,x86354),x86355),x86356),f312(f312(f82(x86357,x86352,x86358,x86359),x863510),x863511))
% 155.93/155.62 [4523]~P99(x45231)+~P103(x45231)+E(f115(x45231),f225(x45231))
% 155.93/155.62 [4524]~P98(x45241)+~P103(x45241)+E(f124(x45241),f226(x45241))
% 155.93/155.62 [4771]~P112(x47711)+~P90(x47711)+E(f312(f84(x47711),f312(f117(x47711),a111)),f87(x47711))
% 155.93/155.62 [5044]E(x50441,f2(a1))+E(f91(a1,x50441),f312(f88(a1),f87(a1)))+P22(f312(f312(f228(a1),f2(a1)),x50441))
% 155.93/155.62 [5255]E(x52551,f2(a1))+E(f91(a1,x52551),f87(a1))+~P22(f312(f312(f228(a1),f2(a1)),x52551))
% 155.93/155.62 [7204]~P43(x72041)+P22(f312(f70(a1),x72041))+~P22(f312(f70(a853),f312(f290(a1,a853,a118),x72041)))
% 155.93/155.62 [8469]~P4(a5000)+~P22(f312(f312(f314(f860(a849,a847)),x84691),f312(f168(f860(a849,a847)),a29)))+P22(f312(f312(f249(a849,a847,a846),f312(f16(f861(a847,a846),a849),a24)),x84691))
% 155.93/155.62 [9518]E(x95181,f189(f861(f860(a853,a853),a846)))+~P22(f312(f70(f860(a853,a853)),x95181))+P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),f189(f861(f860(a853,a853),a846))),x95181)),a46))
% 155.93/155.62 [9679]E(x96791,f2(a853))+E(x96791,f312(a126,f2(a853)))+~P22(f312(f312(f228(a853),x96791),f312(f117(a853),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)))))
% 155.93/155.62 [9970]E(x99701,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,x99701),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,x99701))+E(f54(a113,x99701,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))
% 155.93/155.62 [9814]E(x98141,f2(a113))+~E(f54(a113,x98141,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,x98141),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,x98141))
% 155.93/155.62 [4598]~P57(x45981,x45982)+P46(x45981,x45982)+~P47(a846)
% 155.93/155.62 [4535]~P23(x45351)+P35(x45351,x45352)+~E(x45352,f2(x45351))
% 155.93/155.62 [4536]~P103(x45361)+P33(x45361,x45362)+~E(x45362,f127(x45361))
% 155.93/155.62 [4545]~P112(x45451)+~E(x45452,f2(x45451))+E(f91(x45451,x45452),f2(x45451))
% 155.93/155.62 [4546]~P85(x45461)+~E(x45462,f2(x45461))+E(f91(x45461,x45462),f2(x45461))
% 155.93/155.62 [4554]~P23(x45542)+~P35(x45542,x45541)+E(x45541,f2(x45542))
% 155.93/155.62 [4588]~P112(x45882)+~E(f91(x45882,x45881),f2(x45882))+E(x45881,f2(x45882))
% 155.93/155.62 [4606]~P32(x46062)+~P32(x46061)+P32(f196(x46061,x46062))
% 155.93/155.62 [4607]~P138(x46072)+~P138(x46071)+P138(f860(x46071,x46072))
% 155.93/155.62 [4608]~P62(x46082)+~P62(x46081)+P62(f861(x46081,x46082))
% 155.93/155.62 [4609]~P62(x46092)+~P62(x46091)+P62(f859(x46091,x46092))
% 155.93/155.62 [4610]~P62(x46102)+~P62(x46101)+P62(f860(x46101,x46102))
% 155.93/155.62 [4611]~P63(x46112)+~P63(x46111)+P63(f861(x46111,x46112))
% 155.93/155.62 [4612]~P63(x46122)+~P63(x46121)+P63(f859(x46121,x46122))
% 155.93/155.62 [4613]~P63(x46132)+~P63(x46131)+P63(f860(x46131,x46132))
% 155.93/155.62 [4614]~P63(x46141)+~P92(x46142)+P92(f861(x46141,x46142))
% 155.93/155.62 [4742]~P103(x47421)+~P33(x47421,x47422)+P33(x47421,f148(x47421,x47422))
% 155.93/155.62 [4974]~P32(x49742)+~P32(x49741)+P32(f54(a1,x49741,x49742))
% 155.93/155.62 [4556]~P70(x45561)+~E(x45562,f2(x45561))+E(f312(f88(x45561),x45562),x45562)
% 155.93/155.62 [4560]~P89(x45601)+~E(x45602,f2(a1))+E(f312(f116(x45601),x45602),f2(x45601))
% 155.93/155.62 [4561]~P111(x45611)+~E(x45612,f2(a1))+E(f312(f116(x45611),x45612),f2(x45611))
% 155.93/155.62 [4585]~P71(x45851)+~E(f2(x45851),x45852)+E(f312(f88(x45851),x45852),f2(x45851))
% 155.93/155.62 [4586]~P71(x45861)+~E(x45862,f2(x45861))+E(f312(f88(x45861),x45862),f2(x45861))
% 155.93/155.62 [4587]~P83(x45871)+~E(x45872,f2(x45871))+E(f312(f84(x45871),x45872),f2(x45871))
% 155.93/155.62 [4617]~P70(x46172)+E(x46171,f2(x46172))+~E(f312(f88(x46172),x46171),x46171)
% 155.93/155.62 [4625]E(x46251,f312(a118,x46252))+~E(x46251,f2(a853))+~E(x46252,f312(f114(a1),x46251))
% 155.93/155.62 [4626]E(f312(a118,x46261),x46262)+~E(x46262,f2(a853))+~E(x46261,f312(f114(a1),x46262))
% 155.93/155.62 [4630]~P89(x46302)+E(x46301,f2(a1))+~E(f312(f116(x46302),x46301),f2(x46302))
% 155.93/155.62 [4635]~P71(x46352)+E(x46351,f2(x46352))+~E(f312(f88(x46352),x46351),f2(x46352))
% 155.93/155.62 [4636]~P83(x46362)+E(x46361,f2(x46362))+~E(f312(f84(x46362),x46361),f2(x46362))
% 155.93/155.62 [4637]~P71(x46371)+E(f2(x46371),x46372)+~E(f312(f88(x46371),x46372),f2(x46371))
% 155.93/155.62 [4657]~P60(x46572)+E(x46571,f2(x46572))+E(f312(f47(x46572,x46571),x46571),f87(x46572))
% 155.93/155.62 [4776]~P4(a5000)+~E(f312(a30,x47762),f312(f219(a847),x47761))+P22(f312(a24,x47761))
% 155.93/155.62 [4817]~P103(x48171)+~P33(x48171,x48172)+P33(x48171,f312(f167(x48171),x48172))
% 155.93/155.62 [4843]~P22(x48432)+~P22(x48431)+P22(f312(f312(a310,x48431),x48432))
% 155.93/155.62 [4844]~P32(x48442)+~P32(x48441)+P32(f312(f47(a1,x48441),x48442))
% 155.93/155.62 [4876]~E(f87(a853),f2(a853))+E(f312(f53(x48761),x48762),f2(a853))+~P22(f312(f70(x48761),x48762))
% 155.93/155.62 [4911]~P109(x49111)+~P135(x49111)+E(f312(f312(f240(x49111),f2(x49111)),f312(a126,x49112)),f2(x49111))
% 155.93/155.62 [4943]~P103(x49431)+P33(x49431,f135(x49431,x49432))+~P22(f312(f70(x49431),x49432))
% 155.93/155.62 [4944]~P103(x49441)+P33(x49441,f688(x49442,x49441))+~P22(f312(f70(x49441),x49442))
% 155.93/155.62 [4964]~P103(x49641)+E(f312(f168(x49641),f135(x49641,x49642)),x49642)+~P22(f312(f70(x49641),x49642))
% 155.93/155.62 [4965]~P103(x49651)+E(f312(f168(x49651),f688(x49652,x49651)),x49652)+~P22(f312(f70(x49651),x49652))
% 155.93/155.62 [4994]P22(x49941)+P22(x49942)+~P22(f312(f312(a311,x49942),x49941))
% 155.93/155.62 [5006]E(x50061,f189(f861(x50062,a846)))+~E(f312(f53(x50062),x50061),f2(a853))+~P22(f312(f70(x50062),x50061))
% 155.93/155.62 [5011]P22(x50111)+~P22(x50112)+~P22(f312(f312(a315,x50112),x50111))
% 155.93/155.62 [5062]~P69(x50621)+E(f312(f84(x50621),x50622),x50622)+P22(f312(f312(f228(x50621),x50622),f2(x50621)))
% 155.93/155.62 [5063]~P31(x50632)+~P49(x50632,x50632,x50631)+E(f312(x50631,f110(x50632,x50631)),f110(x50632,x50631))
% 155.93/155.62 [5064]~P31(x50642)+~P49(x50642,x50642,x50641)+E(f312(x50641,f109(x50642,x50641)),f109(x50642,x50641))
% 155.93/155.62 [5135]~P63(x51352)+~P22(f312(f66(x51352),x51351))+P22(f312(x51351,f651(x51351,x51352)))
% 155.93/155.62 [5136]~P63(x51362)+~P22(f312(f66(x51362),x51361))+P22(f312(x51361,f669(x51361,x51362)))
% 155.93/155.62 [5163]~P22(f312(a24,x51632))+~P22(f312(a24,x51631))+P22(f312(a24,f36(x51631,x51632)))
% 155.93/155.62 [5171]E(x51711,f127(x51712))+P22(f312(f133(x51712),f128(x51712,x51711)))+~P22(f312(f133(x51712),x51711))
% 155.93/155.62 [5176]~P103(x51761)+~P22(f312(f70(x51761),x51762))+P22(f312(f133(x51761),f135(x51761,x51762)))
% 155.93/155.62 [5177]~P103(x51771)+~P22(f312(f70(x51771),x51772))+P22(f312(f133(x51771),f688(x51772,x51771)))
% 155.93/155.62 [5183]~P111(x51831)+E(f312(f114(x51831),f312(a118,x51832)),f312(f116(x51831),x51832))+P22(f312(f312(f228(a1),x51832),f2(a1)))
% 155.93/155.62 [5210]P2(x52102,x52101)+E(f312(x52101,f366(x52101)),f312(x52101,f385(x52101)))+P22(f312(f312(x52101,f366(x52101)),f385(x52101)))
% 155.93/155.62 [5223]E(f312(f114(a1),f327(x52231,x52232)),x52231)+P22(f312(x52232,f312(a118,x52231)))+~P22(f312(x52232,f2(a853)))
% 155.93/155.62 [5234]~P63(x52341)+~P22(f312(x52342,f652(x52342,x52341)))+P22(f312(f67(x52341),x52342))
% 155.93/155.62 [5235]~P63(x52351)+~P22(f312(x52352,f670(x52352,x52351)))+P22(f312(f67(x52351),x52352))
% 155.93/155.62 [5264]~P112(x52641)+~E(f91(x52641,x52642),f312(f88(x52641),f87(x52641)))+P22(f312(f312(f228(x52641),x52642),f2(x52641)))
% 155.93/155.62 [5336]~E(x53362,f2(a1))+E(f210(x53361,x53362),f312(f312(f239(a1,a1),f2(a1)),f87(a1)))+P22(f312(f312(f228(a1),x53362),f2(a1)))
% 155.93/155.62 [5337]~E(x53371,f2(a1))+E(f210(x53371,x53372),f312(f312(f239(a1,a1),f2(a1)),f87(a1)))+P22(f312(f312(f228(a1),x53372),f2(a1)))
% 155.93/155.62 [5390]E(f312(f114(a1),f327(x53901,x53902)),x53901)+P22(f312(x53902,f312(a118,x53901)))+P22(f312(f312(f228(a1),x53901),f2(a1)))
% 155.93/155.62 [5452]~P112(x54521)+E(f91(x54521,x54522),f312(f88(x54521),f87(x54521)))+~P22(f312(f312(f228(x54521),x54522),f2(x54521)))
% 155.93/155.62 [5453]~P83(x54531)+E(f312(f84(x54531),x54532),f312(f88(x54531),x54532))+~P22(f312(f312(f228(x54531),x54532),f2(x54531)))
% 155.93/155.62 [5454]~P83(x54541)+E(f312(f84(x54541),x54542),f312(f88(x54541),x54542))+~P22(f312(f312(f227(x54541),x54542),f2(x54541)))
% 155.93/155.62 [5455]~P69(x54551)+E(f312(f84(x54551),x54552),f312(f88(x54551),x54552))+~P22(f312(f312(f228(x54551),x54552),f2(x54551)))
% 155.93/155.62 [5557]~P22(f312(x55571,f327(x55572,x55571)))+P22(f312(x55571,f312(a118,x55572)))+~P22(f312(x55571,f2(a853)))
% 155.93/155.62 [5564]E(x55641,f2(a853))+E(f312(a126,f817(x55642,x55641)),x55641)+~P22(f312(f312(f228(a853),x55641),f312(a126,x55642)))
% 155.93/155.62 [5569]P2(x55691,x55692)+~E(f312(x55692,f366(x55692)),f312(x55692,f385(x55692)))+~P22(f312(f312(x55692,f366(x55692)),f385(x55692)))
% 155.93/155.62 [5588]~P103(x55881)+P33(x55881,x55882)+P22(f312(f312(f227(a853),f653(x55882,x55881)),f654(x55882,x55881)))
% 155.93/155.62 [5589]~P103(x55891)+P33(x55891,x55892)+P22(f312(f312(f227(a853),f656(x55892,x55891)),f666(x55892,x55891)))
% 155.93/155.62 [5672]~P83(x56721)+~E(x56722,f2(x56721))+P22(f312(f312(f227(x56721),f312(f84(x56721),x56722)),f2(x56721)))
% 155.93/155.62 [5741]~P63(x57412)+~P63(x57411)+E(f68(x57411,x57412,f64(x57411),f64(x57412)),f64(f860(x57411,x57412)))
% 155.93/155.62 [5746]~P22(f312(x57461,f327(x57462,x57461)))+P22(f312(x57461,f312(a118,x57462)))+P22(f312(f312(f228(a1),x57462),f2(a1)))
% 155.93/155.62 [5768]~P22(f312(x57681,f312(a118,x57682)))+P22(f312(x57681,f2(a853)))+~P22(f312(f312(f228(a1),x57682),f2(a1)))
% 155.93/155.62 [6103]~P112(x61031)+~P22(f312(f312(f228(x61031),x61032),f2(x61031)))+P22(f312(f312(f228(x61031),f91(x61031,x61032)),f2(x61031)))
% 155.93/155.62 [6219]~P112(x62191)+P22(f312(f312(f228(x62191),f312(f116(x62191),x62192)),f2(x62191)))+~P22(f312(f312(f228(a1),x62192),f2(a1)))
% 155.93/155.62 [6220]~P112(x62201)+P22(f312(f312(f227(x62201),f312(f116(x62201),x62202)),f2(x62201)))+~P22(f312(f312(f227(a1),x62202),f2(a1)))
% 155.93/155.62 [6224]~P83(x62242)+E(x62241,f2(x62242))+~P22(f312(f312(f227(x62242),f312(f84(x62242),x62241)),f2(x62242)))
% 155.93/155.62 [6302]~P111(x63021)+~P22(f312(f312(f314(x63021),x63022),f123(x63021)))+P22(f312(f312(f314(x63021),f312(f88(x63021),x63022)),f123(x63021)))
% 155.93/155.62 [6333]~P112(x63331)+~P22(f312(f312(f228(x63331),f91(x63331,x63332)),f2(x63331)))+P22(f312(f312(f228(x63331),x63332),f2(x63331)))
% 155.93/155.62 [6497]~P112(x64972)+~P22(f312(f312(f228(x64972),f312(f116(x64972),x64971)),f2(x64972)))+P22(f312(f312(f228(a1),x64971),f2(a1)))
% 155.93/155.62 [6498]~P112(x64982)+~P22(f312(f312(f227(x64982),f312(f116(x64982),x64981)),f2(x64982)))+P22(f312(f312(f227(a1),x64981),f2(a1)))
% 155.93/155.62 [6583]~P31(x65831)+~P49(x65831,x65831,x65832)+P22(f312(f312(f227(x65831),f312(x65832,f110(x65831,x65832))),f110(x65831,x65832)))
% 155.93/155.62 [6584]~P31(x65841)+~P49(x65841,x65841,x65842)+P22(f312(f312(f227(x65841),f312(x65842,f109(x65841,x65842))),f109(x65841,x65842)))
% 155.93/155.62 [7002]~P70(x70021)+~P22(f312(f312(f228(x70021),x70022),f2(x70021)))+P22(f312(f312(f228(x70021),f312(f312(f89(x70021),x70022),x70022)),f2(x70021)))
% 155.93/155.62 [7003]~P112(x70031)+~P22(f312(f312(f228(x70031),x70032),f2(x70031)))+P22(f312(f312(f228(x70031),f312(f312(f89(x70031),x70032),x70032)),f2(x70031)))
% 155.93/155.62 [7004]~P70(x70041)+~P22(f312(f312(f227(x70041),x70042),f2(x70041)))+P22(f312(f312(f227(x70041),f312(f312(f89(x70041),x70042),x70042)),f2(x70041)))
% 155.93/155.62 [7557]~P70(x75571)+~P22(f312(f312(f228(x75571),f312(f312(f89(x75571),x75572),x75572)),f2(x75571)))+P22(f312(f312(f228(x75571),x75572),f2(x75571)))
% 155.93/155.62 [7558]~P112(x75581)+~P22(f312(f312(f228(x75581),f312(f312(f89(x75581),x75582),x75582)),f2(x75581)))+P22(f312(f312(f228(x75581),x75582),f2(x75581)))
% 155.93/155.62 [7559]~P70(x75591)+~P22(f312(f312(f227(x75591),f312(f312(f89(x75591),x75592),x75592)),f2(x75591)))+P22(f312(f312(f227(x75591),x75592),f2(x75591)))
% 155.93/155.62 [4677]~E(x46772,f2(a853))+~E(x46771,f2(a853))+E(f312(f312(f89(a853),x46771),x46772),f2(a853))
% 155.93/155.62 [4678]~E(x46782,f87(a853))+~E(x46781,f87(a853))+E(f312(f312(f90(a853),x46781),x46782),f87(a853))
% 155.93/155.62 [4679]~E(x46792,f87(a1))+~E(x46791,f87(a1))+E(f312(f312(f90(a1),x46791),x46792),f87(a1))
% 155.93/155.62 [4730]~P114(x47302)+E(x47301,f2(x47302))+E(f312(f312(f268(x47302),x47301),x47301),f87(x47302))
% 155.93/155.62 [4731]~P115(x47312)+E(x47311,f2(x47312))+E(f312(f312(f268(x47312),x47311),x47311),f87(x47312))
% 155.93/155.62 [4747]~P70(x47471)+~E(x47472,f2(x47471))+E(f312(f312(f89(x47471),x47472),x47472),f2(x47471))
% 155.93/155.62 [4750]~P134(x47501)+~E(x47502,f87(x47501))+E(f312(f312(f90(x47501),x47502),x47502),f87(x47501))
% 155.93/155.62 [4751]~P115(x47511)+~E(x47512,f2(x47511))+E(f312(f312(f268(x47511),x47512),x47512),f2(x47511))
% 155.93/155.62 [4796]~E(x47962,f2(a853))+~E(x47961,f2(a853))+E(f312(f88(a1),f312(f114(a1),x47961)),f312(f114(a1),x47962))
% 155.93/155.62 [4814]E(x48141,f87(a853))+E(x48142,f2(a853))+~E(f312(f312(f90(a853),x48142),x48141),x48142)
% 155.93/155.62 [4824]E(x48241,f2(a853))+E(x48242,f2(a853))+~E(f312(f312(f90(a853),x48242),x48241),f2(a853))
% 155.93/155.62 [4853]~E(x48532,f2(a853))+~E(x48531,f312(a126,f2(a853)))+E(f312(f312(f89(a853),x48531),x48532),f312(a126,f2(a853)))
% 155.93/155.62 [4854]~E(x48541,f2(a853))+~E(x48542,f312(a126,f2(a853)))+E(f312(f312(f89(a853),x48541),x48542),f312(a126,f2(a853)))
% 155.93/155.62 [4859]E(x48591,f87(a1))+E(x48592,f312(f117(a1),a111))+~E(f312(f312(f90(a1),x48591),x48592),f87(a1))
% 155.93/155.62 [4860]E(x48601,f87(a1))+E(x48602,f312(f117(a1),a111))+~E(f312(f312(f90(a1),x48602),x48601),f87(a1))
% 155.93/155.62 [4861]E(x48611,f87(a1))+E(x48611,f312(f117(a1),a111))+~E(f312(f312(f90(a1),x48612),x48611),f87(a1))
% 155.93/155.62 [4863]E(x48631,f87(a1))+E(x48631,f312(f117(a1),a111))+~E(f312(f312(f90(a1),x48631),x48632),f87(a1))
% 155.93/155.62 [4881]~P70(x48812)+E(x48811,f2(x48812))+~E(f312(f312(f89(x48812),x48811),x48811),f2(x48812))
% 155.93/155.62 [4887]~E(x48871,f312(f117(a1),a111))+~E(x48872,f312(f117(a1),a111))+E(f312(f312(f90(a1),x48871),x48872),f87(a1))
% 155.93/155.62 [4900]E(x49001,f2(a853))+E(x49002,f2(a853))+~E(f312(f312(f89(a853),x49002),x49001),f312(a126,f2(a853)))
% 155.93/155.62 [4910]~P90(x49101)+~P64(x49101)+E(f312(f312(f268(x49101),x49102),f312(f117(x49101),a92)),f2(x49101))
% 155.93/155.62 [4916]~P134(x49161)+~E(x49162,f312(f88(x49161),f87(x49161)))+E(f312(f312(f90(x49161),x49162),x49162),f87(x49161))
% 155.93/155.62 [4919]~P32(x49192)+~P32(x49191)+P32(f312(f312(f89(a1),x49191),x49192))
% 155.93/155.62 [4920]~P32(x49202)+~P32(x49201)+P32(f312(f312(f90(a1),x49201),x49202))
% 155.93/155.62 [4941]~E(x49412,f312(a126,f2(a853)))+~E(x49411,f312(a126,f2(a853)))+E(f312(f312(f90(a853),x49411),x49412),f312(a126,f2(a853)))
% 155.93/155.62 [4955]E(x49551,f2(a853))+E(x49552,f312(a126,f2(a853)))+~E(f312(f312(f240(a853),x49552),x49551),f312(a126,f2(a853)))
% 155.93/155.62 [4956]E(x49561,f2(a853))+E(x49561,f312(a126,f2(a853)))+~E(f312(f312(f89(a853),x49562),x49561),f312(a126,f2(a853)))
% 155.93/155.62 [4957]E(x49571,f2(a853))+E(x49571,f312(a126,f2(a853)))+~E(f312(f312(f89(a853),x49571),x49572),f312(a126,f2(a853)))
% 155.93/155.62 [4966]~P90(x49661)+~P64(x49661)+E(f312(f312(f268(x49661),x49662),f312(f117(x49661),a111)),f312(f88(x49661),x49662))
% 155.93/155.62 [4986]E(x49861,f312(a118,x49862))+~E(x49861,f2(a853))+P22(f312(f312(f227(a1),f2(a1)),x49862))
% 155.93/155.62 [4987]E(f312(a118,x49871),x49872)+~E(x49872,f2(a853))+P22(f312(f312(f227(a1),f2(a1)),x49871))
% 155.93/155.62 [5002]E(x50021,f312(a126,f2(a853)))+E(x50022,f312(a126,f2(a853)))+~E(f312(f312(f89(a853),x50021),x50022),f312(a126,f2(a853)))
% 155.93/155.62 [5012]~E(x50121,f312(a118,x50122))+E(x50121,f2(a853))+P22(f312(f312(f227(a1),f2(a1)),x50122))
% 155.93/155.62 [5013]~E(f312(a118,x50132),x50131)+E(x50131,f2(a853))+P22(f312(f312(f227(a1),f2(a1)),x50132))
% 155.93/155.62 [5038]~P87(x50381)+E(f312(f72(x50381,f115(x50381)),x50382),f11(x50381,x50382))+~P22(f312(f70(x50381),x50382))
% 155.93/155.62 [5039]~P87(x50391)+E(f312(f72(x50391,f124(x50391)),x50392),f10(x50391,x50392))+~P22(f312(f70(x50391),x50392))
% 155.93/155.62 [5040]~P103(x50401)+E(f312(f72(x50401,f226(x50401)),x50402),f14(x50401,x50402))+~P22(f312(f70(x50401),x50402))
% 155.93/155.62 [5041]~P103(x50411)+E(f312(f72(x50411,f225(x50411)),x50412),f15(x50411,x50412))+~P22(f312(f70(x50411),x50412))
% 155.93/155.62 [5043]~P63(x50431)+~P22(f312(x50432,f192(x50431)))+P22(f312(f66(f857(x50431)),x50432))
% 155.93/155.62 [5128]~P63(x51282)+P22(f312(x51281,f192(x51282)))+~P22(f312(f67(f857(x51282)),x51281))
% 155.93/155.62 [5129]E(x51291,x51292)+~E(f312(f312(f21(a853),x51292),x51291),f2(a853))+~E(f312(f312(f21(a853),x51291),x51292),f2(a853))
% 155.93/155.62 [5143]P32(x51431)+~P43(x51432)+~P22(f312(f312(f314(a1),x51431),x51432))
% 155.93/155.62 [5172]~P112(x51721)+~E(f91(x51721,x51722),f87(x51721))+P22(f312(f312(f228(x51721),f2(x51721)),x51722))
% 155.93/155.62 [5184]~P90(x51841)+E(f312(f114(x51841),f312(f117(a853),x51842)),f312(f117(x51841),x51842))+P22(f312(a194,f312(f117(a1),x51842)))
% 155.93/155.62 [5189]~P46(x51891,x51892)+P47(a846)+P22(f312(f70(f860(x51891,x51891)),x51892))
% 155.93/155.62 [5256]~P103(x52561)+E(f312(f72(x52561,f226(x52561)),x52562),f12(x52561,f226(x52561),x52562))+~P22(f312(f70(x52561),x52562))
% 155.93/155.62 [5257]~P103(x52571)+E(f312(f72(x52571,f225(x52571)),x52572),f13(x52571,f225(x52571),x52572))+~P22(f312(f70(x52571),x52572))
% 155.93/155.62 [5271]E(x52711,x52712)+P22(f312(f312(f228(a853),x52712),x52711))+P22(f312(f312(f228(a853),x52711),x52712))
% 155.93/155.62 [5272]E(x52721,x52722)+P22(f312(f312(f228(a1),x52722),x52721))+P22(f312(f312(f228(a1),x52721),x52722))
% 155.93/155.62 [5323]~P90(x53231)+E(f312(f114(x53231),f312(f117(a853),x53232)),f2(x53231))+~P22(f312(a194,f312(f117(a1),x53232)))
% 155.93/155.62 [5326]~E(x53262,f312(a118,x53261))+E(x53261,f312(f114(a1),x53262))+~P22(f312(f312(f227(a1),f2(a1)),x53261))
% 155.93/155.62 [5327]~E(f312(a118,x53271),x53272)+E(x53271,f312(f114(a1),x53272))+~P22(f312(f312(f227(a1),f2(a1)),x53271))
% 155.93/155.62 [5328]~E(x53281,f312(a118,x53282))+E(f312(f114(a1),x53281),x53282)+~P22(f312(f312(f227(a1),f2(a1)),x53282))
% 155.93/155.62 [5338]E(x53381,f312(a118,x53382))+~E(x53382,f312(f114(a1),x53381))+~P22(f312(f312(f227(a1),f2(a1)),x53382))
% 155.93/155.62 [5339]E(f312(a118,x53391),x53392)+~E(x53391,f312(f114(a1),x53392))+~P22(f312(f312(f227(a1),f2(a1)),x53391))
% 155.93/155.62 [5379]~P83(x53792)+E(x53791,f2(x53792))+P22(f312(f312(f228(x53792),f2(x53792)),f312(f84(x53792),x53791)))
% 155.93/155.62 [5445]~P112(x54451)+E(f91(x54451,x54452),f87(x54451))+~P22(f312(f312(f228(x54451),f2(x54451)),x54452))
% 155.93/155.62 [5449]~P90(x54491)+E(f312(f114(x54491),f312(f117(a853),x54492)),f2(x54491))+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x54492)))
% 155.93/155.62 [5456]~P83(x54561)+E(f312(f84(x54561),x54562),x54562)+~P22(f312(f312(f228(x54561),f2(x54561)),x54562))
% 155.93/155.62 [5457]~P83(x54571)+E(f312(f84(x54571),x54572),x54572)+~P22(f312(f312(f227(x54571),f2(x54571)),x54572))
% 155.93/155.62 [5464]E(x54641,f2(a853))+~E(f135(a853,f312(f282(a853,x54642),x54641)),f127(a853))+P22(f312(f312(f227(a853),x54641),x54642))
% 155.93/155.62 [5474]~P26(x54741)+E(f312(f312(f6(x54741,x54741),f5(x54741)),f312(f168(x54741),x54742)),f312(f162(x54741),x54742))+~P22(f312(f133(x54741),x54742))
% 155.93/155.62 [5479]~P111(x54791)+E(f312(f114(x54791),f312(a118,x54792)),f312(f116(x54791),x54792))+~P22(f312(f312(f227(a1),f2(a1)),x54792))
% 155.93/155.62 [5506]E(x55061,x55062)+P22(f312(f312(f228(a853),x55061),x55062))+~P22(f312(f312(f227(a853),x55061),x55062))
% 155.93/155.62 [5507]E(x55071,x55072)+P22(f312(f312(f228(a1),x55071),x55072))+~P22(f312(f312(f227(a1),x55071),x55072))
% 155.93/155.62 [5510]E(x55101,f87(a1))+~E(f312(f312(f90(a1),x55102),x55101),f87(a1))+~P22(f312(f312(f228(a1),f2(a1)),x55102))
% 155.93/155.62 [5511]E(x55111,f87(a1))+~E(f312(f312(f90(a1),x55111),x55112),f87(a1))+~P22(f312(f312(f228(a1),f2(a1)),x55111))
% 155.93/155.62 [5513]E(x55131,f2(a1))+~E(f54(a1,x55132,x55131),f2(a1))+E(f312(f47(a1,x55132),f312(f88(a1),x55131)),f312(f88(a1),f312(f47(a1,x55132),x55131)))
% 155.93/155.62 [5554]~P43(x55542)+P22(f312(f312(f227(a1),f2(a1)),x55541))+~P22(f312(f312(f314(a1),x55541),x55542))
% 155.93/155.62 [5575]~P57(x55751,x55752)+P41(x55751,x55752)+~P22(f312(f70(f860(x55751,x55751)),x55752))
% 155.93/155.62 [5577]~P57(x55771,x55772)+P46(x55771,x55772)+~P22(f312(f70(f860(x55771,x55771)),x55772))
% 155.93/155.62 [5614]E(x56141,f189(f861(x56142,a846)))+~P22(f312(f70(x56142),x56141))+P22(f312(f312(f228(a853),f2(a853)),f312(f53(x56142),x56141)))
% 155.93/155.62 [5641]~P22(f312(x56411,x56412))+P22(f312(x56411,f2(a853)))+P22(f312(f312(f228(a853),f839(x56412,x56411)),x56412))
% 155.93/155.62 [5666]E(x56661,f2(a853))+~E(f312(f162(a853),x56662),f2(a853))+~P22(f312(f312(f314(a853),x56661),f312(f168(a853),x56662)))
% 155.93/155.62 [5726]E(x57261,x57262)+~P22(f312(f312(f227(a853),x57262),x57261))+~P22(f312(f312(f227(a853),x57261),x57262))
% 155.93/155.62 [5727]E(x57271,x57272)+~P22(f312(f312(f227(a1),x57272),x57271))+~P22(f312(f312(f227(a1),x57271),x57272))
% 155.93/155.62 [5728]E(f312(f53(x57281),x57282),f2(a853))+~P22(f312(f70(x57281),x57282))+P22(f312(f312(f314(x57281),f725(x57282,x57281)),x57282))
% 155.93/155.62 [5757]~P22(f312(x57571,f321(x57571)))+P22(f312(x57571,f312(a118,x57572)))+~P22(f312(f312(f227(a1),f2(a1)),x57572))
% 155.93/155.62 [5759]P22(f312(f312(f228(a853),x57591),f372(x57592)))+~P22(f312(f70(a853),x57592))+~P22(f312(f312(f314(a853),x57591),x57592))
% 155.93/155.62 [5760]P22(f312(f312(f227(a853),x57601),f368(x57602)))+~P22(f312(f70(a853),x57602))+~P22(f312(f312(f314(a853),x57601),x57602))
% 155.93/155.62 [5791]E(x57911,x57912)+~P22(f312(f312(f228(a853),x57911),f312(a126,x57912)))+P22(f312(f312(f228(a853),x57911),x57912))
% 155.93/155.62 [5824]E(x58241,f312(a126,x58242))+~P22(f312(f312(f227(a853),x58241),f312(a126,x58242)))+P22(f312(f312(f227(a853),x58241),x58242))
% 155.93/155.62 [5835]P22(f312(x58351,f328(x58351)))+~P22(f312(x58351,f312(a118,x58352)))+~P22(f312(f312(f227(a1),f2(a1)),x58352))
% 155.93/155.62 [5848]~P22(f312(x58481,x58482))+~P22(f312(f312(f227(a1),f2(a1)),x58482))+P22(f312(x58481,f312(f114(a1),f832(x58481))))
% 155.93/155.62 [5863]~P83(x58632)+~E(x58631,f2(x58632))+~P22(f312(f312(f228(x58632),f2(x58632)),f312(f84(x58632),x58631)))
% 155.93/155.62 [5890]~P57(x58901,x58902)+P41(x58901,f312(f265(x58901,x58901),x58902))+~P22(f312(f70(f860(x58901,x58901)),x58902))
% 155.93/155.62 [5894]E(f312(f47(a1,x58941),x58942),f2(a1))+~P22(f312(f312(f227(a1),x58941),f2(a1)))+~P22(f312(f312(f228(a1),x58942),x58941))
% 155.93/155.62 [5903]~P90(x59031)+E(f312(f114(x59031),f312(f117(a853),x59032)),f312(f117(x59031),x59032))+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x59032)))
% 155.93/155.62 [5907]E(f312(a126,x59071),x59072)+~P22(f312(f312(f228(a853),x59071),x59072))+P22(f312(f312(f228(a853),f312(a126,x59071)),x59072))
% 155.93/155.62 [5923]E(f312(f47(a1,x59231),x59232),f2(a1))+~P22(f312(f312(f227(a1),f2(a1)),x59231))+~P22(f312(f312(f228(a1),x59231),x59232))
% 155.93/155.62 [5934]E(f54(a1,x59341,x59342),x59341)+~P22(f312(f312(f227(a1),x59341),f2(a1)))+~P22(f312(f312(f228(a1),x59342),x59341))
% 155.93/155.62 [5963]E(f54(a853,f312(f117(a853),x59631),f312(f117(a853),x59632)),f312(f117(a853),x59631))+P22(f312(a194,f312(f117(a1),x59631)))+~P22(f312(a194,f312(f117(a1),x59632)))
% 155.93/155.62 [5965]E(f54(a1,x59651,x59652),x59651)+~P22(f312(f312(f227(a1),f2(a1)),x59651))+~P22(f312(f312(f228(a1),x59651),x59652))
% 155.93/155.62 [5966]E(x59661,x59662)+~P22(f312(f312(f228(a853),x59661),f312(a126,x59662)))+~P22(f312(f312(f227(a853),x59662),x59661))
% 155.93/155.62 [5982]~P112(x59821)+~P22(f312(f312(f228(x59821),x59822),f2(x59821)))+P22(f312(f312(f228(x59821),x59822),f312(f88(x59821),x59822)))
% 155.93/155.62 [5983]~P70(x59831)+~P22(f312(f312(f227(x59831),x59832),f2(x59831)))+P22(f312(f312(f227(x59831),x59832),f312(f88(x59831),x59832)))
% 155.93/155.62 [5993]~P31(x59931)+E(f312(f312(f73(x59931,x59931,f124(x59931)),f189(x59931)),x59932),f48(x59931,x59932))+~P22(f312(f70(x59931),x59932))
% 155.93/155.62 [6006]~P117(x60061)+~P22(f312(f312(f228(a853),f2(a853)),x60062))+P22(f312(f312(f228(x60061),f2(x60061)),f312(f114(x60061),x60062)))
% 155.93/155.62 [6007]~P112(x60071)+~P22(f312(f312(f228(a1),f2(a1)),x60072))+P22(f312(f312(f228(x60071),f2(x60071)),f312(f116(x60071),x60072)))
% 155.93/155.62 [6008]~P112(x60081)+~P22(f312(f312(f227(a1),f2(a1)),x60082))+P22(f312(f312(f227(x60081),f2(x60081)),f312(f116(x60081),x60082)))
% 155.93/155.62 [6011]~P32(x60112)+~P32(x60111)+E(f312(f290(a853,a1,f114(a1)),f283(a853,f312(a118,x60111),f312(a118,x60112))),f283(a1,x60111,x60112))
% 155.93/155.62 [6015]P22(f312(x60151,x60152))+~P22(f312(f312(f227(a1),f2(a1)),x60152))+~P22(f312(x60151,f312(f114(a1),f836(x60151))))
% 155.93/155.62 [6039]E(f312(f312(f89(a853),f312(f117(a853),x60391)),f312(f117(a853),x60392)),f312(f117(a853),x60391))+P22(f312(f312(f228(a1),x60391),a92))+~P22(f312(f312(f228(a1),x60392),a92))
% 155.93/155.62 [6041]~P112(x60411)+P22(f312(f312(f228(x60411),f2(x60411)),f91(x60411,x60412)))+~P22(f312(f312(f228(x60411),f2(x60411)),x60412))
% 155.93/155.62 [6055]~P76(x60551)+~P22(f312(f312(f228(x60551),x60552),f2(x60551)))+P22(f312(f312(f228(x60551),f2(x60551)),f312(f88(x60551),x60552)))
% 155.93/155.62 [6056]~P76(x60561)+~P22(f312(f312(f227(x60561),x60562),f2(x60561)))+P22(f312(f312(f227(x60561),f2(x60561)),f312(f88(x60561),x60562)))
% 155.93/155.62 [6059]E(x60591,f235(f861(x60592,a846)))+~E(f312(f53(x60592),x60591),f312(f53(x60592),f235(f861(x60592,a846))))+~P22(f312(f70(x60592),f235(f861(x60592,a846))))
% 155.93/155.62 [6095]~P112(x60951)+P22(f312(f312(f228(x60951),x60952),f2(x60951)))+~P22(f312(f312(f228(x60951),x60952),f312(f88(x60951),x60952)))
% 155.93/155.62 [6096]~P70(x60961)+P22(f312(f312(f227(x60961),x60962),f2(x60961)))+~P22(f312(f312(f227(x60961),x60962),f312(f88(x60961),x60962)))
% 155.93/155.62 [6105]~P90(x61051)+P22(f312(f312(f314(x61051),f312(f117(x61051),x61052)),f187(x61051)))+~P22(f312(f312(f227(a1),a92),x61052))
% 155.93/155.62 [6139]~E(x61392,f2(a1))+E(x61391,f2(a1))+E(f312(f312(f239(a1,a1),f312(f47(a1,x61391),x61392)),f54(a1,x61391,x61392)),f312(f312(f239(a1,a1),f2(a1)),x61391))
% 155.93/155.62 [6140]E(x61401,f2(a853))+~P22(f312(f312(f228(a853),x61401),f312(a126,x61402)))+P22(f312(f312(f228(a853),f817(x61402,x61401)),x61402))
% 155.93/155.62 [6143]E(f312(f246(a1,a1),f58(x61431,x61432)),f312(f47(a1,x61431),x61432))+~P22(f312(f312(f228(a1),x61431),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x61432))
% 155.93/155.62 [6160]~P112(x61601)+~P22(f312(f312(f228(x61601),f2(x61601)),f91(x61601,x61602)))+P22(f312(f312(f228(x61601),f2(x61601)),x61602))
% 155.93/155.62 [6162]~E(f312(f117(a853),x61622),f312(f117(a853),x61621))+P22(f312(f312(f227(a1),f312(f117(a1),x61621)),f2(a1)))+~P22(f312(a194,f312(f117(a1),x61622)))
% 155.93/155.62 [6197]E(f312(f246(a1,a1),f55(x61971,x61972)),f312(f47(a1,x61971),x61972))+~P22(f312(f312(f228(a1),f2(a1)),x61971))+~P22(f312(f312(f227(a1),f2(a1)),x61972))
% 155.93/155.62 [6222]E(f312(f248(a1,a1),f58(x62221,x62222)),f54(a1,x62221,x62222))+~P22(f312(f312(f228(a1),x62221),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x62222))
% 155.93/155.62 [6225]~P117(x62252)+~P22(f312(f312(f228(x62252),f2(x62252)),f312(f114(x62252),x62251)))+P22(f312(f312(f228(a853),f2(a853)),x62251))
% 155.93/155.62 [6226]~P112(x62262)+~P22(f312(f312(f228(x62262),f2(x62262)),f312(f116(x62262),x62261)))+P22(f312(f312(f228(a1),f2(a1)),x62261))
% 155.93/155.62 [6227]~P112(x62272)+~P22(f312(f312(f227(x62272),f2(x62272)),f312(f116(x62272),x62271)))+P22(f312(f312(f227(a1),f2(a1)),x62271))
% 155.93/155.62 [6245]E(f312(f248(a1,a1),f55(x62451,x62452)),f54(a1,x62451,x62452))+~P22(f312(f312(f228(a1),f2(a1)),x62451))+~P22(f312(f312(f227(a1),f2(a1)),x62452))
% 155.93/155.62 [6262]~P76(x62621)+P22(f312(f312(f228(x62621),x62622),f2(x62621)))+~P22(f312(f312(f228(x62621),f2(x62621)),f312(f88(x62621),x62622)))
% 155.93/155.62 [6263]~P76(x62631)+P22(f312(f312(f227(x62631),x62632),f2(x62631)))+~P22(f312(f312(f227(x62631),f2(x62631)),f312(f88(x62631),x62632)))
% 155.93/155.62 [6284]~P31(x62841)+~P49(x62841,x62841,x62842)+P22(f312(f312(f227(x62841),f110(x62841,x62842)),f312(x62842,f110(x62841,x62842))))
% 155.93/155.62 [6285]~P31(x62851)+~P49(x62851,x62851,x62852)+P22(f312(f312(f227(x62851),f109(x62851,x62852)),f312(x62852,f109(x62851,x62852))))
% 155.93/155.62 [6289]P22(f312(f57(x62891,x62892),f58(x62891,x62892)))+~P22(f312(f312(f228(a1),x62891),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x62892))
% 155.93/155.62 [6309]P22(f312(f57(x63091,x63092),f55(x63091,x63092)))+~P22(f312(f312(f228(a1),f2(a1)),x63092))+~P22(f312(f312(f227(a1),f2(a1)),x63091))
% 155.93/155.62 [6354]~P76(x63541)+P22(f312(f312(f228(x63541),f312(f88(x63541),x63542)),f2(x63541)))+~P22(f312(f312(f228(x63541),f2(x63541)),x63542))
% 155.93/155.62 [6355]~P76(x63551)+P22(f312(f312(f227(x63551),f312(f88(x63551),x63552)),f2(x63551)))+~P22(f312(f312(f227(x63551),f2(x63551)),x63552))
% 155.93/155.62 [6372]E(f312(f312(f21(a853),f312(a118,x63721)),f312(a118,x63722)),f312(a118,f196(x63721,x63722)))+~P22(f312(f312(f227(a1),f2(a1)),x63722))+~P22(f312(f312(f227(a1),f2(a1)),x63721))
% 155.93/155.62 [6389]P22(f312(f312(f227(a1),f2(a1)),f196(x63891,x63892)))+~P22(f312(f312(f227(a1),f2(a1)),x63892))+~P22(f312(f312(f227(a1),f2(a1)),x63891))
% 155.93/155.62 [6426]~P22(f312(x64261,x64262))+P22(f312(x64261,f2(a853)))+P22(f312(x64261,f312(f312(f89(a853),f839(x64262,x64261)),f87(a853))))
% 155.93/155.62 [6474]E(x64741,f2(a1))+E(f54(a1,x64742,x64741),f2(a1))+E(f312(f312(f21(a1),f312(f88(a1),f312(f47(a1,x64742),x64741))),f87(a1)),f312(f47(a1,x64742),f312(f88(a1),x64741)))
% 155.93/155.62 [6504]E(f312(f117(a853),x65041),f312(f117(a853),x65042))+~P22(f312(f312(f227(a1),f312(f117(a1),x65042)),f2(a1)))+~P22(f312(a194,f312(f117(a1),x65041)))
% 155.93/155.62 [6514]~E(x65141,f2(a853))+~E(f615(x65142,x65141),f2(a853))+E(f312(f138(a853,a853,f89(a853),x65141),x65142),f2(a853))
% 155.93/155.62 [6539]~P22(f312(f70(x65391),f675(x65392,x65391)))+~P22(f312(f70(f861(x65391,a846)),x65392))+P22(f312(f70(x65391),f48(f861(x65391,a846),x65392)))
% 155.93/155.62 [6545]E(x65451,x65452)+P22(f312(f312(f228(a1),x65451),x65452))+~P22(f312(f312(f228(a1),x65451),f312(f312(f89(a1),x65452),f87(a1))))
% 155.93/155.62 [6547]P22(f312(f312(f228(a853),f312(a118,x65471)),f312(a118,x65472)))+~P22(f312(f312(f228(a1),f2(a1)),x65472))+~P22(f312(f312(f228(a1),x65471),x65472))
% 155.93/155.62 [6548]P22(f312(f312(f228(a853),f312(a118,x65481)),f312(a118,x65482)))+~P22(f312(f312(f227(a1),f2(a1)),x65481))+~P22(f312(f312(f228(a1),x65481),x65482))
% 155.93/155.62 [6549]P22(f312(f312(f227(a853),f312(a118,x65491)),f312(a118,x65492)))+~P22(f312(f312(f228(a1),f2(a1)),x65491))+~P22(f312(f312(f227(a1),x65491),x65492))
% 155.93/155.62 [6550]P22(f312(f312(f227(a853),f312(a118,x65501)),f312(a118,x65502)))+~P22(f312(f312(f227(a1),f2(a1)),x65502))+~P22(f312(f312(f227(a1),x65501),x65502))
% 155.93/155.62 [6562]E(f54(a853,f312(a118,x65621),f312(a118,x65622)),f312(a118,f54(a1,x65621,x65622)))+~P22(f312(f312(f227(a1),f2(a1)),x65622))+~P22(f312(f312(f227(a1),f2(a1)),x65621))
% 155.93/155.62 [6586]~P76(x65861)+~P22(f312(f312(f228(x65861),f312(f88(x65861),x65862)),f2(x65861)))+P22(f312(f312(f228(x65861),f2(x65861)),x65862))
% 155.93/155.62 [6587]~P76(x65871)+~P22(f312(f312(f227(x65871),f312(f88(x65871),x65872)),f2(x65871)))+P22(f312(f312(f227(x65871),f2(x65871)),x65872))
% 155.93/155.62 [6592]~P22(f312(f312(f228(a1),f2(a1)),x65922))+P22(f312(f312(f228(a1),f2(a1)),f312(f47(a1,x65921),x65922)))+~P22(f312(f312(f227(a1),x65922),x65921))
% 155.93/155.62 [6593]~P22(f312(f312(f228(a1),x65932),f2(a1)))+~P22(f312(f312(f227(a1),x65931),f2(a1)))+P22(f312(f312(f227(a1),f2(a1)),f312(f47(a1,x65931),x65932)))
% 155.93/155.62 [6604]~P22(f312(f312(f228(a1),a92),x66042))+~P22(f312(f312(f228(a1),x66041),x66042))+P22(f312(f312(f228(a853),f312(f117(a853),x66041)),f312(f117(a853),x66042)))
% 155.93/155.62 [6626]~P22(f312(f312(f228(a1),f2(a1)),x66262))+~P22(f312(f312(f227(a1),f2(a1)),x66261))+P22(f312(f312(f227(a1),f2(a1)),f312(f47(a1,x66261),x66262)))
% 155.93/155.62 [6627]~P22(f312(f312(f227(a1),f2(a1)),x66272))+~P22(f312(f312(f227(a1),f2(a1)),x66271))+P22(f312(f312(f227(a1),f2(a1)),f312(f47(a1,x66271),x66272)))
% 155.93/155.62 [6691]~P22(f312(f312(f227(a1),f2(a1)),x66911))+P22(f312(f312(f228(a853),f312(a118,x66911)),x66912))+~P22(f312(f312(f228(a1),x66911),f312(f114(a1),x66912)))
% 155.93/155.62 [6713]E(f312(f312(f239(a1,a1),f312(f47(a1,x67131),x67132)),f54(a1,x67131,x67132)),f58(x67131,x67132))+P22(f312(f312(f227(a1),f2(a1)),x67131))+~P22(f312(f312(f228(a1),f2(a1)),x67132))
% 155.93/155.62 [6720]~P22(f312(f312(f227(a1),f2(a1)),x67201))+~P22(f312(f312(f228(a853),f312(a118,x67201)),x67202))+P22(f312(f312(f228(a1),x67201),f312(f114(a1),x67202)))
% 155.93/155.62 [6754]~P22(f312(f312(f227(a853),f312(a118,x67541)),f312(a118,x67542)))+~P22(f312(f312(f228(a1),f2(a1)),x67541))+P22(f312(f312(f227(a1),x67541),x67542))
% 155.93/155.62 [6755]~P22(f312(f312(f227(a853),f312(a118,x67551)),f312(a118,x67552)))+~P22(f312(f312(f227(a1),f2(a1)),x67552))+P22(f312(f312(f227(a1),x67551),x67552))
% 155.93/155.62 [6780]P22(f312(f312(f227(a1),x67801),x67802))+~P22(f312(f312(f227(a853),f312(f117(a853),x67801)),f312(f117(a853),x67802)))+P22(f312(f312(f227(a1),x67801),a92))
% 155.93/155.62 [6804]P22(f312(f312(f227(a1),f2(a1)),f54(a1,x68041,x68042)))+~P22(f312(f312(f227(a1),f2(a1)),x68042))+~P22(f312(f312(f227(a1),f2(a1)),x68041))
% 155.93/155.62 [6811]P22(f312(f312(f227(a1),x68111),f2(a1)))+~P22(f312(f312(f228(a1),x68112),f2(a1)))+~P22(f312(f312(f227(a1),f2(a1)),f312(f47(a1,x68111),x68112)))
% 155.93/155.62 [6825]~P22(f312(f312(f228(a1),f2(a1)),x68251))+~P22(f312(f312(f228(a1),f2(a1)),f312(f47(a1,x68252),x68251)))+P22(f312(f312(f227(a1),x68251),x68252))
% 155.93/155.62 [6826]~P22(f312(f312(f227(a1),f2(a1)),x68262))+~P22(f312(f312(f228(a1),f2(a1)),f312(f47(a1,x68262),x68261)))+P22(f312(f312(f227(a1),x68261),x68262))
% 155.93/155.62 [6855]E(f312(f312(f239(a1,a1),f312(f47(a1,x68551),x68552)),f54(a1,x68551,x68552)),f58(x68551,x68552))+~P22(f312(f312(f228(a1),x68551),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x68552))
% 155.93/155.62 [6856]P22(f312(f312(f228(a1),f2(a1)),x68561))+~P22(f312(f312(f227(a1),f2(a1)),x68562))+~P22(f312(f312(f228(a1),f2(a1)),f312(f47(a1,x68562),x68561)))
% 155.93/155.62 [6857]P22(f312(f312(f227(a1),f2(a1)),x68571))+~P22(f312(f312(f228(a1),f2(a1)),x68572))+~P22(f312(f312(f227(a1),f2(a1)),f312(f47(a1,x68571),x68572)))
% 155.93/155.62 [6881]E(f312(f312(f239(a1,a1),f312(f47(a1,x68811),x68812)),f54(a1,x68811,x68812)),f55(x68811,x68812))+~P22(f312(f312(f227(a1),f2(a1)),x68812))+~P22(f312(f312(f227(a1),f2(a1)),x68811))
% 155.93/155.62 [6911]P22(f312(f312(f228(a1),a92),x69111))+~P22(f312(f312(f228(a1),x69112),x69111))+~P22(f312(f312(f228(a853),f312(f117(a853),x69112)),f312(f117(a853),x69111)))
% 155.93/155.62 [6979]~P22(f312(f312(f228(a1),x69792),f2(a1)))+P22(f312(f312(f228(a1),f312(f47(a1,x69791),x69792)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x69791))
% 155.93/155.62 [6981]~P22(f312(f312(f228(a1),x69811),f2(a1)))+P22(f312(f312(f228(a1),f312(f47(a1,x69811),x69812)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x69812))
% 155.93/155.62 [6982]~P22(f312(f312(f228(a1),x69822),f2(a1)))+P22(f312(f312(f227(a1),f312(f47(a1,x69821),x69822)),f2(a1)))+~P22(f312(f312(f227(a1),f2(a1)),x69821))
% 155.93/155.62 [6983]~P22(f312(f312(f227(a1),x69831),f2(a1)))+P22(f312(f312(f227(a1),f312(f47(a1,x69831),x69832)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x69832))
% 155.93/155.62 [7033]~P93(x70332)+E(x70331,f127(x70332))+E(f312(f138(x70332,x70332,f90(x70332),f312(f137(x70332),x70331)),f312(f167(x70332),x70331)),f312(f72(x70332,f90(x70332)),f312(f168(x70332),x70331)))
% 155.93/155.62 [7145]~E(x71451,f2(a853))+E(f312(f138(a853,a853,f89(a853),x71451),x71452),f2(a853))+P22(f312(f312(f314(a853),f615(x71452,x71451)),f312(f168(a853),x71452)))
% 155.93/155.62 [7192]P22(f312(f312(f314(f861(x71921,a846)),f675(x71922,x71921)),x71922))+~P22(f312(f70(f861(x71921,a846)),x71922))+P22(f312(f70(x71921),f48(f861(x71921,a846),x71922)))
% 155.93/155.62 [7292]P19(x72921,x72921,x72922,f235(f861(x72921,a846)))+~E(f312(f290(x72921,x72921,x72922),f235(f861(x72921,a846))),f235(f861(x72921,a846)))+~P22(f312(f70(x72921),f235(f861(x72921,a846))))
% 155.93/155.62 [7362]~P22(f312(f312(f228(a1),x73622),f2(a1)))+~P22(f312(f312(f228(a1),f312(f47(a1,x73621),x73622)),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x73621))
% 155.93/155.62 [7365]P22(f312(f312(f228(a1),x73651),f2(a1)))+~P22(f312(f312(f228(a1),f312(f47(a1,x73651),x73652)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x73652))
% 155.93/155.62 [7415]~P19(x74151,x74151,x74152,f235(f861(x74151,a846)))+E(f312(f290(x74151,x74151,x74152),f235(f861(x74151,a846))),f235(f861(x74151,a846)))+~P22(f312(f70(x74151),f235(f861(x74151,a846))))
% 155.93/155.62 [7528]E(f312(f47(a1,x75281),x75282),f312(f117(a1),a111))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x75281),x75282)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x75281))
% 155.93/155.62 [7614]E(f312(f312(f89(a1),x76141),x76142),f54(a1,x76141,x76142))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),x76141),x76142)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x76141))
% 155.93/155.62 [8002]~P63(x80021)+~P22(f312(f67(f857(x80021)),x80022))+P22(f312(f67(x80021),f312(f312(f8(f857(x80021),a846,x80021),x80022),f219(x80021))))
% 155.93/155.62 [8320]~P103(x83201)+P33(x83201,x83202)+~P22(f312(f312(f227(x83201),f312(f312(f161(x83201),x83202),f653(x83202,x83201))),f312(f312(f161(x83201),x83202),f654(x83202,x83201))))
% 155.93/155.62 [8321]~P103(x83211)+P33(x83211,x83212)+~P22(f312(f312(f227(x83211),f312(f312(f161(x83211),x83212),f656(x83212,x83211))),f312(f312(f161(x83211),x83212),f666(x83212,x83211))))
% 155.93/155.62 [8485]~P63(x84851)+P22(f312(f66(f857(x84851)),x84852))+~P22(f312(f66(x84851),f312(f312(f8(f857(x84851),a846,x84851),x84852),f219(x84851))))
% 155.93/155.62 [9630]~P63(x96301)+~P63(x96302)+E(f312(f312(f150(f854(x96301),f861(x96302,x96301)),f312(f312(f8(f861(x96302,f857(x96301)),f861(x96302,x96301),f854(x96301)),f82(f857(x96301),x96301,x96302,f223(x96301))),f312(f312(f8(f854(f860(x96302,x96301)),f861(x96302,f857(x96301)),f854(x96301)),f173(x96302,x96301)),f312(f177(x96302,x96301),f64(x96302))))),f63(x96301,f312(f190(f854(x96302)),f64(x96302)),f64(x96301))),f64(f861(x96302,x96301)))
% 155.93/155.62 [5626]~P43(x56262)+~P43(x56261)+P43(f312(f312(f124(f861(a1,a846)),x56261),x56262))
% 155.93/155.62 [5627]~P43(x56272)+~P43(x56271)+P43(f312(f312(f115(f861(a1,a846)),x56271),x56272))
% 155.93/155.62 [5634]E(x56341,f2(a1))+~E(f54(a1,x56342,x56341),f2(a1))+E(f312(f47(a1,f312(f88(a1),x56342)),x56341),f312(f88(a1),f312(f47(a1,x56342),x56341)))
% 155.93/155.62 [5644]~P90(x56441)+~P64(x56441)+E(f312(f88(x56441),f312(f312(f268(x56441),f87(x56441)),x56442)),f312(f312(f268(x56441),f312(f117(x56441),a111)),x56442))
% 155.93/155.62 [5884]~P103(x58841)+P33(x58841,x58842)+P22(f312(f312(f228(a853),f654(x58842,x58841)),f312(f190(f854(x58841)),x58842)))
% 155.93/155.62 [5885]~P103(x58851)+P33(x58851,x58852)+P22(f312(f312(f228(a853),f666(x58852,x58851)),f312(f190(f854(x58851)),x58852)))
% 155.93/155.62 [6036]~P90(x60361)+~E(f312(f117(x60361),x60362),f2(x60361))+P35(x60361,f312(f117(x60361),f312(f312(f89(a1),x60362),f312(f88(a1),a92))))
% 155.93/155.62 [6037]~P90(x60371)+~E(f312(f117(x60371),x60372),f2(x60371))+P35(x60371,f312(f117(x60371),f312(f312(f89(a1),a92),f312(f88(a1),x60372))))
% 155.93/155.62 [6168]~E(x61682,f2(a853))+~E(x61681,f2(a853))+P22(f312(f312(f227(a1),f312(f114(a1),x61681)),f312(f88(a1),f312(f114(a1),x61682))))
% 155.93/155.62 [6187]E(f312(f312(f89(a113),f87(a113)),f258(x61871,f312(f47(a113,x61872),x61871))),f258(x61871,x61872))+P22(f312(f312(f227(a113),x61871),f87(a113)))+P22(f312(f312(f228(a113),x61872),x61871))
% 155.93/155.62 [6196]E(f312(f312(f89(a853),f312(f117(a853),x61961)),f312(f117(a853),x61962)),f312(f117(a853),f312(f312(f89(a1),x61961),x61962)))+P22(f312(f312(f228(a1),x61961),a92))+P22(f312(f312(f228(a1),x61962),a92))
% 155.93/155.62 [6320]~P70(x63201)+~P22(f312(f312(f228(x63201),f2(x63201)),x63202))+P22(f312(f312(f228(x63201),f312(f88(x63201),x63202)),x63202))
% 155.93/155.62 [6321]~P70(x63211)+~P22(f312(f312(f227(x63211),f2(x63211)),x63212))+P22(f312(f312(f227(x63211),f312(f88(x63211),x63212)),x63212))
% 155.93/155.62 [6490]E(f312(f312(f21(a853),f312(a118,x64901)),f312(a118,x64902)),f312(a118,f312(f312(f21(a1),x64901),x64902)))+~P22(f312(f312(f227(a1),f2(a1)),x64902))+~P22(f312(f312(f227(a1),x64902),x64901))
% 155.93/155.62 [6523]E(f312(a118,f54(a1,f312(f117(a1),x65231),f312(f117(a1),x65232))),f54(a853,f312(f117(a853),x65231),f312(f117(a853),x65232)))+P22(f312(a194,f312(f117(a1),x65231)))+P22(f312(a194,f312(f117(a1),x65232)))
% 155.93/155.62 [6540]~P70(x65401)+P22(f312(f312(f228(x65401),f2(x65401)),x65402))+~P22(f312(f312(f228(x65401),f312(f88(x65401),x65402)),x65402))
% 155.93/155.62 [6541]~P70(x65411)+P22(f312(f312(f227(x65411),f2(x65411)),x65412))+~P22(f312(f312(f227(x65411),f312(f88(x65411),x65412)),x65412))
% 155.93/155.62 [6553]~P70(x65531)+~P22(f312(f312(f228(x65531),f2(x65531)),x65532))+P22(f312(f312(f228(x65531),f2(x65531)),f312(f312(f89(x65531),x65532),x65532)))
% 155.93/155.62 [6555]~P70(x65551)+~P22(f312(f312(f227(x65551),f2(x65551)),x65552))+P22(f312(f312(f227(x65551),f2(x65551)),f312(f312(f89(x65551),x65552),x65552)))
% 155.93/155.62 [6566]E(f312(f312(f89(a853),f312(a118,x65661)),f312(a118,x65662)),f312(a118,f312(f312(f89(a1),x65661),x65662)))+~P22(f312(f312(f227(a1),f2(a1)),x65662))+~P22(f312(f312(f227(a1),f2(a1)),x65661))
% 155.93/155.62 [6578]E(x65781,f2(a1))+E(f54(a1,x65782,x65781),f2(a1))+E(f312(f312(f21(a1),f312(f88(a1),f312(f47(a1,x65782),x65781))),f87(a1)),f312(f47(a1,f312(f88(a1),x65782)),x65781))
% 155.93/155.62 [6580]E(x65801,f2(a853))+P22(f312(f312(f228(a853),f2(a853)),x65802))+~P22(f312(f312(f228(a853),f2(a853)),f312(f312(f240(a853),x65802),x65801)))
% 155.93/155.62 [6608]~P90(x66081)+E(f312(f117(x66081),x66082),f2(x66081))+~P35(x66081,f312(f117(x66081),f312(f312(f89(a1),a92),f312(f88(a1),x66082))))
% 155.93/155.62 [6609]~P90(x66091)+E(f312(f117(x66091),x66092),f2(x66091))+~P35(x66091,f312(f117(x66091),f312(f312(f89(a1),x66092),f312(f88(a1),a92))))
% 155.93/155.62 [6669]~P22(f312(f70(x66691),x66692))+~P22(f312(f70(x66691),f235(f861(x66691,a846))))+P22(f312(f70(x66691),f312(f88(f861(x66691,a846)),x66692)))
% 155.93/155.62 [6727]~P22(f312(f312(f228(a853),f2(a853)),x67272))+~P22(f312(f312(f228(a853),f2(a853)),x67271))+P22(f312(f312(f228(a853),f2(a853)),f312(f312(f90(a853),x67271),x67272)))
% 155.93/155.62 [6728]~P22(f312(f312(f227(a1),f2(a1)),x67282))+~P22(f312(f312(f227(a1),f2(a1)),x67281))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),x67281),x67282)))
% 155.93/155.62 [6729]~P22(f312(f312(f227(a1),f2(a1)),x67292))+~P22(f312(f312(f227(a1),f2(a1)),x67291))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f90(a1),x67291),x67292)))
% 155.93/155.62 [6848]P22(f312(f312(f228(a853),f2(a853)),x68481))+P22(f312(f312(f228(a853),f2(a853)),x68482))+~P22(f312(f312(f228(a853),f2(a853)),f312(f312(f89(a853),x68482),x68481)))
% 155.93/155.62 [6850]~P70(x68501)+P22(f312(f312(f228(x68501),f2(x68501)),x68502))+~P22(f312(f312(f228(x68501),f2(x68501)),f312(f312(f89(x68501),x68502),x68502)))
% 155.93/155.62 [6851]~P70(x68511)+P22(f312(f312(f227(x68511),f2(x68511)),x68512))+~P22(f312(f312(f227(x68511),f2(x68511)),f312(f312(f89(x68511),x68512),x68512)))
% 155.93/155.62 [6912]~P22(f312(f70(x69121),x69122))+P22(f312(f70(x69121),f235(f861(x69121,a846))))+~P22(f312(f70(x69121),f312(f88(f861(x69121,a846)),x69122)))
% 155.93/155.62 [6969]E(f312(f312(f239(a1,a1),f312(f47(a1,x69691),x69692)),f54(a1,x69691,x69692)),f312(a59,f55(f312(f88(a1),x69691),f312(f88(a1),x69692))))+P22(f312(f312(f228(a1),f2(a1)),x69692))+P22(f312(f312(f227(a1),f2(a1)),x69691))
% 155.93/155.62 [6996]~P22(f312(f312(f228(a853),f2(a853)),x69961))+~P22(f312(f312(f228(a853),f87(a853)),x69962))+P22(f312(f312(f228(a853),f312(f47(a853,x69961),x69962)),x69961))
% 155.93/155.62 [6997]~P22(f312(f312(f228(a1),f2(a1)),x69971))+~P22(f312(f312(f228(a1),f87(a1)),x69972))+P22(f312(f312(f228(a1),f312(f47(a1,x69971),x69972)),x69971))
% 155.93/155.62 [7445]~P22(f312(f70(x74452),f235(f861(x74452,a846))))+~P22(f312(f70(x74451),f235(f861(x74451,a846))))+P22(f312(f70(f859(x74451,x74452)),f235(f861(f859(x74451,x74452),a846))))
% 155.93/155.62 [7446]~P22(f312(f70(x74462),f235(f861(x74462,a846))))+~P22(f312(f70(x74461),f235(f861(x74461,a846))))+P22(f312(f70(f860(x74461,x74462)),f235(f861(f860(x74461,x74462),a846))))
% 155.93/155.62 [7516]~P22(f312(f312(f228(a853),f312(a126,f2(a853))),x75161))+~P22(f312(f312(f228(a853),f312(a126,f2(a853))),x75162))+P22(f312(f312(f228(a853),x75161),f312(f312(f90(a853),x75162),x75161)))
% 155.93/155.62 [7517]~P22(f312(f312(f228(a853),f312(a126,f2(a853))),x75171))+~P22(f312(f312(f228(a853),f312(a126,f2(a853))),x75172))+P22(f312(f312(f228(a853),x75171),f312(f312(f90(a853),x75171),x75172)))
% 155.93/155.62 [7550]E(f312(f53(x75501),f235(f861(x75501,a846))),f312(a126,f2(a853)))+P22(f312(f70(x75502),f235(f861(x75502,a846))))+~P22(f312(f70(f861(x75502,x75501)),f235(f861(f861(x75502,x75501),a846))))
% 155.93/155.62 [7679]~P22(f312(f312(f228(a853),f312(a126,f2(a853))),x76792))+~P22(f312(f312(f228(a853),f312(a126,f2(a853))),x76791))+P22(f312(f312(f228(a853),f312(a126,f2(a853))),f312(f312(f90(a853),x76791),x76792)))
% 155.93/155.62 [7680]~P22(f312(f312(f227(a853),f312(a126,f2(a853))),x76801))+~P22(f312(f312(f227(a853),f312(a126,f2(a853))),x76802))+P22(f312(f312(f227(a853),f312(a126,f2(a853))),f312(f312(f90(a853),x76801),x76802)))
% 155.93/155.62 [8019]~P105(x80191)+P49(a853,x80191,x80192)+~P22(f312(f312(f227(x80191),f312(x80192,f833(x80192,x80191))),f312(x80192,f312(a126,f833(x80192,x80191)))))
% 155.93/155.62 [8373]E(x83731,f127(x83732))+~P22(f312(f133(x83732),x83731))+E(f172(x83732,f312(f312(f8(a846,a846,x83732),a307),f312(f312(f7(x83732,x83732,a846),a309),f140(x83732,x83731))),x83731),f128(x83732,x83731))
% 155.93/155.62 [8474]~P43(x84742)+~P43(x84741)+E(f312(f290(a853,a1,f114(a1)),f312(f312(f124(f861(a853,a846)),f312(f290(a1,a853,a118),x84741)),f312(f290(a1,a853,a118),x84742))),f312(f312(f124(f861(a1,a846)),x84741),x84742))
% 155.93/155.62 [8475]~P43(x84752)+~P43(x84751)+E(f312(f290(a853,a1,f114(a1)),f312(f312(f115(f861(a853,a846)),f312(f290(a1,a853,a118),x84751)),f312(f290(a1,a853,a118),x84752))),f312(f312(f115(f861(a1,a846)),x84751),x84752))
% 155.93/155.62 [9117]~P90(x91171)+~E(f312(f117(x91171),x91172),f87(x91171))+P35(x91171,f312(f117(x91171),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f88(a1),x91172))))
% 155.93/155.62 [9351]~P90(x93511)+E(f312(f117(x93511),x93512),f87(x93511))+~P35(x93511,f312(f117(x93511),f312(f312(f89(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),f312(f88(a1),x93512))))
% 155.93/155.62 [10084]E(x100841,f2(a1))+E(x100842,f2(a1))+E(f312(f250(a1,a1,a1,a1,f39(a1),f312(f90(a1),f91(a1,x100842))),f312(f312(f312(f108(f860(a1,a1)),f312(f312(a309,f91(a1,x100841)),f91(a1,x100842))),f61(x100841,x100842)),f312(f312(f249(a1,a1,f860(a1,a1)),f312(f312(f18(a1,f861(a1,f860(a1,a1)),f861(a1,f860(a1,a1))),f312(f312(f8(f861(a1,f861(f860(a1,a1),f860(a1,a1))),f861(f861(a1,f860(a1,a1)),f861(a1,f860(a1,a1))),a1),f18(a1,f860(a1,a1),f860(a1,a1))),f312(f312(f8(f860(a1,a1),f861(a1,f861(f860(a1,a1),f860(a1,a1))),a1),f312(f7(a1,f860(a1,a1),f861(f860(a1,a1),f860(a1,a1))),f312(f312(f8(a846,f861(f860(a1,a1),f861(f860(a1,a1),f860(a1,a1))),a1),f108(f860(a1,a1))),f312(f312(f7(a1,a1,a846),a309),f2(a1))))),f312(f312(f7(a1,a1,f860(a1,a1)),f312(f312(f8(a1,f861(a1,f860(a1,a1)),a1),f239(a1,a1)),f88(a1))),f2(a1))))),f312(f312(f7(a1,f861(a1,a1),f861(a1,f860(a1,a1))),f312(f312(f8(f861(a1,f860(a1,a1)),f861(f861(a1,a1),f861(a1,f860(a1,a1))),a1),f8(a1,f860(a1,a1),a1)),f312(f312(f8(a1,f861(a1,f860(a1,a1)),a1),f239(a1,a1)),f312(f312(f7(a1,a1,a1),f312(f312(f8(a1,f861(a1,a1),a1),f21(a1)),f88(a1))),f87(a1))))),f312(f21(a1),f312(f84(a1),x100842))))),f61(x100841,x100842)))),f312(f312(f239(a1,a1),f312(f47(a1,x100841),x100842)),f54(a1,x100841,x100842)))
% 155.93/155.62 [10085]E(x100851,f2(a1))+E(x100852,f2(a1))+E(f312(f250(a1,a1,a1,a1,f39(a1),f312(f90(a1),f91(a1,x100852))),f312(f312(f312(f108(f860(a1,a1)),f312(f312(a311,f312(f312(a310,f312(f312(f228(a1),f2(a1)),x100852)),f312(f312(f227(a1),f2(a1)),x100851))),f312(f312(a310,f312(f312(f228(a1),x100852),f2(a1))),f312(f312(f228(a1),x100851),f2(a1))))),f61(x100851,x100852)),f312(f312(f249(a1,a1,f860(a1,a1)),f312(f312(f18(a1,f861(a1,f860(a1,a1)),f861(a1,f860(a1,a1))),f312(f312(f8(f861(a1,f861(f860(a1,a1),f860(a1,a1))),f861(f861(a1,f860(a1,a1)),f861(a1,f860(a1,a1))),a1),f18(a1,f860(a1,a1),f860(a1,a1))),f312(f312(f8(f860(a1,a1),f861(a1,f861(f860(a1,a1),f860(a1,a1))),a1),f312(f7(a1,f860(a1,a1),f861(f860(a1,a1),f860(a1,a1))),f312(f312(f8(a846,f861(f860(a1,a1),f861(f860(a1,a1),f860(a1,a1))),a1),f108(f860(a1,a1))),f312(f312(f7(a1,a1,a846),a309),f2(a1))))),f312(f312(f7(a1,a1,f860(a1,a1)),f312(f312(f8(a1,f861(a1,f860(a1,a1)),a1),f239(a1,a1)),f88(a1))),f2(a1))))),f312(f312(f7(a1,f861(a1,a1),f861(a1,f860(a1,a1))),f312(f312(f8(f861(a1,f860(a1,a1)),f861(f861(a1,a1),f861(a1,f860(a1,a1))),a1),f8(a1,f860(a1,a1),a1)),f312(f312(f8(a1,f861(a1,f860(a1,a1)),a1),f239(a1,a1)),f312(f312(f7(a1,a1,a1),f312(f312(f8(a1,f861(a1,a1),a1),f21(a1)),f88(a1))),f87(a1))))),f312(f21(a1),f312(f84(a1),x100852))))),f61(x100851,x100852)))),f312(f312(f239(a1,a1),f312(f47(a1,x100851),x100852)),f54(a1,x100851,x100852)))
% 155.93/155.62 [5635]~P112(x56351)+~P90(x56351)+E(f312(f84(x56351),f312(f312(f240(x56351),f312(f117(x56351),a111)),x56352)),f87(x56351))
% 155.93/155.62 [6106]~P111(x61061)+~P22(f312(f312(f228(a1),x61062),f2(a1)))+E(f312(f88(x61061),f312(f114(x61061),f312(a118,f312(f88(a1),x61062)))),f312(f116(x61061),x61062))
% 155.93/155.62 [6894]~P89(x68941)+~P22(f312(f312(f314(x68941),x68942),f123(x68941)))+~E(f312(f312(f89(x68941),f312(f312(f89(x68941),f87(x68941)),x68942)),x68942),f2(x68941))
% 155.93/155.62 [6998]~P22(f312(f312(f228(a1),x69981),f2(a1)))+~P22(f312(f312(f227(a1),x69982),f2(a1)))+E(f312(f246(a1,a1),f312(a59,f55(f312(f88(a1),x69981),f312(f88(a1),x69982)))),f312(f47(a1,x69981),x69982))
% 155.93/155.62 [7012]~P22(f312(f312(f228(a1),x70122),f2(a1)))+E(f312(f246(a1,a1),f312(a59,f58(f312(f88(a1),x70121),f312(f88(a1),x70122)))),f312(f47(a1,x70121),x70122))+~P22(f312(f312(f228(a1),f2(a1)),x70121))
% 155.93/155.62 [7029]~P22(f312(f312(f228(a1),x70291),f2(a1)))+~P22(f312(f312(f227(a1),x70292),f2(a1)))+E(f312(f248(a1,a1),f312(a59,f55(f312(f88(a1),x70291),f312(f88(a1),x70292)))),f54(a1,x70291,x70292))
% 155.93/155.62 [7054]~P22(f312(f312(f228(a1),x70542),f2(a1)))+E(f312(f248(a1,a1),f312(a59,f58(f312(f88(a1),x70541),f312(f88(a1),x70542)))),f54(a1,x70541,x70542))+~P22(f312(f312(f228(a1),f2(a1)),x70541))
% 155.93/155.62 [7063]E(f312(f47(a1,f312(f312(f240(a1),x70631),x70632)),x70631),f312(f312(f240(a1),x70631),f312(f312(f21(a853),x70632),f312(a126,f2(a853)))))+~P22(f312(f312(f228(a853),f2(a853)),x70632))+~P22(f312(f312(f228(a1),f2(a1)),x70631))
% 155.93/155.62 [7191]~P22(f312(f312(f228(a853),f2(a853)),x71911))+~P22(f312(f312(f228(a853),f2(a853)),x71912))+P22(f312(f312(f228(a853),f312(f312(f21(a853),x71911),x71912)),x71911))
% 155.93/155.62 [7339]E(x73391,f2(a853))+~E(x73392,f2(a1))+~P22(f312(f312(f228(a1),f2(a1)),f312(f312(f240(a1),f312(f84(a1),x73392)),x73391)))
% 155.93/155.62 [7710]~P22(f312(x77101,x77102))+P22(f312(x77101,f2(a853)))+E(f312(a126,f231(a853,f312(f312(f8(a853,a846,a853),x77101),a126))),f231(a853,x77101))
% 155.93/155.62 [7759]~E(x77592,f127(f854(x77591)))+E(f312(f190(f854(f854(x77591))),f175(x77591,x77592)),f2(a853))+~P33(a853,f312(f165(a853),f312(f312(f150(f854(x77591),a853),f190(f854(x77591))),x77592)))
% 155.93/155.62 [8001]P22(f312(x80011,x80012))+~P22(f312(x80011,f312(a121,f550(x80011,x80012))))+~P22(f312(f312(f314(f861(f860(a853,a853),a846)),x80012),a112))
% 155.93/155.62 [8023]E(x80231,f127(f854(x80232)))+E(f312(f190(f854(x80232)),f312(f312(f161(f854(x80232)),x80231),f2(a853))),f312(f190(f854(f854(x80232))),f175(x80232,x80231)))+~P33(a853,f312(f165(a853),f312(f312(f150(f854(x80232),a853),f190(f854(x80232))),x80231)))
% 155.93/155.62 [8731]~P22(f312(f70(x87311),f312(f233(x87311),x87312)))+~P22(f312(f70(x87311),f235(f861(x87311,a846))))+P22(f312(f70(x87311),f312(f233(x87311),f312(f312(f8(a846,a846,x87311),a307),x87312))))
% 155.93/155.62 [8755]E(f312(f312(f239(a853,a853),f312(a126,f312(f47(a853,f312(f312(f21(a853),x87551),x87552)),x87552))),f54(a853,f312(f312(f21(a853),x87551),x87552),x87552)),f94(f860(a853,a853),f56(x87551,x87552)))+~P22(f312(f312(f228(a853),f2(a853)),x87552))+~P22(f312(f312(f227(a853),x87552),x87551))
% 155.93/155.62 [9080]~P22(f312(f70(x90801),f312(f233(x90801),x90802)))+P22(f312(f70(x90801),f235(f861(x90801,a846))))+~P22(f312(f70(x90801),f312(f233(x90801),f312(f312(f8(a846,a846,x90801),a307),x90802))))
% 155.93/155.62 [9797]P20(x97971,x97972)+~P41(x97971,f312(f246(f861(f860(x97971,x97971),a846),f861(f860(x97971,x97971),a846)),x97972))+~P22(f312(f312(f227(f861(f860(x97971,x97971),a846)),f312(f312(f267(x97971,x97971,x97971),f312(f246(f861(f860(x97971,x97971),a846),f861(f860(x97971,x97971),a846)),x97972)),f312(f248(f861(f860(x97971,x97971),a846),f861(f860(x97971,x97971),a846)),x97972))),f312(f246(f861(f860(x97971,x97971),a846),f861(f860(x97971,x97971),a846)),x97972)))
% 155.93/155.62 [7053]~P22(f312(f312(f228(a853),f2(a853)),x70532))+P22(f312(f312(f228(a853),x70531),x70532))+E(f312(a126,f312(f47(a853,f312(f312(f21(a853),x70531),x70532)),x70532)),f312(f47(a853,x70531),x70532))
% 155.93/155.62 [7206]~P22(f312(f312(f228(a853),f2(a853)),x72062))+~P22(f312(f312(f227(a853),x72062),x72061))+E(f312(a126,f312(f47(a853,f312(f312(f21(a853),x72061),x72062)),x72062)),f312(f47(a853,x72061),x72062))
% 155.93/155.62 [8236]~P90(x82361)+~P89(x82361)+~P35(x82361,f312(f117(x82361),f312(f312(f21(a1),f312(f312(f89(a1),x82362),x82362)),a111)))
% 155.93/155.62 [8989]E(x89891,f2(a853))+E(f312(f312(f249(a853,a853,f860(a853,a853)),f312(f312(f8(a853,f861(a853,f860(a853,a853)),a853),f239(a853,a853)),a126)),f94(f860(a853,a853),f56(f312(f312(f21(a853),x89892),x89891),x89891))),f94(f860(a853,a853),f56(x89892,x89891)))+P22(f312(f312(f228(a853),x89892),x89891))
% 155.93/155.62 [7474]~P90(x74741)+~P65(x74741)+E(f312(f312(f268(x74741),x74742),f312(f117(x74741),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111))),x74742)
% 155.93/155.62 [9116]~P90(x91161)+~E(f312(f117(x91161),x91162),f87(x91161))+P35(x91161,f312(f117(x91161),f312(f312(f89(a1),x91162),f312(f88(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 155.93/155.62 [9292]~P134(x92921)+~E(x92922,f2(x92921))+E(f312(f312(f240(x92921),x92922),f312(f117(a853),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(x92921))
% 155.93/155.62 [9293]~P134(x92931)+~E(x92932,f87(x92931))+E(f312(f312(f240(x92931),x92932),f312(f117(a853),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(x92931))
% 155.93/155.62 [9306]~P134(x93061)+~E(x93062,f312(f88(x93061),f87(x93061)))+E(f312(f312(f240(x93061),x93062),f312(f117(a853),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(x93061))
% 155.93/155.62 [9352]~P90(x93521)+E(f312(f117(x93521),x93522),f87(x93521))+~P35(x93521,f312(f117(x93521),f312(f312(f89(a1),x93522),f312(f88(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))))
% 155.93/155.62 [9727]~P112(x97272)+E(x97271,f2(x97272))+P22(f312(f312(f228(x97272),f2(x97272)),f312(f312(f240(x97272),x97271),f312(f117(a853),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))))))
% 155.93/155.62 [9796]~P112(x97962)+~E(x97961,f2(x97962))+~P22(f312(f312(f228(x97962),f2(x97962)),f312(f312(f240(x97962),x97961),f312(f117(a853),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))))))
% 155.93/155.62 [9823]P22(f312(f312(f227(a1),x98231),f2(a1)))+P22(f312(f312(f228(a1),x98232),x98231))+E(f312(f52(x98231),f55(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))),f55(x98232,x98231))
% 155.93/155.62 [9824]~P22(f312(f312(f228(a1),f2(a1)),x98241))+P22(f312(f312(f228(a1),x98242),x98241))+E(f312(f52(x98241),f55(x98242,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)))),x98241))),f55(x98242,x98241))
% 155.93/155.62 [9825]P22(f312(f312(f227(a1),x98251),f2(a1)))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),x98252),x98251)))+E(f312(f52(x98251),f58(x98252,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)))),x98251))),f58(x98252,x98251))
% 155.93/155.62 [9826]~P22(f312(f312(f228(a1),f2(a1)),x98261))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),x98262),x98261)))+E(f312(f52(x98261),f58(x98262,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)))),x98261))),f58(x98262,x98261))
% 155.93/155.62 [9827]~P23(x98271)+~P22(f312(f312(f227(a1),f2(a1)),x98272))+E(f312(f114(x98271),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)))),x98272))),f312(f312(f89(x98271),f312(f114(x98271),f312(a118,x98272))),f312(f114(x98271),f312(a118,x98272))))
% 155.93/155.62 [4975]~P139(x49751,x49753,x49752)+~E(x49753,f2(a1))+P22(f312(x49751,x49752))
% 155.93/155.62 [5101]~P103(x51011)+~P33(x51011,x51013)+P33(x51011,f166(x51011,x51012,x51013))
% 155.93/155.62 [5102]~P103(x51021)+~P33(x51021,x51023)+P33(x51021,f172(x51021,x51022,x51023))
% 155.93/155.62 [4688]~P71(x46882)+~E(x46883,f312(f88(x46882),x46881))+E(x46881,f312(f88(x46882),x46883))
% 155.93/155.62 [4690]~P71(x46901)+~E(f312(f88(x46901),x46903),x46902)+E(f312(f88(x46901),x46902),x46903)
% 155.93/155.62 [4761]~P71(x47613)+E(x47611,x47612)+~E(f312(f88(x47613),x47611),f312(f88(x47613),x47612))
% 155.93/155.62 [4762]~P88(x47623)+E(x47621,x47622)+~E(f312(f88(x47623),x47621),f312(f88(x47623),x47622))
% 155.93/155.62 [4763]~P100(x47633)+E(x47631,x47632)+~E(f312(f114(x47633),x47631),f312(f114(x47633),x47632))
% 155.93/155.62 [4764]~P89(x47643)+E(x47641,x47642)+~E(f312(f116(x47643),x47641),f312(f116(x47643),x47642))
% 155.93/155.62 [4765]~P103(x47653)+E(x47651,x47652)+~E(f312(f281(x47653),x47651),f312(f281(x47653),x47652))
% 155.93/155.62 [4766]~P103(x47663)+E(x47661,x47662)+~E(f312(f280(x47663),x47661),f312(f280(x47663),x47662))
% 155.93/155.62 [4767]~P103(x47673)+E(x47671,x47672)+~E(f312(f234(x47673),x47671),f312(f234(x47673),x47672))
% 155.93/155.62 [4768]~P103(x47683)+E(x47681,x47682)+~E(f312(f279(x47683),x47681),f312(f279(x47683),x47682))
% 155.93/155.62 [4867]~P63(x48671)+~P22(f312(x48672,x48673))+P22(f312(f66(x48671),x48672))
% 155.93/155.62 [4902]~P63(x49023)+P22(f312(x49021,x49022))+~P22(f312(f67(x49023),x49021))
% 155.93/155.62 [4993]~P140(x49931,x49932,x49933)+~E(x49932,f2(a1))+P22(f312(x49931,f2(a1)))
% 155.93/155.62 [5027]~P101(x50272)+~P22(f312(x50271,x50273))+P22(f312(x50271,f231(x50272,x50271)))
% 155.93/155.62 [5033]~E(x50331,f2(a853))+E(f365(x50331,x50332,x50333),f189(f861(x50333,a846)))+~E(f312(f53(x50333),x50332),f312(a126,x50331))
% 155.93/155.62 [5188]~E(x51882,f2(a853))+E(f312(f246(a853,a853),x51881),f2(a853))+~P22(f312(f56(x51883,x51882),x51881))
% 155.93/155.62 [5232]P22(f312(x52321,x52322))+~E(x52323,f312(f114(a1),x52322))+~P22(f312(x52321,f312(a118,x52323)))
% 155.93/155.62 [5694]~E(x56943,f2(a853))+~P22(f312(x56941,x56942))+P22(f312(x56941,f54(a853,x56942,x56943)))
% 155.93/155.62 [5742]~P101(x57421)+~P22(f312(x57422,x57423))+~P22(f312(f312(f228(x57421),x57423),f231(x57421,x57422)))
% 155.93/155.62 [5819]~P22(f312(a24,x58193))+~P22(f312(a24,x58192))+P22(f312(a24,f33(x58191,x58192,x58193)))
% 155.93/155.62 [5849]~P63(x58493)+~P7(x58493,x58491,x58492)+P22(f312(x58491,f667(x58492,x58491,x58493)))
% 155.93/155.62 [6089]~E(x60893,f2(a853))+P22(f312(x60891,x60892))+~P22(f312(x60891,f54(a853,x60892,x60893)))
% 155.93/155.62 [6100]~P31(x61001)+~P22(f312(f312(f227(x61001),x61002),f312(x61003,x61002)))+P22(f312(f312(f227(x61001),x61002),f110(x61001,x61003)))
% 155.93/155.62 [6236]~P63(x62361)+P8(x62361,x62362,x62363)+~P22(f312(x62362,f668(x62363,x62362,x62361)))
% 155.93/155.62 [6751]E(x67511,f2(a853))+~P22(f312(x67512,f332(x67511,x67513,x67512)))+P22(f312(x67512,f54(a853,x67513,x67511)))
% 155.93/155.62 [6858]~P31(x68581)+~P22(f312(f312(f227(x68581),x68582),f679(x68583,x68582,x68581)))+P22(f312(f312(f227(x68581),x68582),f49(x68581,x68583)))
% 155.93/155.62 [6860]~P22(f312(x68601,x68602))+~P22(f312(x68601,f332(x68603,x68602,x68601)))+P22(f312(x68601,f54(a853,x68602,x68603)))
% 155.93/155.62 [6966]E(x69661,f127(x69662))+E(f312(f312(f147(x69662),f630(x69663,x69661,x69662)),f633(x69663,x69661,x69662)),x69661)+~P22(f312(f312(f314(f854(x69662)),x69661),f157(x69662,x69663)))
% 155.93/155.62 [7001]~P111(x70011)+~P22(f312(f312(f314(x70011),x70012),f123(x70011)))+P22(f312(f312(f314(x70011),f312(f312(f240(x70011),x70012),x70013)),f123(x70011)))
% 155.93/155.62 [7577]E(x75771,f127(x75772))+~P22(f312(f312(f314(f854(x75772)),x75771),f157(x75772,x75773)))+P22(f312(f312(f314(f854(x75772)),f633(x75773,x75771,x75772)),f157(x75772,x75773)))
% 155.93/155.62 [7630]E(x76301,f2(a853))+E(f312(f312(f89(a853),f312(f312(f90(a853),x76301),f333(x76301,x76302,x76303))),f332(x76301,x76302,x76303)),x76302)+P22(f312(x76303,f54(a853,x76302,x76301)))
% 155.93/155.62 [7668]P22(f312(f312(f228(a1),x76681),f334(x76682,x76683,x76681)))+P22(f312(f312(x76683,f312(f47(a1,x76682),x76681)),f54(a1,x76682,x76681)))+~P22(f312(f312(f228(a1),x76681),f2(a1)))
% 155.93/155.62 [7674]~P22(f312(x76743,x76742))+E(f312(f312(f89(a853),f312(f312(f90(a853),x76741),f333(x76741,x76742,x76743))),f332(x76741,x76742,x76743)),x76742)+P22(f312(x76743,f54(a853,x76742,x76741)))
% 155.93/155.62 [8000]P22(f312(f312(x80002,f312(f47(a1,x80001),x80003)),f54(a1,x80001,x80003)))+~P22(f312(f312(f228(a1),x80003),f2(a1)))+P22(f312(f312(f227(a1),f334(x80001,x80002,x80003)),f2(a1)))
% 155.93/155.62 [8226]E(f312(f312(f89(a1),f312(f312(f90(a1),x82261),f335(x82262,x82263,x82261))),f334(x82262,x82263,x82261)),x82262)+P22(f312(f312(x82263,f312(f47(a1,x82262),x82261)),f54(a1,x82262,x82261)))+~P22(f312(f312(f228(a1),x82261),f2(a1)))
% 155.93/155.62 [8483]~P22(f312(f312(x84831,f335(x84832,x84831,x84833)),f334(x84832,x84831,x84833)))+P22(f312(f312(x84831,f312(f47(a1,x84832),x84833)),f54(a1,x84832,x84833)))+~P22(f312(f312(f228(a1),x84833),f2(a1)))
% 155.93/155.62 [8740]~P103(x87401)+~P33(x87401,x87403)+P33(x87401,f146(x87401,x87401,f5(x87401),x87402,x87403))
% 155.93/155.62 [9242]~P118(x92422)+E(x92421,f2(x92422))+~P22(f312(f312(f227(x92422),f312(f312(f89(x92422),f312(f312(f90(x92422),x92423),x92423)),f312(f312(f90(x92422),x92421),x92421))),f2(x92422)))
% 155.93/155.62 [9243]~P118(x92432)+E(x92431,f2(x92432))+~P22(f312(f312(f227(x92432),f312(f312(f89(x92432),f312(f312(f90(x92432),x92431),x92431)),f312(f312(f90(x92432),x92433),x92433))),f2(x92432)))
% 155.93/155.62 [10019]~P112(x100191)+~P22(f312(f312(f228(x100191),x100192),f2(x100191)))+P22(f312(f312(f228(x100191),f312(f312(f240(x100191),x100192),f312(a126,f312(f312(f90(a853),f312(f117(a853),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)))),x100193)))),f2(x100191)))
% 155.93/155.62 [10028]~P112(x100282)+E(x100281,f2(x100282))+~P22(f312(f312(f227(x100282),f312(f312(f89(x100282),f312(f312(f240(x100282),x100283),f312(f117(a853),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(x100282),x100281),f312(f117(a853),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(x100282)))
% 155.93/155.62 [10029]~P112(x100292)+E(x100291,f2(x100292))+~P22(f312(f312(f227(x100292),f312(f312(f89(x100292),f312(f312(f240(x100292),x100291),f312(f117(a853),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(x100292),x100293),f312(f117(a853),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(x100292)))
% 155.93/155.62 [4720]~E(x47202,x47203)+~P30(x47201)+E(f312(f312(f21(x47201),x47202),x47203),f2(x47201))
% 155.93/155.62 [4721]~E(x47212,x47213)+~P71(x47211)+E(f312(f312(f21(x47211),x47212),x47213),f2(x47211))
% 155.93/155.62 [4732]~P136(x47321)+~E(x47323,f2(x47321))+E(f312(f312(f89(x47321),x47322),x47323),x47322)
% 155.93/155.62 [4748]~P133(x47481)+~E(x47483,f2(x47481))+E(f312(f312(f90(x47481),x47482),x47483),f2(x47481))
% 155.93/155.62 [4749]~P133(x47491)+~E(x47492,f2(x47491))+E(f312(f312(f90(x47491),x47492),x47493),f2(x47491))
% 155.93/155.62 [4770]~E(x47703,f127(x47701))+~E(x47702,f127(x47701))+E(f312(f312(f129(x47701),x47702),x47703),f127(x47701))
% 155.93/155.62 [4857]~P136(x48572)+E(x48571,f2(x48572))+~E(f312(f312(f89(x48572),x48573),x48571),x48573)
% 155.93/155.62 [4858]~P71(x48581)+~E(x48582,f312(f88(x48581),x48583))+E(f312(f312(f89(x48581),x48582),x48583),f2(x48581))
% 155.93/155.62 [4865]E(x48651,f127(x48652))+E(x48653,f2(a853))+~E(f312(f312(f169(x48652),x48653),x48651),f127(x48652))
% 155.93/155.62 [4871]~P30(x48713)+E(x48711,x48712)+~E(f312(f312(f21(x48713),x48711),x48712),f2(x48713))
% 155.93/155.62 [4872]~P71(x48723)+E(x48721,x48722)+~E(f312(f312(f21(x48723),x48721),x48722),f2(x48723))
% 155.93/155.62 [4882]~P134(x48822)+E(x48821,f2(x48822))+~E(f312(f312(f240(x48822),x48821),x48823),f2(x48822))
% 155.93/155.62 [4883]~P94(x48832)+E(x48831,f189(x48832))+~E(f312(f312(f124(x48832),x48833),x48831),f189(x48832))
% 155.93/155.62 [4884]~P94(x48842)+E(x48841,f189(x48842))+~E(f312(f312(f124(x48842),x48841),x48843),f189(x48842))
% 155.93/155.62 [4885]~P97(x48852)+E(x48851,f235(x48852))+~E(f312(f312(f115(x48852),x48853),x48851),f235(x48852))
% 155.93/155.62 [4886]~P97(x48862)+E(x48861,f235(x48862))+~E(f312(f312(f115(x48862),x48861),x48863),f235(x48862))
% 155.93/155.62 [4947]~P71(x49472)+E(x49471,f312(f88(x49472),x49473))+~E(f312(f312(f89(x49472),x49471),x49473),f2(x49472))
% 155.93/155.62 [4948]~P71(x49481)+E(f312(f88(x49481),x49482),x49483)+~E(f312(f312(f89(x49481),x49482),x49483),f2(x49481))
% 155.93/155.62 [4950]~E(x49502,x49503)+~P102(x49501)+P22(f312(f312(f227(x49501),x49502),x49503))
% 155.93/155.62 [4952]~E(x49522,x49523)+~P105(x49521)+P22(f312(f312(f227(x49521),x49522),x49523))
% 155.93/155.62 [5049]~P113(x50491)+~E(x50492,f312(f88(x50491),x50493))+E(f312(f312(f90(x50491),x50492),x50492),f312(f312(f90(x50491),x50493),x50493))
% 155.93/155.62 [5057]~P103(x50571)+~P33(x50571,x50573)+P33(x50571,f312(f312(f169(x50571),x50572),x50573))
% 155.93/155.62 [5058]~P103(x50581)+~P33(x50581,x50583)+P33(x50581,f312(f312(f134(x50581),x50582),x50583))
% 155.93/155.62 [5099]E(x50991,x50992)+E(x50993,f2(a853))+~E(f312(f312(f90(a853),x50993),x50991),f312(f312(f90(a853),x50993),x50992))
% 155.93/155.62 [5100]E(x51001,x51002)+E(x51003,f2(a853))+~E(f312(f312(f90(a853),x51001),x51003),f312(f312(f90(a853),x51002),x51003))
% 155.93/155.62 [5180]~E(x51802,x51803)+~P105(x51801)+E(f283(x51801,x51802,x51803),f312(f312(f289(x51801),x51802),f189(f861(x51801,a846))))
% 155.93/155.62 [5230]~E(x52301,x52302)+~P103(x52303)+~P22(f312(f312(f228(x52303),x52301),x52302))
% 155.93/155.62 [5231]~E(x52311,x52312)+~P105(x52313)+~P22(f312(f312(f228(x52313),x52311),x52312))
% 155.93/155.62 [5240]~P105(x52401)+E(f312(f282(x52401,x52402),x52403),f189(f861(x52401,a846)))+P22(f312(f312(f228(x52401),x52402),x52403))
% 155.93/155.62 [5285]~P105(x52851)+E(f284(x52851,x52852,x52853),f189(f861(x52851,a846)))+P22(f312(f312(f228(x52851),x52852),x52853))
% 155.93/155.62 [5286]~P105(x52861)+E(f283(x52861,x52862,x52863),f189(f861(x52861,a846)))+P22(f312(f312(f227(x52861),x52862),x52863))
% 155.93/155.62 [5287]~P105(x52871)+E(f189(f861(x52871,a846)),f284(x52871,x52872,x52873))+P22(f312(f312(f228(x52871),x52872),x52873))
% 155.93/155.62 [5288]~P105(x52881)+E(f189(f861(x52881,a846)),f283(x52881,x52882,x52883))+P22(f312(f312(f227(x52881),x52882),x52883))
% 155.93/155.62 [5294]~P98(x52941)+~E(f312(f312(f124(x52941),x52942),x52943),x52943)+P22(f312(f312(f227(x52941),x52942),x52943))
% 155.93/155.62 [5295]~P99(x52951)+~E(f312(f312(f115(x52951),x52952),x52953),x52952)+P22(f312(f312(f227(x52951),x52952),x52953))
% 155.93/155.62 [5296]~P103(x52961)+~E(f312(f312(f225(x52961),x52962),x52963),x52962)+P22(f312(f312(f227(x52961),x52962),x52963))
% 155.93/155.62 [5297]~P103(x52971)+~E(f312(f312(f226(x52971),x52972),x52973),x52973)+P22(f312(f312(f227(x52971),x52972),x52973))
% 155.93/155.62 [5315]~P103(x53151)+P33(x53151,x53152)+~P33(x53151,f312(f312(f147(x53151),x53153),x53152))
% 155.93/155.62 [5316]~P103(x53161)+P33(x53161,x53162)+~P33(x53161,f312(f312(f129(x53161),x53163),x53162))
% 155.93/155.62 [5317]~P103(x53171)+P33(x53171,x53172)+~P33(x53171,f312(f312(f129(x53171),x53172),x53173))
% 155.93/155.62 [5386]~P103(x53861)+P22(f312(f312(f227(x53861),x53863),x53862))+P22(f312(f312(f228(x53861),x53862),x53863))
% 155.93/155.62 [5388]~P103(x53881)+P22(f312(f312(f227(x53881),x53883),x53882))+P22(f312(f312(f227(x53881),x53882),x53883))
% 155.93/155.62 [5425]~P98(x54251)+E(f312(f312(f124(x54251),x54252),x54253),x54252)+~P22(f312(f312(f227(x54251),x54253),x54252))
% 155.93/155.62 [5427]~P98(x54271)+E(f312(f312(f124(x54271),x54272),x54273),x54273)+~P22(f312(f312(f227(x54271),x54272),x54273))
% 155.93/155.62 [5428]~P99(x54281)+E(f312(f312(f115(x54281),x54282),x54283),x54283)+~P22(f312(f312(f227(x54281),x54283),x54282))
% 155.93/155.62 [5430]~P99(x54301)+E(f312(f312(f115(x54301),x54302),x54303),x54302)+~P22(f312(f312(f227(x54301),x54302),x54303))
% 155.93/155.62 [5431]~P103(x54311)+E(f312(f312(f225(x54311),x54312),x54313),x54313)+~P22(f312(f312(f227(x54311),x54313),x54312))
% 155.93/155.62 [5433]~P103(x54331)+E(f312(f312(f225(x54331),x54332),x54333),x54332)+~P22(f312(f312(f227(x54331),x54332),x54333))
% 155.93/155.62 [5434]~P103(x54341)+E(f312(f312(f226(x54341),x54342),x54343),x54342)+~P22(f312(f312(f227(x54341),x54343),x54342))
% 155.93/155.62 [5436]~P103(x54361)+E(f312(f312(f226(x54361),x54362),x54363),x54363)+~P22(f312(f312(f227(x54361),x54362),x54363))
% 155.93/155.62 [5443]~P114(x54432)+E(x54431,f2(x54432))+E(f312(f312(f268(x54432),f312(f88(x54432),x54433)),f312(f88(x54432),x54431)),f312(f312(f268(x54432),x54433),x54431))
% 155.93/155.62 [5478]~E(x54783,f2(a853))+~P22(f312(x54781,f2(a853)))+P22(f312(x54781,f312(f47(a853,x54782),x54783)))
% 155.93/155.62 [5490]~P105(x54901)+E(f312(f282(x54901,x54902),x54903),f189(f861(x54901,a846)))+~P22(f312(f312(f227(x54901),x54903),x54902))
% 155.93/155.62 [5523]~P105(x55231)+E(f285(x55231,x55232,x55233),f189(f861(x55231,a846)))+~P22(f312(f312(f227(x55231),x55233),x55232))
% 155.93/155.62 [5524]~P105(x55241)+E(f284(x55241,x55242,x55243),f189(f861(x55241,a846)))+~P22(f312(f312(f227(x55241),x55243),x55242))
% 155.93/155.62 [5525]~P105(x55251)+E(f283(x55251,x55252,x55253),f189(f861(x55251,a846)))+~P22(f312(f312(f228(x55251),x55253),x55252))
% 155.93/155.62 [5571]~P101(x55711)+~P22(f312(x55712,x55713))+P22(f312(f312(f227(x55711),f231(x55711,x55712)),x55713))
% 155.93/155.62 [5582]~E(f312(f312(f21(a853),x55821),x55823),x55822)+E(x55821,f312(f312(f89(a853),x55822),x55823))+~P22(f312(f312(f227(a853),x55823),x55821))
% 155.93/155.62 [5583]~E(x55831,f312(f312(f89(a853),x55833),x55832))+E(f312(f312(f21(a853),x55831),x55832),x55833)+~P22(f312(f312(f227(a853),x55832),x55831))
% 155.93/155.62 [5622]~P22(f312(x56221,x56223))+P22(f312(x56221,f430(x56221,x56222)))+~P22(f312(f312(f227(a853),x56223),x56222))
% 155.93/155.62 [5623]~P22(f312(x56231,x56233))+P22(f312(x56231,f462(x56231,x56232)))+~P22(f312(f312(f228(a853),x56233),x56232))
% 155.93/155.62 [5632]~P105(x56321)+~E(f312(f282(x56321,x56322),x56323),f189(f861(x56321,a846)))+~P22(f312(f312(f228(x56321),x56322),x56323))
% 155.93/155.62 [5637]~P102(x56371)+~P22(f312(f312(f228(x56371),x56372),x56373))+P22(f312(f312(f227(x56371),x56372),x56373))
% 155.93/155.62 [5639]~P105(x56391)+~P22(f312(f312(f228(x56391),x56392),x56393))+P22(f312(f312(f227(x56391),x56392),x56393))
% 155.93/155.62 [5736]~P105(x57361)+~E(f284(x57361,x57362,x57363),f189(f861(x57361,a846)))+~P22(f312(f312(f228(x57361),x57362),x57363))
% 155.93/155.62 [5737]~P105(x57371)+~E(f283(x57371,x57372,x57373),f189(f861(x57371,a846)))+~P22(f312(f312(f227(x57371),x57372),x57373))
% 155.93/155.62 [5738]~P105(x57381)+~E(f189(f861(x57381,a846)),f284(x57381,x57382,x57383))+~P22(f312(f312(f228(x57381),x57382),x57383))
% 155.93/155.62 [5739]~P105(x57391)+~E(f189(f861(x57391,a846)),f283(x57391,x57392,x57393))+~P22(f312(f312(f227(x57391),x57392),x57393))
% 155.93/155.62 [5748]P22(f312(x57481,x57482))+~P22(f312(x57481,f454(x57481,x57483)))+~P22(f312(f312(f227(a853),x57482),x57483))
% 155.93/155.62 [5749]P22(f312(x57491,x57492))+~P22(f312(x57491,f463(x57491,x57493)))+~P22(f312(f312(f228(a853),x57492),x57493))
% 155.93/155.62 [5756]~E(x57561,f312(a126,x57563))+P22(f312(f312(f228(a853),x57561),f312(a126,x57562)))+~P22(f312(f312(f228(a853),x57563),x57562))
% 155.93/155.62 [5772]E(x57721,x57722)+~E(f312(f312(f90(a853),x57723),x57721),f312(f312(f90(a853),x57723),x57722))+~P22(f312(f312(f228(a853),f2(a853)),x57723))
% 155.93/155.62 [5775]~E(x57752,f2(a853))+P22(f312(x57751,f2(a853)))+~P22(f312(x57751,f312(f47(a853,x57753),x57752)))
% 155.93/155.62 [5830]E(f312(x58301,f495(x58301,x58302,x58303)),f87(a853))+~E(f312(f312(f6(x58303,a853),x58301),x58302),f87(a853))+~P22(f312(f70(x58303),x58302))
% 155.93/155.62 [5840]~P31(x58401)+P22(f312(f312(f227(x58401),x58402),f48(x58401,x58403)))+~P22(f312(f312(f314(x58401),x58402),x58403))
% 155.93/155.62 [5870]~P102(x58701)+~P22(f312(f312(f228(x58701),x58703),x58702))+~P22(f312(f312(f228(x58701),x58702),x58703))
% 155.93/155.62 [5871]~P102(x58711)+~P22(f312(f312(f227(x58711),x58713),x58712))+~P22(f312(f312(f228(x58711),x58712),x58713))
% 155.93/155.62 [5872]~P103(x58721)+~P22(f312(f312(f228(x58721),x58723),x58722))+~P22(f312(f312(f228(x58721),x58722),x58723))
% 155.93/155.62 [5875]~P103(x58751)+~P22(f312(f312(f227(x58751),x58753),x58752))+~P22(f312(f312(f228(x58751),x58752),x58753))
% 155.93/155.62 [5876]~P105(x58761)+~P22(f312(f312(f228(x58761),x58763),x58762))+~P22(f312(f312(f228(x58761),x58762),x58763))
% 155.93/155.62 [5910]~E(f312(x59102,f395(x59102,x59103,x59101)),f87(a853))+E(f312(f312(f9(x59101,a853),x59102),x59103),f87(a853))+~P22(f312(f70(x59101),x59103))
% 155.93/155.62 [5911]~E(f312(x59112,f483(x59112,x59113,x59111)),f2(a853))+E(f312(f312(f6(x59111,a853),x59112),x59113),f2(a853))+~P22(f312(f70(x59111),x59113))
% 155.93/155.62 [5928]~P104(x59281)+~P22(f312(f312(f228(x59281),x59283),x59282))+P22(f312(f312(f314(x59281),x59282),f312(f280(x59281),x59283)))
% 155.93/155.62 [5929]~P104(x59291)+~P22(f312(f312(f227(x59291),x59293),x59292))+P22(f312(f312(f314(x59291),x59292),f312(f234(x59291),x59293)))
% 155.93/155.62 [5930]~P104(x59301)+~P22(f312(f312(f227(x59301),x59302),x59303))+P22(f312(f312(f314(x59301),x59302),f312(f281(x59301),x59303)))
% 155.93/155.62 [5931]~P104(x59311)+~P22(f312(f312(f228(x59311),x59312),x59313))+P22(f312(f312(f314(x59311),x59312),f312(f279(x59311),x59313)))
% 155.93/155.62 [5942]E(f312(x59421,f492(x59421,x59422,x59423)),f312(a126,f2(a853)))+~E(f312(f312(f6(x59423,a853),x59421),x59422),f312(a126,f2(a853)))+~P22(f312(f70(x59423),x59422))
% 155.93/155.62 [6016]~P31(x60161)+~P22(f312(f312(f314(x60161),x60163),x60162))+P22(f312(f312(f227(x60161),f49(x60161,x60162)),x60163))
% 155.93/155.62 [6033]~P22(f312(f312(f227(a853),x60331),x60333))+P22(f312(f312(f227(a853),x60331),x60332))+~P22(f312(f312(f227(a853),x60333),x60332))
% 155.93/155.62 [6034]~P22(f312(f312(f227(a1),x60341),x60343))+P22(f312(f312(f227(a1),x60341),x60342))+~P22(f312(f312(f227(a1),x60343),x60342))
% 155.93/155.62 [6051]~P104(x60511)+~P22(f312(f312(f314(x60511),x60513),f312(f280(x60511),x60512)))+P22(f312(f312(f228(x60511),x60512),x60513))
% 155.93/155.62 [6052]~P104(x60521)+~P22(f312(f312(f314(x60521),x60522),f312(f279(x60521),x60523)))+P22(f312(f312(f228(x60521),x60522),x60523))
% 155.93/155.62 [6053]~P104(x60531)+~P22(f312(f312(f314(x60531),x60533),f312(f234(x60531),x60532)))+P22(f312(f312(f227(x60531),x60532),x60533))
% 155.93/155.62 [6054]~P104(x60541)+~P22(f312(f312(f314(x60541),x60542),f312(f281(x60541),x60543)))+P22(f312(f312(f227(x60541),x60542),x60543))
% 155.93/155.62 [6174]P22(f312(x61741,x61742))+~P22(f312(x61741,f824(x61741)))+~P22(f312(f312(f314(x61743),x61742),f235(f861(x61743,a846))))
% 155.93/155.62 [6235]~P105(x62351)+~P49(a853,x62351,x62352)+P22(f312(f312(f227(x62351),f312(x62352,x62353)),f312(x62352,f312(a126,x62353))))
% 155.93/155.62 [6272]~P66(x62721)+P22(f312(f312(f228(x62721),f2(x62721)),f505(x62723,x62722,x62721)))+P22(f312(f312(f227(x62721),x62722),x62723))
% 155.93/155.62 [6338]~P76(x63381)+~P22(f312(f312(f228(x63381),x63383),f312(f88(x63381),x63382)))+P22(f312(f312(f228(x63381),x63382),f312(f88(x63381),x63383)))
% 155.93/155.62 [6340]~P76(x63401)+~P22(f312(f312(f227(x63401),x63403),f312(f88(x63401),x63402)))+P22(f312(f312(f227(x63401),x63402),f312(f88(x63401),x63403)))
% 155.93/155.62 [6351]~P22(f312(f312(f228(a853),x63511),x63513))+~P22(f312(f312(f228(a853),x63513),x63512))+P22(f312(f312(f228(a853),f312(a126,x63511)),x63512))
% 155.93/155.62 [6378]~P112(x63781)+P22(f312(f312(f228(x63781),f312(f116(x63781),x63782)),f312(f116(x63781),x63783)))+~P22(f312(f312(f228(a1),x63782),x63783))
% 155.93/155.62 [6379]~P117(x63791)+P22(f312(f312(f228(x63791),f312(f114(x63791),x63792)),f312(f114(x63791),x63793)))+~P22(f312(f312(f228(a853),x63792),x63793))
% 155.93/155.62 [6380]~P117(x63801)+P22(f312(f312(f227(x63801),f312(f114(x63801),x63802)),f312(f114(x63801),x63803)))+~P22(f312(f312(f227(a853),x63802),x63803))
% 155.93/155.62 [6381]~P112(x63811)+P22(f312(f312(f227(x63811),f312(f116(x63811),x63812)),f312(f116(x63811),x63813)))+~P22(f312(f312(f227(a1),x63812),x63813))
% 155.93/155.62 [6387]~P103(x63871)+E(f312(f312(f124(f861(x63871,a846)),f312(f279(x63871),x63872)),f312(f282(x63871,x63872),x63873)),f312(f279(x63871),x63873))+~P22(f312(f312(f227(x63871),x63872),x63873))
% 155.93/155.62 [6415]~P76(x64151)+~P22(f312(f312(f228(x64151),x64153),x64152))+P22(f312(f312(f228(x64151),f312(f88(x64151),x64152)),f312(f88(x64151),x64153)))
% 155.93/155.62 [6417]~P76(x64171)+~P22(f312(f312(f227(x64171),x64173),x64172))+P22(f312(f312(f227(x64171),f312(f88(x64171),x64172)),f312(f88(x64171),x64173)))
% 155.93/155.62 [6419]~P88(x64191)+~P22(f312(f312(f227(x64191),x64193),x64192))+P22(f312(f312(f227(x64191),f312(f88(x64191),x64192)),f312(f88(x64191),x64193)))
% 155.93/155.62 [6445]E(x64451,f2(a853))+P22(f312(x64452,f330(x64451,x64453,x64452)))+~P22(f312(x64452,f312(f47(a853,x64453),x64451)))
% 155.93/155.62 [6449]~P103(x64491)+E(f312(f312(f124(f861(x64491,a846)),f312(f281(x64491),x64492)),f285(x64491,x64492,x64493)),f312(f279(x64491),x64493))+~P22(f312(f312(f228(x64491),x64492),x64493))
% 155.93/155.62 [6450]~P103(x64501)+E(f312(f312(f124(f861(x64501,a846)),f312(f281(x64501),x64502)),f284(x64501,x64502,x64503)),f312(f281(x64501),x64503))+~P22(f312(f312(f227(x64501),x64502),x64503))
% 155.93/155.62 [6451]~P103(x64511)+E(f312(f312(f124(f861(x64511,a846)),f312(f279(x64511),x64512)),f283(x64511,x64512,x64513)),f312(f281(x64511),x64513))+~P22(f312(f312(f227(x64511),x64512),x64513))
% 155.93/155.62 [6485]~P103(x64851)+E(f312(f312(f124(f861(x64851,a846)),f312(f282(x64851,x64852),x64853)),f312(f234(x64851),x64853)),f312(f234(x64851),x64852))+~P22(f312(f312(f227(x64851),x64852),x64853))
% 155.93/155.62 [6552]~P31(x65521)+~P22(f312(f312(f227(x65521),f312(x65522,x65523)),x65523))+P22(f312(f312(f227(x65521),f109(x65521,x65522)),x65523))
% 155.93/155.62 [6571]P22(f312(x65711,f330(x65712,x65713,x65711)))+P22(f312(x65711,f2(a853)))+~P22(f312(x65711,f312(f47(a853,x65713),x65712)))
% 155.93/155.62 [6579]E(x65791,f2(a853))+~P22(f312(x65792,f331(x65791,x65793,x65792)))+P22(f312(x65792,f312(f47(a853,x65793),x65791)))
% 155.93/155.62 [6641]~P103(x66411)+E(f312(f312(f124(f861(x66411,a846)),f285(x66411,x66412,x66413)),f312(f234(x66411),x66413)),f312(f280(x66411),x66412))+~P22(f312(f312(f228(x66411),x66412),x66413))
% 155.93/155.62 [6642]~P103(x66421)+E(f312(f312(f124(f861(x66421,a846)),f284(x66421,x66422,x66423)),f312(f280(x66421),x66423)),f312(f280(x66421),x66422))+~P22(f312(f312(f227(x66421),x66422),x66423))
% 155.93/155.62 [6643]~P103(x66431)+E(f312(f312(f124(f861(x66431,a846)),f283(x66431,x66432,x66433)),f312(f280(x66431),x66433)),f312(f234(x66431),x66432))+~P22(f312(f312(f227(x66431),x66432),x66433))
% 155.93/155.62 [6651]~E(x66513,f312(f47(a853,x66511),x66512))+~P22(f312(f312(f228(a853),f2(a853)),x66512))+P22(f312(f312(f228(a853),x66511),f312(f312(f90(a853),x66512),f312(a126,x66513))))
% 155.93/155.62 [6661]P22(f312(x66611,x66612))+~P22(f312(f312(f227(a853),x66612),x66613))+P22(f312(f312(f314(a853),f454(x66611,x66613)),f283(a853,f2(a853),x66613)))
% 155.93/155.62 [6692]E(x66921,x66922)+~E(f312(f312(f161(x66923),x66921),f587(x66923,x66922,x66921)),f312(f312(f161(x66923),x66922),f587(x66923,x66922,x66921)))+~E(f312(f190(f854(x66923)),x66921),f312(f190(f854(x66923)),x66922))
% 155.93/155.62 [6711]~P22(f312(x67111,x67113))+~P22(f312(f312(f227(a853),x67113),x67112))+P22(f312(f312(f314(a853),f430(x67111,x67112)),f283(a853,f2(a853),x67112)))
% 155.93/155.62 [6712]~P22(f312(x67121,f331(x67123,x67122,x67121)))+~P22(f312(x67121,f2(a853)))+P22(f312(x67121,f312(f47(a853,x67122),x67123)))
% 155.93/155.62 [6748]~P22(f312(x67481,x67483))+P22(f312(x67481,f455(x67481,x67482)))+~P22(f312(f312(f314(a853),x67483),f283(a853,f2(a853),x67482)))
% 155.93/155.62 [6768]~P117(x67683)+~P22(f312(f312(f228(x67683),f312(f114(x67683),x67681)),f312(f114(x67683),x67682)))+P22(f312(f312(f228(a853),x67681),x67682))
% 155.93/155.62 [6769]~P112(x67693)+~P22(f312(f312(f228(x67693),f312(f116(x67693),x67691)),f312(f116(x67693),x67692)))+P22(f312(f312(f228(a1),x67691),x67692))
% 155.93/155.62 [6770]~P117(x67703)+~P22(f312(f312(f227(x67703),f312(f114(x67703),x67701)),f312(f114(x67703),x67702)))+P22(f312(f312(f227(a853),x67701),x67702))
% 155.93/155.62 [6771]~P112(x67713)+~P22(f312(f312(f227(x67713),f312(f116(x67713),x67711)),f312(f116(x67713),x67712)))+P22(f312(f312(f227(a1),x67711),x67712))
% 155.93/155.62 [6784]~P117(x67841)+~P22(f312(f312(f228(x67841),f87(x67841)),x67842))+P22(f312(f312(f228(x67841),f87(x67841)),f312(f312(f240(x67841),x67842),f312(a126,x67843))))
% 155.93/155.62 [6787]~P76(x67871)+~P22(f312(f312(f228(x67871),f312(f88(x67871),x67873)),f312(f88(x67871),x67872)))+P22(f312(f312(f228(x67871),x67872),x67873))
% 155.93/155.62 [6788]~P76(x67881)+~P22(f312(f312(f227(x67881),f312(f88(x67881),x67883)),f312(f88(x67881),x67882)))+P22(f312(f312(f227(x67881),x67882),x67883))
% 155.93/155.62 [6789]~P88(x67891)+~P22(f312(f312(f227(x67891),f312(f88(x67891),x67893)),f312(f88(x67891),x67892)))+P22(f312(f312(f227(x67891),x67892),x67893))
% 155.93/155.62 [6814]P22(f312(x68141,x68142))+~P22(f312(x68141,f456(x68141,x68143)))+~P22(f312(f312(f314(a853),x68142),f283(a853,f2(a853),x68143)))
% 155.93/155.62 [6835]~P66(x68351)+P22(f312(f312(f228(x68351),f505(x68353,x68352,x68351)),f87(x68351)))+P22(f312(f312(f227(x68351),x68352),x68353))
% 155.93/155.62 [6853]~E(f54(a853,x68533,x68532),f54(a853,x68531,x68532))+E(f312(f312(f89(a853),x68531),f312(f312(f90(a853),x68532),f719(x68531,x68532,x68533))),x68533)+~P22(f312(f312(f227(a853),x68531),x68533))
% 155.93/155.62 [6874]E(f312(x68741,f690(x68741,x68742,x68743)),f192(x68742))+~P22(f312(f70(x68743),f179(x68743,x68742,x68741)))+P22(f312(f70(x68743),f235(f861(x68743,a846))))
% 155.93/155.62 [6919]E(f312(f312(f9(x69191,a853),x69192),x69193),f87(a853))+~P22(f312(f70(x69191),x69193))+P22(f312(f312(f314(x69191),f395(x69192,x69193,x69191)),x69193))
% 155.93/155.62 [6920]E(f312(f312(f6(x69201,a853),x69202),x69203),f2(a853))+~P22(f312(f70(x69201),x69203))+P22(f312(f312(f314(x69201),f483(x69202,x69203,x69201)),x69203))
% 155.93/155.62 [6942]~P103(x69421)+~P22(f312(f312(f228(x69421),x69422),x69423))+P22(f312(f312(f228(f861(x69421,a846)),f312(f279(x69421),x69422)),f312(f279(x69421),x69423)))
% 155.93/155.62 [6943]~P105(x69431)+~P22(f312(f312(f227(x69431),x69432),x69433))+P22(f312(f312(f227(f861(x69431,a846)),f312(f281(x69431),x69432)),f312(f281(x69431),x69433)))
% 155.93/155.62 [6944]~P103(x69441)+~P22(f312(f312(f227(x69441),x69443),x69442))+P22(f312(f312(f227(f861(x69441,a846)),f312(f280(x69441),x69442)),f312(f280(x69441),x69443)))
% 155.93/155.62 [6945]~P105(x69451)+~P22(f312(f312(f227(x69451),x69453),x69452))+P22(f312(f312(f227(f861(x69451,a846)),f312(f234(x69451),x69452)),f312(f234(x69451),x69453)))
% 155.93/155.62 [6946]~P103(x69461)+~P22(f312(f312(f227(x69461),x69462),x69463))+P22(f312(f312(f227(f861(x69461,a846)),f312(f279(x69461),x69462)),f312(f279(x69461),x69463)))
% 155.93/155.62 [6953]E(x69531,f2(a853))+P22(f312(x69532,f312(f47(a853,x69533),x69531)))+P22(f312(f312(f228(a853),f338(x69531,x69533,x69532)),x69531))
% 155.93/155.62 [6954]~P31(x69541)+P22(f312(f312(f227(x69541),x69542),f49(x69541,x69543)))+P22(f312(f312(f314(x69541),f679(x69543,x69542,x69541)),x69543))
% 155.93/155.62 [6959]~P76(x69591)+P22(f312(f312(f228(x69591),f312(f312(f21(x69591),x69592),x69593)),f2(x69591)))+~P22(f312(f312(f228(x69591),x69592),x69593))
% 155.93/155.62 [6960]~P76(x69601)+P22(f312(f312(f227(x69601),f312(f312(f21(x69601),x69602),x69603)),f2(x69601)))+~P22(f312(f312(f227(x69601),x69602),x69603))
% 155.93/155.62 [7005]P22(f312(x70051,x70052))+P22(f312(f312(f227(a853),f456(x70051,x70053)),x70053))+~P22(f312(f312(f314(a853),x70052),f283(a853,f2(a853),x70053)))
% 155.93/155.62 [7041]~E(f312(f312(f6(x70411,a853),x70412),x70413),f87(a853))+~P22(f312(f70(x70411),x70413))+P22(f312(f312(f314(x70411),f495(x70412,x70413,x70411)),x70413))
% 155.93/155.62 [7042]~P22(f312(x70421,x70423))+P22(f312(f312(f227(a853),f455(x70421,x70422)),x70422))+~P22(f312(f312(f314(a853),x70423),f283(a853,f2(a853),x70422)))
% 155.93/155.62 [7085]~P31(x70851)+P22(f312(f312(f314(x70851),f677(x70853,x70852,x70851)),x70852))+P22(f312(f312(f227(x70851),f48(x70851,x70852)),x70853))
% 155.93/155.62 [7086]~P22(f312(x70861,f2(a853)))+P22(f312(x70861,f312(f47(a853,x70862),x70863)))+P22(f312(f312(f228(a853),f338(x70863,x70862,x70861)),x70863))
% 155.93/155.62 [7116]~E(f312(f312(f6(x71161,a853),x71162),x71163),f312(a126,f2(a853)))+~P22(f312(f70(x71161),x71163))+P22(f312(f312(f314(x71161),f492(x71162,x71163,x71161)),x71163))
% 155.93/155.62 [7127]E(x71271,f2(a853))+P22(f312(x71272,f54(a853,x71273,x71271)))+P22(f312(f312(f228(a853),f332(x71271,x71273,x71272)),x71271))
% 155.93/155.62 [7222]~P22(f312(x72221,x72222))+P22(f312(x72221,f54(a853,x72222,x72223)))+P22(f312(f312(f228(a853),f332(x72223,x72222,x72221)),x72223))
% 155.93/155.62 [7277]~P22(f312(f312(f228(a1),x72772),f2(a1)))+~P22(f312(f312(f227(a1),x72773),x72771))+P22(f312(f312(f227(a1),f312(f47(a1,x72771),x72772)),f312(f47(a1,x72773),x72772)))
% 155.93/155.62 [7285]~P22(f312(f312(f228(a853),f2(a853)),x72853))+~P22(f312(f312(f227(a853),x72853),x72852))+P22(f312(f312(f227(a853),f312(f47(a853,x72851),x72852)),f312(f47(a853,x72851),x72853)))
% 155.93/155.62 [7286]~P22(f312(f312(f228(a1),f2(a1)),x72862))+~P22(f312(f312(f227(a1),x72861),x72863))+P22(f312(f312(f227(a1),f312(f47(a1,x72861),x72862)),f312(f47(a1,x72863),x72862)))
% 155.93/155.62 [7343]E(x73431,f127(x73432))+~P22(f312(f312(f314(f854(x73432)),x73431),f157(x73432,x73433)))+P22(f312(f312(f314(x73432),f630(x73433,x73431,x73432)),x73433))
% 155.93/155.62 [7366]~P103(x73661)+E(f312(f312(f124(f861(x73661,a846)),f312(f312(f289(x73661),x73662),f189(f861(x73661,a846)))),f285(x73661,x73662,x73663)),f312(f282(x73661,x73662),x73663))+~P22(f312(f312(f228(x73661),x73662),x73663))
% 155.93/155.62 [7390]~P103(x73901)+E(f312(f312(f124(f861(x73901,a846)),f312(f312(f289(x73901),x73902),f189(f861(x73901,a846)))),f284(x73901,x73902,x73903)),f283(x73901,x73902,x73903))+~P22(f312(f312(f227(x73901),x73902),x73903))
% 155.93/155.62 [7496]~P103(x74961)+P22(f312(f312(f228(x74961),x74962),x74963))+~P22(f312(f312(f228(f861(x74961,a846)),f312(f279(x74961),x74962)),f312(f279(x74961),x74963)))
% 155.93/155.62 [7497]~P103(x74971)+P22(f312(f312(f227(x74971),x74972),x74973))+~P22(f312(f312(f227(f861(x74971,a846)),f312(f280(x74971),x74973)),f312(f280(x74971),x74972)))
% 155.93/155.62 [7498]~P105(x74981)+P22(f312(f312(f227(x74981),x74982),x74983))+~P22(f312(f312(f227(f861(x74981,a846)),f312(f234(x74981),x74983)),f312(f234(x74981),x74982)))
% 155.93/155.62 [7499]~P103(x74991)+P22(f312(f312(f227(x74991),x74992),x74993))+~P22(f312(f312(f227(f861(x74991,a846)),f312(f279(x74991),x74992)),f312(f279(x74991),x74993)))
% 155.93/155.62 [7500]~P105(x75001)+P22(f312(f312(f227(x75001),x75002),x75003))+~P22(f312(f312(f227(f861(x75001,a846)),f312(f281(x75001),x75002)),f312(f281(x75001),x75003)))
% 155.93/155.62 [7519]E(x75191,f2(a853))+E(f312(f312(f89(a853),f312(f312(f90(a853),x75191),f331(x75191,x75192,x75193))),f338(x75191,x75192,x75193)),x75192)+P22(f312(x75193,f312(f47(a853,x75192),x75191)))
% 155.93/155.62 [7523]~P76(x75231)+~P22(f312(f312(f228(x75231),f312(f312(f21(x75231),x75232),x75233)),f2(x75231)))+P22(f312(f312(f228(x75231),x75232),x75233))
% 155.93/155.62 [7524]~P76(x75241)+~P22(f312(f312(f227(x75241),f312(f312(f21(x75241),x75242),x75243)),f2(x75241)))+P22(f312(f312(f227(x75241),x75242),x75243))
% 155.93/155.62 [7617]E(f312(f312(f89(a853),f312(f312(f90(a853),x76171),f331(x76171,x76172,x76173))),f338(x76171,x76172,x76173)),x76172)+~P22(f312(x76173,f2(a853)))+P22(f312(x76173,f312(f47(a853,x76172),x76171)))
% 155.93/155.62 [7681]E(x76811,f2(a853))+~E(f312(f138(a853,a853,f89(a853),x76812),x76813),f2(a853))+~P22(f312(f312(f314(a853),x76811),f312(f168(a853),x76813)))
% 155.93/155.62 [7685]~P31(x76851)+~P22(f312(f312(f227(x76851),f677(x76853,x76852,x76851)),x76853))+P22(f312(f312(f227(x76851),f48(x76851,x76852)),x76853))
% 155.93/155.62 [7711]P22(f312(f312(f227(a1),f2(a1)),f336(x77111,x77112,x77113)))+P22(f312(f312(x77112,f312(f47(a1,x77111),x77113)),f54(a1,x77111,x77113)))+~P22(f312(f312(f228(a1),f2(a1)),x77113))
% 155.93/155.62 [7924]E(x79241,x79242)+~E(f312(f190(f854(x79243)),x79241),f312(f190(f854(x79243)),x79242))+~P22(f312(f312(f249(x79243,x79243,a846),a309),f588(x79243,x79241,x79242)))
% 155.93/155.62 [7991]~P41(x79912,x79913)+E(x79911,f189(f861(x79912,a846)))+~P22(f312(f312(f227(f861(x79912,a846)),x79911),f312(f264(x79912,x79912,x79913),x79911)))
% 155.93/155.62 [8011]P22(f312(f312(x80112,f312(f47(a1,x80111),x80113)),f54(a1,x80111,x80113)))+~P22(f312(f312(f228(a1),f2(a1)),x80113))+P22(f312(f312(f228(a1),f336(x80111,x80112,x80113)),x80113))
% 155.93/155.62 [8066]P50(x80661,x80662,x80663)+P22(f312(f312(f314(x80661),f419(x80663,x80662,x80661)),x80662))+P22(f312(f312(f314(f860(x80661,x80661)),f420(x80663,x80662,x80661)),x80663))
% 155.93/155.62 [8112]E(f312(f290(a853,a853,f312(f312(f7(a853,a853,a853),f21(a853)),x81121)),f312(f282(a853,x81122),x81123)),f189(f861(a853,a846)))+P22(f312(f312(f228(a853),x81121),x81123))+P22(f312(f312(f228(a853),x81122),x81123))
% 155.93/155.62 [8219]E(f312(f290(a853,a853,f312(f312(f7(a853,a853,a853),f21(a853)),x82191)),f312(f282(a853,x82192),x82193)),f312(f312(f289(a853),f2(a853)),f189(f861(a853,a846))))+P22(f312(f312(f228(a853),x82191),x82193))+~P22(f312(f312(f228(a853),x82192),x82193))
% 155.93/155.62 [8238]~P103(x82381)+E(f146(x82381,x82381,f5(x82381),x82382,x82383),x82383)+~P22(f312(f312(f314(x82381),x82382),f312(f168(x82381),x82383)))
% 155.93/155.62 [8239]E(f312(f312(f89(a1),f312(f312(f90(a1),x82391),f337(x82392,x82393,x82391))),f336(x82392,x82393,x82391)),x82392)+P22(f312(f312(x82393,f312(f47(a1,x82392),x82391)),f54(a1,x82392,x82391)))+~P22(f312(f312(f228(a1),f2(a1)),x82391))
% 155.93/155.62 [8255]P19(x82551,x82551,x82552,x82553)+~P22(f312(f70(x82551),x82553))+~P22(f312(f312(f227(f861(x82551,a846)),x82553),f312(f290(x82551,x82551,x82552),x82553)))
% 155.93/155.62 [8484]~P22(f312(f312(x84841,f337(x84842,x84841,x84843)),f336(x84842,x84841,x84843)))+P22(f312(f312(x84841,f312(f47(a1,x84842),x84843)),f54(a1,x84842,x84843)))+~P22(f312(f312(f228(a1),f2(a1)),x84843))
% 155.93/155.62 [9378]~P22(f312(f70(x93781),x93782))+~P22(f312(f312(f314(x93781),x93783),x93782))+P22(f312(f312(f228(a853),f312(f53(x93781),f312(f312(f21(f861(x93781,a846)),x93782),f312(f312(f289(x93781),x93783),f189(f861(x93781,a846)))))),f312(f53(x93781),x93782)))
% 155.93/155.62 [9978]P50(x99781,x99782,x99783)+~P22(f312(f312(f249(x99781,x99781,a846),f312(f312(f7(x99781,f861(x99781,a846),f861(x99781,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x99781,a846),f861(x99781,a846)),x99781),f8(a846,a846,x99781)),f312(f312(f8(a846,f861(a846,a846),x99781),a310),f312(f312(f7(x99781,f861(x99781,a846),a846),f314(x99781)),x99782)))),f312(f312(f7(x99781,f861(x99781,a846),a846),f314(x99781)),x99782))),f420(x99783,x99782,x99781)))+P22(f312(f312(f314(x99781),f419(x99783,x99782,x99781)),x99782))
% 155.93/155.62 [5405]~P114(x54052)+E(x54051,f2(x54052))+E(f312(f312(f268(x54052),x54053),f312(f88(x54052),x54051)),f312(f88(x54052),f312(f312(f268(x54052),x54053),x54051)))
% 155.93/155.62 [5541]~E(x55413,f189(f861(x55411,a846)))+~E(x55412,f189(f861(x55411,a846)))+E(f312(f312(f124(f861(x55411,a846)),x55412),x55413),f189(f861(x55411,a846)))
% 155.93/155.62 [5732]~P67(x57322)+E(x57321,f2(x57322))+E(f312(f312(f268(x57322),f312(f84(x57322),x57323)),f312(f84(x57322),x57321)),f312(f84(x57322),f312(f312(f268(x57322),x57323),x57321)))
% 155.93/155.62 [5896]~P22(f312(f70(x58961),x58963))+E(f312(f53(x58961),f312(f312(f289(x58961),x58962),x58963)),f312(a126,f312(f53(x58961),x58963)))+P22(f312(f312(f314(x58961),x58962),x58963))
% 155.93/155.62 [5988]~P22(f312(f70(x59881),x59883))+E(f312(f53(x59881),f312(f312(f289(x59881),x59882),x59883)),f312(f53(x59881),x59883))+~P22(f312(f312(f314(x59881),x59882),x59883))
% 155.93/155.62 [6019]~P22(f312(f70(x60191),x60193))+E(f312(f53(x60191),f312(f312(f289(x60191),x60192),x60193)),f312(f312(f89(a853),f87(a853)),f312(f53(x60191),x60193)))+P22(f312(f312(f314(x60191),x60192),x60193))
% 155.93/155.62 [6136]E(f312(f312(f89(a853),x61361),f823(x61361,x61362,x61363)),x61362)+~P22(f312(x61363,f2(a853)))+P22(f312(x61363,f312(f312(f21(a853),x61362),x61361)))
% 155.93/155.62 [6137]E(f312(f312(f89(a853),x61371),f827(x61371,x61372,x61373)),x61372)+~P22(f312(x61373,f2(a853)))+P22(f312(x61373,f312(f312(f21(a853),x61372),x61371)))
% 155.93/155.62 [6184]~P31(x61841)+~P22(f312(f70(x61841),x61843))+E(f312(f312(f73(x61841,x61841,f124(x61841)),x61842),x61843),f312(f312(f124(x61841),x61842),f48(x61841,x61843)))
% 155.93/155.62 [6185]~P31(x61851)+~P22(f312(f70(x61851),x61853))+E(f312(f312(f73(x61851,x61851,f115(x61851)),x61852),x61853),f312(f312(f115(x61851),x61852),f49(x61851,x61853)))
% 155.93/155.62 [6192]~P90(x61921)+~E(f312(f117(x61921),x61922),f312(f117(x61921),x61923))+P35(x61921,f312(f117(x61921),f312(f312(f89(a1),x61922),f312(f88(a1),x61923))))
% 155.93/155.62 [6199]~P111(x61991)+E(f312(f312(f21(x61991),f312(f114(x61991),x61992)),f312(f114(x61991),x61993)),f312(f114(x61991),f312(f312(f21(a853),x61992),x61993)))+~P22(f312(f312(f227(a853),x61993),x61992))
% 155.93/155.62 [6282]E(f312(f312(f89(a853),x62821),f823(x62821,x62822,x62823)),x62822)+P22(f312(f312(f228(a853),x62822),x62821))+P22(f312(x62823,f312(f312(f21(a853),x62822),x62821)))
% 155.93/155.62 [6283]E(f312(f312(f89(a853),x62831),f827(x62831,x62832,x62833)),x62832)+P22(f312(f312(f228(a853),x62832),x62831))+P22(f312(x62833,f312(f312(f21(a853),x62832),x62831)))
% 155.93/155.62 [6299]~P112(x62991)+E(f312(f312(f90(x62991),f312(f84(x62991),x62992)),x62993),f312(f84(x62991),f312(f312(f90(x62991),x62992),x62993)))+~P22(f312(f312(f227(x62991),f2(x62991)),x62993))
% 155.93/155.62 [6300]~P66(x63001)+E(f312(f312(f268(x63001),f312(f84(x63001),x63002)),x63003),f312(f84(x63001),f312(f312(f268(x63001),x63002),x63003)))+~P22(f312(f312(f228(x63001),f2(x63001)),x63003))
% 155.93/155.62 [6353]E(x63531,f127(x63532))+~E(f175(x63532,x63533),f127(f854(x63532)))+~P22(f312(f312(f314(f854(x63532)),x63531),f312(f168(f854(x63532)),x63533)))
% 155.93/155.62 [6395]~P22(f312(f133(x63951),x63953))+P22(f312(f312(f314(x63951),x63952),f312(f168(x63951),x63953)))+P22(f312(f133(x63951),f312(f312(f147(x63951),x63952),x63953)))
% 155.93/155.62 [6429]P22(f312(x64291,f2(a853)))+~P22(f312(f312(f228(a853),x64292),x64293))+~P22(f312(x64291,f312(f312(f21(a853),x64292),x64293)))
% 155.93/155.62 [6446]~P112(x64461)+P22(f312(f312(f228(x64461),x64462),x64463))+~P22(f312(f312(f228(x64461),f312(f84(x64461),x64462)),x64463))
% 155.93/155.62 [6448]~P83(x64481)+P22(f312(f312(f227(x64481),x64482),x64483))+~P22(f312(f312(f227(x64481),f312(f84(x64481),x64482)),x64483))
% 155.93/155.62 [6465]E(x64651,f127(x64652))+E(f312(f137(x64652),f312(f312(f134(x64652),x64653),x64651)),f312(f312(f161(x64652),x64651),x64653))+~P22(f312(f312(f228(a853),x64653),f312(f190(f854(x64652)),x64651)))
% 155.93/155.62 [6516]~P22(f312(x65161,x65163))+P22(f312(x65161,f484(x65161,x65162)))+~P22(f312(f312(f314(a853),x65163),f312(f282(a853,f2(a853)),x65162)))
% 155.93/155.62 [6537]P22(f312(x65371,x65372))+~P22(f312(f312(f228(a853),x65372),x65373))+P22(f312(f312(f314(a853),f463(x65371,x65373)),f312(f282(a853,f2(a853)),x65373)))
% 155.93/155.62 [6554]~P117(x65541)+~P22(f312(f312(f228(x65541),f2(x65541)),x65542))+P22(f312(f312(f228(x65541),f2(x65541)),f312(f312(f240(x65541),x65542),x65543)))
% 155.93/155.62 [6556]~P117(x65561)+~P22(f312(f312(f227(x65561),f2(x65561)),x65562))+P22(f312(f312(f227(x65561),f2(x65561)),f312(f312(f240(x65561),x65562),x65563)))
% 155.93/155.62 [6557]~P117(x65571)+~P22(f312(f312(f227(x65571),f87(x65571)),x65572))+P22(f312(f312(f227(x65571),f87(x65571)),f312(f312(f240(x65571),x65572),x65573)))
% 155.93/155.62 [6582]~P22(f312(x65821,x65823))+~P22(f312(f312(f228(a853),x65823),x65822))+P22(f312(f312(f314(a853),f462(x65821,x65822)),f312(f282(a853,f2(a853)),x65822)))
% 155.93/155.62 [6590]P22(f312(f70(x65901),x65902))+~P22(f312(f70(x65901),x65903))+~P22(f312(f312(f227(f861(x65901,a846)),x65902),x65903))
% 155.93/155.62 [6600]P22(f312(x66001,x66002))+~P22(f312(x66001,f464(x66001,x66003)))+~P22(f312(f312(f314(a853),x66002),f312(f282(a853,f2(a853)),x66003)))
% 155.93/155.62 [6614]~P118(x66142)+E(x66141,f2(x66142))+~E(f312(f312(f89(x66142),f312(f312(f90(x66142),x66143),x66143)),f312(f312(f90(x66142),x66141),x66141)),f2(x66142))
% 155.93/155.62 [6615]~P118(x66152)+E(x66151,f2(x66152))+~E(f312(f312(f89(x66152),f312(f312(f90(x66152),x66151),x66151)),f312(f312(f90(x66152),x66153),x66153)),f2(x66152))
% 155.93/155.62 [6666]~P103(x66661)+~P33(x66661,x66663)+P33(x66661,f312(f312(f145(x66661,x66661,f5(x66661)),x66662),x66663))
% 155.93/155.62 [6710]~P90(x67101)+E(f312(f117(x67101),x67102),f312(f117(x67101),x67103))+~P35(x67101,f312(f117(x67101),f312(f312(f89(a1),x67102),f312(f88(a1),x67103))))
% 155.93/155.62 [6773]E(x67731,f2(a1))+E(x67732,f2(a1))+~P22(f312(f57(x67732,x67732),f312(f312(f239(a1,a1),x67733),x67731)))
% 155.93/155.62 [6774]E(x67741,f87(a1))+E(x67742,f2(a1))+~P22(f312(f57(x67742,x67742),f312(f312(f239(a1,a1),x67741),x67743)))
% 155.93/155.62 [6785]P22(f312(x67851,x67852))+P22(f312(f312(f228(a853),f464(x67851,x67853)),x67853))+~P22(f312(f312(f314(a853),x67852),f312(f282(a853,f2(a853)),x67853)))
% 155.93/155.62 [6809]~P22(f312(x68091,f823(x68093,x68092,x68091)))+~P22(f312(x68091,f2(a853)))+P22(f312(x68091,f312(f312(f21(a853),x68092),x68093)))
% 155.93/155.62 [6810]~P22(f312(x68101,f827(x68103,x68102,x68101)))+~P22(f312(x68101,f2(a853)))+P22(f312(x68101,f312(f312(f21(a853),x68102),x68103)))
% 155.93/155.62 [6831]~P22(f312(x68311,x68313))+P22(f312(f312(f228(a853),f484(x68311,x68312)),x68312))+~P22(f312(f312(f314(a853),x68313),f312(f282(a853,f2(a853)),x68312)))
% 155.93/155.62 [6832]E(f312(f312(f21(a853),f312(f312(f21(a853),x68321),x68322)),f312(f312(f21(a853),x68323),x68322)),f312(f312(f21(a853),x68321),x68323))+~P22(f312(f312(f227(a853),x68322),x68321))+~P22(f312(f312(f227(a853),x68322),x68323))
% 155.93/155.62 [6868]~P76(x68681)+~P22(f312(f312(f228(x68681),f312(f88(x68681),x68683)),x68682))+P22(f312(f312(f228(x68681),f312(f88(x68681),x68682)),x68683))
% 155.93/155.62 [6869]~P112(x68691)+~P22(f312(f312(f228(x68691),f312(f84(x68691),x68692)),x68693))+P22(f312(f312(f228(x68691),f312(f88(x68691),x68692)),x68693))
% 155.93/155.62 [6871]~P76(x68711)+~P22(f312(f312(f227(x68711),f312(f88(x68711),x68713)),x68712))+P22(f312(f312(f227(x68711),f312(f88(x68711),x68712)),x68713))
% 155.93/155.62 [6873]~P83(x68731)+~P22(f312(f312(f227(x68731),f312(f84(x68731),x68732)),x68733))+P22(f312(f312(f227(x68731),f312(f88(x68731),x68732)),x68733))
% 155.93/155.62 [6913]~P22(f312(x69133,f823(x69132,x69131,x69133)))+P22(f312(f312(f228(a853),x69131),x69132))+P22(f312(x69133,f312(f312(f21(a853),x69131),x69132)))
% 155.93/155.62 [6914]~P22(f312(x69143,f827(x69142,x69141,x69143)))+P22(f312(f312(f228(a853),x69141),x69142))+P22(f312(x69143,f312(f312(f21(a853),x69141),x69142)))
% 155.93/155.62 [6962]~E(f680(x69623,x69622,x69621),f681(x69623,x69622,x69621))+E(f312(f312(f115(f861(x69621,a846)),x69622),f48(f861(x69621,a846),x69623)),f189(f861(x69621,a846)))+P22(f312(f312(f314(f861(x69621,a846)),x69622),x69623))
% 155.93/155.62 [6972]~P22(f312(f70(x69721),x69723))+P22(f312(f70(x69721),f49(f861(x69721,a846),x69722)))+~P22(f312(f312(f314(f861(x69721,a846)),x69723),x69722))
% 155.93/155.62 [7032]~P103(x70321)+E(f312(f312(f124(f861(x70321,a846)),f312(f282(x70321,x70322),x70323)),f312(f312(f289(x70321),x70323),f189(f861(x70321,a846)))),f283(x70321,x70322,x70323))+~P22(f312(f312(f227(x70321),x70322),x70323))
% 155.93/155.62 [7069]E(x70691,x70692)+~P22(f312(f312(f227(f861(x70693,a846)),x70691),x70692))+P22(f312(f312(f228(f861(x70693,a846)),x70691),x70692))
% 155.93/155.62 [7082]E(x70821,x70822)+~E(f312(f190(f854(x70823)),x70821),f312(f190(f854(x70823)),x70822))+P22(f312(f312(f228(a853),f587(x70823,x70821,x70822)),f312(f190(f854(x70823)),x70822)))
% 155.93/155.62 [7128]P3(x71281,x71282,x71283)+~E(f312(f238(x71281,x71281),x71283),x71282)+~E(f312(f312(f267(x71281,x71281,x71281),f312(f265(x71281,x71281),x71283)),x71283),x71283)
% 155.93/155.62 [7197]~P103(x71971)+E(f312(f312(f124(f861(x71971,a846)),f285(x71971,x71972,x71973)),f312(f312(f289(x71971),x71973),f189(f861(x71971,a846)))),f284(x71971,x71972,x71973))+~P22(f312(f312(f228(x71971),x71972),x71973))
% 155.93/155.62 [7300]~P22(f312(f70(x73001),x73003))+P22(f312(f312(f228(a853),f312(f53(x73001),x73002)),f312(f53(x73001),x73003)))+~P22(f312(f312(f228(f861(x73001,a846)),x73002),x73003))
% 155.93/155.62 [7301]~P22(f312(f70(x73011),x73013))+P22(f312(f312(f227(a853),f312(f53(x73011),x73012)),f312(f53(x73011),x73013)))+~P22(f312(f312(f227(f861(x73011,a846)),x73012),x73013))
% 155.93/155.62 [7337]~P22(f312(x73373,x73372))+P22(f312(f312(f195(x73371),x73372),f814(x73372,x73371,x73373)))+~P22(f312(f312(f195(f35(x73373,x73371)),x73372),x73372))
% 155.93/155.62 [7433]E(x74331,x74332)+~P22(f312(f312(f227(f861(x74333,a846)),x74332),x74331))+~P22(f312(f312(f227(f861(x74333,a846)),x74331),x74332))
% 155.93/155.62 [7436]~P103(x74361)+P33(x74361,x74362)+~P33(x74361,f312(f312(f145(x74361,x74361,f5(x74361)),x74363),x74362))
% 155.93/155.62 [7504]~P22(f312(f312(f228(a853),x75043),x75042))+~P22(f312(f312(f228(a853),x75043),x75041))+P22(f312(f312(f228(a853),f312(f312(f21(a853),x75041),x75042)),f312(f312(f21(a853),x75041),x75043)))
% 155.93/155.62 [7505]~P22(f312(f312(f228(a853),x75051),x75053))+~P22(f312(f312(f227(a853),x75052),x75051))+P22(f312(f312(f228(a853),f312(f312(f21(a853),x75051),x75052)),f312(f312(f21(a853),x75053),x75052)))
% 155.93/155.62 [7542]~P22(f312(f312(f228(a853),f2(a853)),x75422))+~P22(f312(f312(f228(a853),x75421),x75423))+P22(f312(f312(f228(a853),f312(f312(f90(a853),x75421),x75422)),f312(f312(f90(a853),x75423),x75422)))
% 155.93/155.62 [7543]~P22(f312(f312(f228(a853),f2(a853)),x75431))+~P22(f312(f312(f228(a853),x75432),x75433))+P22(f312(f312(f228(a853),f312(f312(f90(a853),x75431),x75432)),f312(f312(f90(a853),x75431),x75433)))
% 155.93/155.62 [7544]~P22(f312(f312(f228(a1),f2(a1)),x75441))+~P22(f312(f312(f228(a1),x75442),x75443))+P22(f312(f312(f228(a1),f312(f312(f90(a1),x75441),x75442)),f312(f312(f90(a1),x75441),x75443)))
% 155.93/155.62 [7672]~P22(f312(f70(x76721),x76723))+P22(f312(f312(f314(x76721),f398(x76722,x76723,x76721)),x76723))+P22(f312(f312(f228(a853),f2(a853)),f312(f312(f9(x76721,a853),x76722),x76723)))
% 155.93/155.62 [7673]~P22(f312(f70(x76731),x76733))+P22(f312(f312(f314(x76731),f542(x76732,x76733,x76731)),x76733))+P22(f312(f312(f228(a853),f2(a853)),f312(f312(f9(x76731,a853),x76732),x76733)))
% 155.93/155.62 [7957]E(x79571,f189(f861(x79572,a846)))+E(x79571,f312(f312(f289(x79572),x79573),f189(f861(x79572,a846))))+~P22(f312(f312(f227(f861(x79572,a846)),x79571),f312(f312(f289(x79572),x79573),f189(f861(x79572,a846)))))
% 155.93/155.62 [7975]~P63(x79751)+P8(x79751,x79752,x79753)+P22(f312(f312(f314(f854(x79751)),f668(x79753,x79752,x79751)),f312(f168(f854(x79751)),f63(x79751,x79753,f64(x79751)))))
% 155.93/155.62 [7993]~P22(f312(f312(f228(a853),f2(a853)),x79933))+P22(f312(f312(f228(a853),x79931),x79932))+~P22(f312(f312(f228(a853),f312(f312(f240(a853),x79933),x79931)),f312(f312(f240(a853),x79933),x79932)))
% 155.93/155.62 [7995]~P22(f312(f312(f228(a853),f2(a853)),x79953))+P22(f312(f312(f227(a853),x79951),x79952))+~P22(f312(f312(f227(a853),f312(f312(f90(a853),x79953),x79951)),f312(f312(f90(a853),x79953),x79952)))
% 155.93/155.62 [7996]~P22(f312(f312(f228(a853),f2(a853)),x79963))+P22(f312(f312(f227(a853),x79961),x79962))+~P22(f312(f312(f227(a853),f312(f312(f90(a853),x79961),x79963)),f312(f312(f90(a853),x79962),x79963)))
% 155.93/155.62 [8026]~P63(x80261)+~P7(x80261,x80263,x80262)+P22(f312(f312(f314(f854(x80261)),f667(x80262,x80263,x80261)),f312(f168(f854(x80261)),f63(x80261,x80262,f64(x80261)))))
% 155.93/155.62 [8034]~P22(f312(x80341,x80343))+P22(f312(f312(f195(f35(x80341,x80342)),f814(x80343,x80342,x80341)),x80343))+~P22(f312(f312(f195(f35(x80341,x80342)),x80343),x80343))
% 155.93/155.62 [8043]~E(f312(f312(f115(f861(x80431,a846)),f681(x80433,x80432,x80431)),f680(x80433,x80432,x80431)),f189(f861(x80431,a846)))+E(f312(f312(f115(f861(x80431,a846)),x80432),f48(f861(x80431,a846),x80433)),f189(f861(x80431,a846)))+P22(f312(f312(f314(f861(x80431,a846)),x80432),x80433))
% 155.93/155.62 [8061]E(x80611,f127(x80612))+~E(f312(f138(f854(x80612),f854(x80612),f129(x80612),f127(x80612)),x80613),f127(x80612))+~P22(f312(f312(f314(f854(x80612)),x80611),f312(f168(f854(x80612)),x80613)))
% 155.93/155.62 [8117]E(x81171,f189(f861(f861(x81172,a846),a846)))+P22(f312(f312(f314(f861(x81172,a846)),f698(x81173,x81171,x81172)),x81171))+P22(f312(f312(f227(f861(x81172,a846)),f49(f861(x81172,a846),x81171)),x81173))
% 155.93/155.62 [8124]~P26(x81241)+~P72(x81241)+E(f312(f312(f9(a1,x81241),f312(f312(f8(a853,x81241,a1),x81242),a118)),f312(f290(a853,a1,f114(a1)),x81243)),f312(f312(f9(a853,x81241),x81242),x81243))
% 155.93/155.62 [8125]~P26(x81251)+~P72(x81251)+E(f312(f312(f6(a1,x81251),f312(f312(f8(a853,x81251,a1),x81252),a118)),f312(f290(a853,a1,f114(a1)),x81253)),f312(f312(f6(a853,x81251),x81252),x81253))
% 155.93/155.62 [8165]~P22(f312(f70(x81651),x81653))+~P22(f312(f312(f228(a853),f2(a853)),f312(x81652,f398(x81652,x81653,x81651))))+P22(f312(f312(f228(a853),f2(a853)),f312(f312(f9(x81651,a853),x81652),x81653)))
% 155.93/155.62 [8166]~P22(f312(f70(x81661),x81663))+~P22(f312(f312(f228(a853),f2(a853)),f312(x81662,f542(x81662,x81663,x81661))))+P22(f312(f312(f228(a853),f2(a853)),f312(f312(f9(x81661,a853),x81662),x81663)))
% 155.93/155.62 [8202]~P65(x82022)+E(x82021,f87(x82022))+E(f312(f312(f268(x82022),f312(f312(f21(x82022),f312(f312(f240(x82022),x82021),x82023)),f87(x82022))),f312(f312(f21(x82022),x82021),f87(x82022))),f312(f312(f6(a853,x82022),f312(f240(x82022),x82021)),f312(f282(a853,f2(a853)),x82023)))
% 155.93/155.62 [8231]E(x82311,f2(a853))+~P22(f312(x82313,f312(f47(a853,x82312),x82311)))+P22(f312(f312(f228(a853),x82312),f312(f312(f90(a853),x82311),f312(a126,f330(x82311,x82312,x82313)))))
% 155.93/155.62 [8258]P22(f312(x82581,f2(a853)))+~P22(f312(x82581,f312(f47(a853,x82582),x82583)))+P22(f312(f312(f228(a853),x82582),f312(f312(f90(a853),x82583),f312(a126,f330(x82583,x82582,x82581)))))
% 155.93/155.62 [8277]E(x82771,f2(a853))+~P22(f312(x82773,f312(f47(a853,x82772),x82771)))+P22(f312(f312(f227(a853),f312(f312(f90(a853),x82771),f330(x82771,x82772,x82773))),x82772))
% 155.93/155.62 [8297]P22(f312(x82971,f2(a853)))+~P22(f312(x82971,f312(f47(a853,x82973),x82972)))+P22(f312(f312(f227(a853),f312(f312(f90(a853),x82972),f330(x82972,x82973,x82971))),x82973))
% 155.93/155.62 [8367]~P103(x83671)+E(f312(f312(f145(x83671,x83671,f5(x83671)),x83672),x83673),f146(x83671,x83671,f5(x83671),x83672,x83673))+P22(f312(f312(f314(x83671),x83672),f312(f168(x83671),x83673)))
% 155.93/155.62 [8408]~E(f312(x84083,f704(x84082,x84083,x84081)),f312(x84083,f711(x84082,x84083,x84081)))+~P59(x84081,f312(x84083,f705(x84082,x84083,x84081)))+P59(x84081,f312(f312(f50(x84082,f861(x84081,f861(x84081,a846))),f235(f861(x84082,a846))),x84083))
% 155.93/155.62 [8415]E(x84151,f189(f861(f861(x84152,a846),a846)))+~P22(f312(f312(f227(f861(x84152,a846)),f698(x84153,x84151,x84152)),x84153))+P22(f312(f312(f227(f861(x84152,a846)),f49(f861(x84152,a846),x84151)),x84153))
% 155.93/155.62 [8477]~P67(x84771)+~P22(f312(f312(f228(x84771),x84772),x84773))+P22(f312(f312(f228(x84771),x84772),f312(f312(f268(x84771),f312(f312(f89(x84771),x84772),x84773)),f312(f312(f89(x84771),f87(x84771)),f87(x84771)))))
% 155.93/155.62 [8529]~P22(f312(f312(x85291,f347(x85291,x85293,x85292)),f348(x85291,x85293,x85292)))+P22(f312(f312(x85291,x85292),x85293))+~P22(f312(f300(f860(a1,a1),a60),f312(f312(f239(a1,a1),x85292),x85293)))
% 155.93/155.62 [8530]~P22(f312(f312(x85301,f349(x85301,x85303,x85302)),f354(x85301,x85303,x85302)))+P22(f312(f312(x85301,x85302),x85303))+~P22(f312(f300(f860(a1,a1),a65),f312(f312(f239(a1,a1),x85302),x85303)))
% 155.93/155.62 [8531]~P22(f312(f312(x85311,f355(x85311,x85313,x85312)),f356(x85311,x85313,x85312)))+P22(f312(f312(x85311,x85312),x85313))+~P22(f312(f300(f860(a1,a1),a212),f312(f312(f239(a1,a1),x85312),x85313)))
% 155.93/155.62 [8532]~P22(f312(f312(x85321,f357(x85321,x85323,x85322)),f358(x85321,x85323,x85322)))+P22(f312(f312(x85321,x85322),x85323))+~P22(f312(f300(f860(a853,a853),a211),f312(f312(f239(a853,a853),x85322),x85323)))
% 155.93/155.62 [8533]~P22(f312(f312(x85331,f617(x85331,x85333,x85332)),f619(x85331,x85333,x85332)))+P22(f312(f312(x85331,x85332),x85333))+~P22(f312(f300(f860(a1,a1),a178),f312(f312(f239(a1,a1),x85332),x85333)))
% 155.93/155.62 [8782]P22(f312(f312(x87821,x87822),x87823))+P22(f312(f300(f860(a853,a853),a211),f312(f312(f239(a853,a853),f357(x87821,x87823,x87822)),f358(x87821,x87823,x87822))))+~P22(f312(f300(f860(a853,a853),a211),f312(f312(f239(a853,a853),x87822),x87823)))
% 155.93/155.62 [8783]P22(f312(f312(x87831,x87832),x87833))+P22(f312(f300(f860(a1,a1),a60),f312(f312(f239(a1,a1),f347(x87831,x87833,x87832)),f348(x87831,x87833,x87832))))+~P22(f312(f300(f860(a1,a1),a60),f312(f312(f239(a1,a1),x87832),x87833)))
% 155.93/155.62 [8784]P22(f312(f312(x87841,x87842),x87843))+P22(f312(f300(f860(a1,a1),a65),f312(f312(f239(a1,a1),f349(x87841,x87843,x87842)),f354(x87841,x87843,x87842))))+~P22(f312(f300(f860(a1,a1),a65),f312(f312(f239(a1,a1),x87842),x87843)))
% 155.93/155.62 [8785]P22(f312(f312(x87851,x87852),x87853))+P22(f312(f300(f860(a1,a1),a212),f312(f312(f239(a1,a1),f355(x87851,x87853,x87852)),f356(x87851,x87853,x87852))))+~P22(f312(f300(f860(a1,a1),a212),f312(f312(f239(a1,a1),x87852),x87853)))
% 155.93/155.62 [8786]P22(f312(f312(x87861,x87862),x87863))+P22(f312(f300(f860(a1,a1),a178),f312(f312(f239(a1,a1),f617(x87861,x87863,x87862)),f619(x87861,x87863,x87862))))+~P22(f312(f300(f860(a1,a1),a178),f312(f312(f239(a1,a1),x87862),x87863)))
% 155.93/155.62 [9128]~P22(f312(f70(x91281),x91283))+P22(f312(f312(f314(f860(f861(x91281,a846),f861(x91281,a846))),f312(f312(f239(f861(x91281,a846),f861(x91281,a846)),x91282),x91283)),f286(x91281)))+~P22(f312(f312(f228(f861(x91281,a846)),x91282),x91283))
% 155.93/155.62 [9201]~P59(x92011,f312(x92013,f705(x92012,x92013,x92011)))+P59(x92011,f312(f312(f50(x92012,f861(x92011,f861(x92011,a846))),f235(f861(x92012,a846))),x92013))+~E(f312(f312(f115(f861(x92011,a846)),f244(x92011,x92011,f312(x92013,f704(x92012,x92013,x92011)))),f245(x92011,x92011,f312(x92013,f711(x92012,x92013,x92011)))),f189(f861(x92011,a846)))
% 155.93/155.62 [9397]P50(x93971,x93972,x93973)+P22(f312(f312(f314(f860(x93971,x93971)),f420(x93973,x93972,x93971)),x93973))+~P22(f312(f312(f314(f860(x93971,x93971)),f312(f312(f239(x93971,x93971),f419(x93973,x93972,x93971)),f419(x93973,x93972,x93971))),x93973))
% 155.93/155.62 [9979]P50(x99791,x99792,x99793)+~P22(f312(f312(f249(x99791,x99791,a846),f312(f312(f7(x99791,f861(x99791,a846),f861(x99791,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x99791,a846),f861(x99791,a846)),x99791),f8(a846,a846,x99791)),f312(f312(f8(a846,f861(a846,a846),x99791),a310),f312(f312(f7(x99791,f861(x99791,a846),a846),f314(x99791)),x99792)))),f312(f312(f7(x99791,f861(x99791,a846),a846),f314(x99791)),x99792))),f420(x99793,x99792,x99791)))+~P22(f312(f312(f314(f860(x99791,x99791)),f312(f312(f239(x99791,x99791),f419(x99793,x99792,x99791)),f419(x99793,x99792,x99791))),x99793))
% 155.93/155.62 [5532]~P60(x55322)+E(x55321,f2(x55322))+E(f312(f47(x55322,f312(f312(f90(x55322),x55323),x55321)),x55321),x55323)
% 155.93/155.62 [5533]~P60(x55332)+E(x55331,f2(x55332))+E(f312(f47(x55332,f312(f312(f90(x55332),x55331),x55333)),x55331),x55333)
% 155.93/155.62 [6312]~P60(x63122)+E(x63121,f2(x63122))+E(f312(f47(x63122,f312(f312(f89(x63122),x63123),x63121)),x63121),f312(f312(f89(x63122),f312(f47(x63122,x63123),x63121)),f87(x63122)))
% 155.93/155.62 [6313]~P60(x63132)+E(x63131,f2(x63132))+E(f312(f47(x63132,f312(f312(f89(x63132),x63131),x63133)),x63131),f312(f312(f89(x63132),f312(f47(x63132,x63133),x63131)),f87(x63132)))
% 155.93/155.62 [6352]~P26(x63521)+~E(f312(x63522,f2(a853)),f2(x63521))+E(f312(f312(f6(a853,x63521),x63522),f312(f282(a853,f312(a126,f2(a853))),x63523)),f312(f312(f6(a853,x63521),x63522),f312(f282(a853,f2(a853)),x63523)))
% 155.93/155.62 [6696]~P22(f312(x66963,f2(a1)))+P22(f312(f312(f227(a853),x66961),x66962))+P22(f312(x66963,f312(f114(a1),f312(f312(f21(a853),x66962),x66961))))
% 155.93/155.62 [6791]P22(f312(f312(f227(a853),x67912),x67911))+P22(f312(f312(f228(a853),x67911),x67912))+P22(f312(x67913,f312(f114(a1),f312(f312(f21(a853),x67911),x67912))))
% 155.93/155.62 [6866]E(f312(f312(f89(a853),f312(f117(a853),x68661)),f312(f312(f89(a853),f312(f117(a853),x68662)),x68663)),f312(f312(f89(a853),f312(f117(a853),x68661)),x68663))+P22(f312(a194,f312(f117(a1),x68661)))+~P22(f312(a194,f312(f117(a1),x68662)))
% 155.93/155.62 [6899]~E(x68992,f312(f47(a853,x68993),x68991))+~P22(f312(f312(f228(a853),f2(a853)),x68991))+P22(f312(f312(f227(a853),f312(f312(f90(a853),x68991),x68992)),x68993))
% 155.93/155.62 [7067]~P22(f312(f70(x70671),x70673))+~P22(f312(f70(x70671),x70672))+P22(f312(f70(x70671),f312(f312(f124(f861(x70671,a846)),x70672),x70673)))
% 155.93/155.62 [7349]~P103(x73491)+~P22(f312(f70(x73491),x73492))+E(f135(x73491,f312(f312(f21(f861(x73491,a846)),x73492),f312(f312(f289(x73491),x73493),f189(f861(x73491,a846))))),f166(x73491,x73493,f135(x73491,x73492)))
% 155.93/155.62 [7413]P22(f312(x74131,f2(a1)))+~P22(f312(f312(f228(a853),x74132),x74133))+~P22(f312(x74131,f312(f114(a1),f312(f312(f21(a853),x74132),x74133))))
% 155.93/155.62 [7430]~P22(f312(f70(x74301),x74302))+E(f312(f53(x74301),f312(f312(f21(f861(x74301,a846)),x74302),f312(f312(f289(x74301),x74303),f189(f861(x74301,a846))))),f312(f53(x74301),x74302))+P22(f312(f312(f314(x74301),x74303),x74302))
% 155.93/155.62 [7560]~P117(x75601)+~P22(f312(f312(f228(x75601),f87(x75601)),x75602))+P22(f312(f312(f228(x75601),f87(x75601)),f312(f312(f90(x75601),x75602),f312(f312(f240(x75601),x75602),x75603))))
% 155.93/155.62 [7605]~P22(f312(f70(x76051),x76053))+E(f312(f312(f21(a853),f312(f53(x76051),x76052)),f312(f53(x76051),x76053)),f312(f53(x76051),f312(f312(f21(f861(x76051,a846)),x76052),x76053)))+~P22(f312(f312(f227(f861(x76051,a846)),x76053),x76052))
% 155.93/155.62 [7663]~P22(f312(f312(f227(a853),x76632),x76633))+~P22(f312(f312(f227(a853),x76631),f312(f312(f21(a853),x76633),x76632)))+P22(f312(f312(f227(a853),f312(f312(f89(a853),x76631),x76632)),x76633))
% 155.93/155.62 [7717]P22(f312(f70(x77171),x77172))+~P22(f312(f70(x77171),x77173))+~P22(f312(f70(x77171),f312(f312(f21(f861(x77171,a846)),x77172),x77173)))
% 155.93/155.62 [7723]~P22(f312(f70(x77231),x77232))+E(f312(f53(x77231),f312(f312(f21(f861(x77231,a846)),x77232),f312(f312(f289(x77231),x77233),f189(f861(x77231,a846))))),f312(f312(f21(a853),f312(f53(x77231),x77232)),f87(a853)))+~P22(f312(f312(f314(x77231),x77233),x77232))
% 155.93/155.62 [7797]P59(x77971,x77972)+~P59(x77971,x77973)+~P22(f312(f312(f227(f861(x77971,f861(x77971,a846))),x77972),x77973))
% 155.93/155.62 [7833]~P22(f312(f312(f227(a853),x78333),x78332))+P22(f312(f312(f227(a853),x78331),f312(f312(f21(a853),x78332),x78333)))+~P22(f312(f312(f227(a853),f312(f312(f89(a853),x78331),x78333)),x78332))
% 155.93/155.62 [7850]P41(x78501,x78502)+~P41(x78501,x78503)+~P22(f312(f312(f227(f861(f860(x78501,x78501),a846)),x78502),x78503))
% 155.93/155.62 [7851]P57(x78511,x78512)+~P57(x78511,x78513)+~P22(f312(f312(f227(f861(f860(x78511,x78511),a846)),x78512),x78513))
% 155.93/155.62 [8094]~P117(x80941)+~P22(f312(f312(f228(x80941),f87(x80941)),x80942))+P22(f312(f312(f228(x80941),f312(f312(f240(x80941),x80942),x80943)),f312(f312(f90(x80941),x80942),f312(f312(f240(x80941),x80942),x80943))))
% 155.93/155.62 [8185]~P22(f312(x81851,f2(a1)))+~P22(f312(x81851,f312(f312(f21(a1),f312(f114(a1),x81852)),f312(f114(a1),x81853))))+P22(f312(x81851,f312(f114(a1),f312(f312(f21(a853),x81852),x81853))))
% 155.93/155.62 [8198]~P22(f312(f312(f227(a853),x81983),x81982))+P22(f312(x81981,f312(f312(f21(a1),f312(f114(a1),x81982)),f312(f114(a1),x81983))))+~P22(f312(x81981,f312(f114(a1),f312(f312(f21(a853),x81982),x81983))))
% 155.93/155.62 [8216]P22(f312(f312(f228(a853),x82161),x82162))+~P22(f312(x82163,f312(f312(f21(a1),f312(f114(a1),x82161)),f312(f114(a1),x82162))))+P22(f312(x82163,f312(f114(a1),f312(f312(f21(a853),x82161),x82162))))
% 155.93/155.62 [8272]~P118(x82722)+E(x82721,f2(x82722))+P22(f312(f312(f228(x82722),f2(x82722)),f312(f312(f89(x82722),f312(f312(f90(x82722),x82723),x82723)),f312(f312(f90(x82722),x82721),x82721))))
% 155.93/155.62 [8273]~P118(x82732)+E(x82731,f2(x82732))+P22(f312(f312(f228(x82732),f2(x82732)),f312(f312(f89(x82732),f312(f312(f90(x82732),x82731),x82731)),f312(f312(f90(x82732),x82733),x82733))))
% 155.93/155.62 [8388]~P22(f312(f312(f228(a853),f2(a853)),x83881))+~P22(f312(f312(f228(a1),x83882),x83883))+P22(f312(f312(f228(a1),f312(f312(f90(a1),f312(f114(a1),x83881)),x83882)),f312(f312(f90(a1),f312(f114(a1),x83881)),x83883)))
% 155.93/155.62 [8444]E(f312(f312(f115(f861(x84441,a846)),x84442),f48(f861(x84441,a846),x84443)),f189(f861(x84441,a846)))+P22(f312(f312(f314(f861(x84441,a846)),x84442),x84443))+P22(f312(f312(f314(f861(x84441,a846)),f681(x84443,x84442,x84441)),f312(f312(f289(f861(x84441,a846)),x84442),x84443)))
% 155.93/155.62 [8445]E(f312(f312(f115(f861(x84451,a846)),x84452),f48(f861(x84451,a846),x84453)),f189(f861(x84451,a846)))+P22(f312(f312(f314(f861(x84451,a846)),x84452),x84453))+P22(f312(f312(f314(f861(x84451,a846)),f680(x84453,x84452,x84451)),f312(f312(f289(f861(x84451,a846)),x84452),x84453)))
% 155.93/155.62 [8476]E(x84761,x84762)+~E(f312(f190(f854(x84763)),x84761),f312(f190(f854(x84763)),x84762))+P22(f312(f312(f314(f860(x84763,x84763)),f588(x84763,x84761,x84762)),f312(f168(f860(x84763,x84763)),f312(f312(f177(x84763,x84763),x84762),x84761))))
% 155.93/155.62 [8701]E(f287(x87011,x87012),f287(x87011,x87013))+~P22(f312(f312(f227(f861(f860(x87011,x87011),a846)),x87013),f287(x87011,x87012)))+~P22(f312(f312(f227(f861(f860(x87011,x87011),a846)),x87012),x87013))
% 155.93/155.62 [8760]~P50(x87601,f235(f861(x87601,a846)),x87603)+P22(f312(f312(f227(f861(f860(f854(x87601),f854(x87601)),a846)),f153(x87601,x87602)),f154(x87601,x87603)))+~P22(f312(f312(f227(f861(f860(x87601,x87601),a846)),x87602),x87603))
% 155.93/155.62 [8999]~P22(f312(f70(x89991),x89992))+P22(f312(f70(f861(x89991,a846)),f312(f312(f69(x89991),x89992),x89993)))+~P22(f312(f312(f227(f861(f860(x89991,x89991),a846)),x89993),f312(f312(f247(x89991,x89991),x89992),f312(f16(f861(x89991,a846),x89991),x89992))))
% 155.93/155.62 [9035]P50(x90351,x90352,x90353)+P22(f312(f312(f314(x90351),f515(x90353,x90352,x90351)),x90352))+~P22(f312(f312(f227(f861(f860(x90351,x90351),a846)),x90353),f312(f312(f247(x90351,x90351),x90352),f312(f16(f861(x90351,a846),x90351),x90352))))
% 155.93/155.62 [9036]P50(x90361,x90362,x90363)+P22(f312(f312(f314(x90361),f526(x90362,x90363,x90361)),x90362))+~P22(f312(f312(f227(f861(f860(x90361,x90361),a846)),x90363),f312(f312(f247(x90361,x90361),x90362),f312(f16(f861(x90361,a846),x90361),x90362))))
% 155.93/155.62 [9068]~P67(x90681)+~P22(f312(f312(f228(x90681),x90682),x90683))+P22(f312(f312(f228(x90681),f312(f312(f268(x90681),f312(f312(f89(x90681),x90682),x90683)),f312(f312(f89(x90681),f87(x90681)),f87(x90681)))),x90683))
% 155.93/155.62 [9097]~P66(x90971)+P22(f312(f312(f227(x90971),x90972),x90973))+~P22(f312(f312(f227(x90971),f312(f312(f90(x90971),f505(x90973,x90972,x90971)),x90972)),x90973))
% 155.93/155.62 [9235]E(f312(f190(f854(f854(x92351))),f312(f132(f854(x92351),f312(f312(f8(a853,a846,f854(x92351)),f312(f228(a853),x92352)),f190(f854(x92351)))),f175(x92351,x92353))),f312(f190(f854(x92351)),f312(f312(f161(f854(x92351)),x92353),x92352)))+~P33(a853,f312(f165(a853),f312(f312(f150(f854(x92351),a853),f190(f854(x92351))),x92353)))+~P22(f312(f312(f228(a853),x92352),f312(f190(f854(f854(x92351))),x92353)))
% 155.93/155.62 [9342]~P41(x93421,x93422)+P20(x93421,f312(f312(f239(f861(f860(x93421,x93421),a846),f861(f860(x93421,x93421),a846)),x93422),x93423))+~P22(f312(f312(f227(f861(f860(x93421,x93421),a846)),f312(f312(f267(x93421,x93421,x93421),x93422),x93423)),x93422))
% 155.93/155.62 [9349]E(f312(f312(f150(f854(x93491),x93491),f312(f312(f7(f854(x93491),a853,x93491),f161(x93491)),x93492)),f312(f132(f854(x93491),f312(f312(f8(a853,a846,f854(x93491)),f312(f228(a853),x93492)),f190(f854(x93491)))),f175(x93491,x93493))),f312(f312(f161(f854(x93491)),x93493),x93492))+~P33(a853,f312(f165(a853),f312(f312(f150(f854(x93491),a853),f190(f854(x93491))),x93493)))+~P22(f312(f312(f228(a853),x93492),f312(f190(f854(f854(x93491))),x93493)))
% 155.93/155.62 [9481]P50(x94811,x94812,x94813)+~P22(f312(f312(f314(f860(x94811,x94811)),f312(f312(f239(x94811,x94811),f515(x94813,x94812,x94811)),f515(x94813,x94812,x94811))),x94813))+~P22(f312(f312(f227(f861(f860(x94811,x94811),a846)),x94813),f312(f312(f247(x94811,x94811),x94812),f312(f16(f861(x94811,a846),x94811),x94812))))
% 155.93/155.62 [9482]P50(x94821,x94822,x94823)+~P22(f312(f312(f314(f860(x94821,x94821)),f312(f312(f239(x94821,x94821),f526(x94822,x94823,x94821)),f526(x94822,x94823,x94821))),x94823))+~P22(f312(f312(f227(f861(f860(x94821,x94821),a846)),x94823),f312(f312(f247(x94821,x94821),x94822),f312(f16(f861(x94821,a846),x94821),x94822))))
% 155.93/155.62 [9855]~E(x98553,f2(a853))+~E(f312(f190(f854(x98551)),f312(f312(f161(f854(x98551)),x98552),f660(x98553,x98551,x98552))),x98553)+E(f312(f312(f150(a853,f854(x98551)),f312(f312(f7(a853,f854(a853),f854(x98551)),f312(f312(f8(f861(a853,x98551),f861(f854(a853),f854(x98551)),a853),f150(a853,x98551)),f312(f7(a853,a853,x98551),f312(f312(f8(f854(x98551),f861(a853,x98551),a853),f161(x98551)),f312(f161(f854(x98551)),x98552))))),f135(a853,f312(f282(a853,f2(a853)),f312(f190(f854(f854(x98551))),x98552))))),f135(a853,f312(f282(a853,f2(a853)),x98553))),f175(x98551,x98552))
% 155.93/155.62 [9856]E(x98561,f127(f854(x98562)))+~E(f312(f190(f854(x98562)),f312(f312(f161(f854(x98562)),x98561),f660(x98563,x98562,x98561))),x98563)+E(f312(f312(f150(a853,f854(x98562)),f312(f312(f7(a853,f854(a853),f854(x98562)),f312(f312(f8(f861(a853,x98562),f861(f854(a853),f854(x98562)),a853),f150(a853,x98562)),f312(f7(a853,a853,x98562),f312(f312(f8(f854(x98562),f861(a853,x98562),a853),f161(x98562)),f312(f161(f854(x98562)),x98561))))),f135(a853,f312(f282(a853,f2(a853)),f312(f190(f854(f854(x98562))),x98561))))),f135(a853,f312(f282(a853,f2(a853)),x98563))),f175(x98562,x98561))
% 155.93/155.62 [9857]~E(x98573,f2(a853))+E(f312(f312(f150(a853,f854(x98571)),f312(f312(f7(a853,f854(a853),f854(x98571)),f312(f312(f8(f861(a853,x98571),f861(f854(a853),f854(x98571)),a853),f150(a853,x98571)),f312(f7(a853,a853,x98571),f312(f312(f8(f854(x98571),f861(a853,x98571),a853),f161(x98571)),f312(f161(f854(x98571)),x98572))))),f135(a853,f312(f282(a853,f2(a853)),f312(f190(f854(f854(x98571))),x98572))))),f135(a853,f312(f282(a853,f2(a853)),x98573))),f175(x98571,x98572))+P22(f312(f312(f228(a853),f660(x98573,x98571,x98572)),f312(f190(f854(f854(x98571))),x98572)))
% 155.93/155.62 [9858]E(x98581,f127(f854(x98582)))+E(f312(f312(f150(a853,f854(x98582)),f312(f312(f7(a853,f854(a853),f854(x98582)),f312(f312(f8(f861(a853,x98582),f861(f854(a853),f854(x98582)),a853),f150(a853,x98582)),f312(f7(a853,a853,x98582),f312(f312(f8(f854(x98582),f861(a853,x98582),a853),f161(x98582)),f312(f161(f854(x98582)),x98581))))),f135(a853,f312(f282(a853,f2(a853)),f312(f190(f854(f854(x98582))),x98581))))),f135(a853,f312(f282(a853,f2(a853)),x98583))),f175(x98582,x98581))+P22(f312(f312(f228(a853),f660(x98583,x98582,x98581)),f312(f190(f854(f854(x98582))),x98581)))
% 155.93/155.62 [7602]E(f312(f312(f89(a853),f312(f117(a853),x76021)),f312(f312(f89(a853),f312(f117(a853),x76022)),x76023)),f312(f312(f89(a853),f312(f117(a853),f312(f312(f89(a1),x76021),x76022))),x76023))+P22(f312(a194,f312(f117(a1),x76021)))+P22(f312(a194,f312(f117(a1),x76022)))
% 155.93/155.62 [8379]~P22(f312(f70(x83791),x83792))+~P22(f312(f312(f314(x83791),x83793),x83792))+E(f312(a126,f312(f53(x83791),f312(f312(f21(f861(x83791,a846)),x83792),f312(f312(f289(x83791),x83793),f189(f861(x83791,a846)))))),f312(f53(x83791),x83792))
% 155.93/155.62 [8398]~P22(f312(f70(x83981),x83982))+~P22(f312(f312(f314(x83981),x83983),x83982))+E(f312(f312(f89(a853),f87(a853)),f312(f53(x83981),f312(f312(f21(f861(x83981,a846)),x83982),f312(f312(f289(x83981),x83983),f189(f861(x83981,a846)))))),f312(f53(x83981),x83982))
% 155.93/155.62 [8487]~P103(x84871)+~P22(f312(f70(x84871),x84873))+E(f312(f312(f145(x84871,x84871,f5(x84871)),x84872),f135(x84871,f312(f312(f21(f861(x84871,a846)),x84873),f312(f312(f289(x84871),x84872),f189(f861(x84871,a846)))))),f135(x84871,f312(f312(f289(x84871),x84872),x84873)))
% 155.93/155.62 [8631]~P22(f312(f70(x86311),x86313))+~P22(f312(f70(x86311),x86312))+E(f312(f312(f89(a853),f312(f53(x86311),f312(f312(f124(f861(x86311,a846)),x86312),x86313))),f312(f53(x86311),f312(f312(f115(f861(x86311,a846)),x86312),x86313))),f312(f312(f89(a853),f312(f53(x86311),x86312)),f312(f53(x86311),x86313)))
% 155.93/155.62 [9803]~P19(x98031,f861(f861(x98031,a846),a846),f312(f312(f7(x98031,f861(f860(x98031,x98031),a846),f861(f861(x98031,a846),a846)),f312(f312(f8(f861(x98031,a846),f861(f861(f860(x98031,x98031),a846),f861(f861(x98031,a846),a846)),x98031),f69(x98031)),f312(f312(f7(x98031,f861(x98031,a846),f861(x98031,a846)),f289(x98031)),f189(f861(x98031,a846))))),x98033),x98032)+~P22(f312(f70(x98031),x98032))+E(f312(f53(f861(x98031,a846)),f312(f312(f69(x98031),x98032),x98033)),f312(f53(x98031),x98032))
% 155.93/155.62 [10075]~P49(f861(x100751,a846),f861(x100751,a846),x100752)+~P22(f312(f312(f227(f861(x100751,a846)),x100753),f312(x100752,f109(f861(x100751,a846),f312(f312(f7(f861(x100751,a846),f861(x100751,a846),f861(x100751,a846)),f312(f312(f8(f861(x100751,a846),f861(f861(x100751,a846),f861(x100751,a846)),f861(x100751,a846)),f124(f861(x100751,a846))),f312(f312(f7(f861(x100751,a846),f861(x100751,a846),f861(x100751,a846)),f312(f312(f8(f861(x100751,a846),f861(f861(x100751,a846),f861(x100751,a846)),f861(x100751,a846)),f124(f861(x100751,a846))),x100752)),x100753))),f110(f861(x100751,a846),x100752))))))+P22(f312(f312(f227(f861(x100751,a846)),f109(f861(x100751,a846),f312(f312(f7(f861(x100751,a846),f861(x100751,a846),f861(x100751,a846)),f312(f312(f8(f861(x100751,a846),f861(f861(x100751,a846),f861(x100751,a846)),f861(x100751,a846)),f124(f861(x100751,a846))),f312(f312(f7(f861(x100751,a846),f861(x100751,a846),f861(x100751,a846)),f312(f312(f8(f861(x100751,a846),f861(f861(x100751,a846),f861(x100751,a846)),f861(x100751,a846)),f124(f861(x100751,a846))),x100752)),x100753))),f110(f861(x100751,a846),x100752)))),f312(x100752,f109(f861(x100751,a846),f312(f312(f7(f861(x100751,a846),f861(x100751,a846),f861(x100751,a846)),f312(f312(f8(f861(x100751,a846),f861(f861(x100751,a846),f861(x100751,a846)),f861(x100751,a846)),f124(f861(x100751,a846))),f312(f312(f7(f861(x100751,a846),f861(x100751,a846),f861(x100751,a846)),f312(f312(f8(f861(x100751,a846),f861(f861(x100751,a846),f861(x100751,a846)),f861(x100751,a846)),f124(f861(x100751,a846))),x100752)),x100753))),f110(f861(x100751,a846),x100752))))))
% 155.93/155.62 [7866]~P90(x78661)+P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x78663)))+E(f312(f312(f240(x78661),x78662),f312(f117(a853),f312(f312(f21(a1),f312(f312(f89(a1),x78663),x78663)),a111))),f87(x78661))
% 155.93/155.62 [9325]~P90(x93251)+~P22(f312(f312(f227(a1),f2(a1)),f312(f117(a1),x93253)))+E(f312(f312(f240(x93251),x93252),f312(f117(a853),f312(f312(f21(a1),f312(f312(f89(a1),x93253),x93253)),a111))),f312(f312(f95(x93251,x93251),f312(f312(f240(x93251),x93252),f312(f117(a853),x93253))),f312(f312(f18(x93251,x93251,x93251),f312(f312(f8(x93251,f861(x93251,x93251),x93251),f90(x93251)),f312(f90(x93251),x93252))),f5(x93251))))
% 155.93/155.62 [9707]~P22(f312(f133(x97071),x97073))+~P22(f312(f312(f314(x97071),x97072),f312(f168(x97071),x97073)))+E(f312(f312(f134(x97071),f312(f190(f854(x97071)),f172(x97071,f312(f312(f8(a846,a846,x97071),a307),f312(f312(f7(x97071,x97071,a846),a309),x97072)),f312(f165(x97071),x97073)))),f312(f165(x97071),x97073)),f312(f312(f147(x97071),x97072),f312(f165(x97071),f172(x97071,f312(f312(f8(a846,a846,x97071),a307),f312(f312(f7(x97071,x97071,a846),a309),x97072)),x97073))))
% 155.93/155.62 [9779]P22(f312(f312(f227(f861(f860(x97791,x97791),a846)),f287(x97791,x97792)),x97793))+~P22(f312(f312(f227(f861(f860(x97791,x97791),a846)),f287(x97791,f189(f861(f860(x97791,x97791),a846)))),x97793))+~P22(f312(f312(f227(f861(f860(x97791,x97791),a846)),f312(f312(f267(x97791,x97791,x97791),f312(f312(f115(f861(f860(x97791,x97791),a846)),f287(x97791,x97792)),x97793)),x97792)),x97793))
% 155.93/155.62 [9623]~P22(f312(f70(x96231),f312(f233(x96231),x96233)))+~P22(f312(f70(x96231),f312(f233(x96231),x96232)))+P22(f312(f70(x96231),f312(f233(x96231),f312(f312(f18(x96231,a846,a846),f312(f312(f8(a846,f861(a846,a846),x96231),a311),x96232)),x96233))))
% 155.93/155.62 [9922]P22(f312(f312(f227(f861(f860(x99221,x99221),a846)),f312(f312(f267(x99221,x99221,x99221),x99222),f287(x99221,x99222))),x99223))+~P22(f312(f312(f227(f861(f860(x99221,x99221),a846)),x99222),x99223))+~P22(f312(f312(f227(f861(f860(x99221,x99221),a846)),f312(f312(f267(x99221,x99221,x99221),f312(f312(f115(f861(f860(x99221,x99221),a846)),f312(f312(f267(x99221,x99221,x99221),x99222),f287(x99221,x99222))),x99223)),x99222)),x99223))
% 155.93/155.62 [9873]~P112(x98732)+E(x98731,f2(x98732))+~E(f312(f312(f89(x98732),f312(f312(f240(x98732),x98733),f312(f117(a853),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(x98732),x98731),f312(f117(a853),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(x98732))
% 155.93/155.62 [9874]~P112(x98742)+E(x98741,f2(x98742))+~E(f312(f312(f89(x98742),f312(f312(f240(x98742),x98741),f312(f117(a853),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(x98742),x98743),f312(f117(a853),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(x98742))
% 155.93/155.62 [9880]~P22(f312(f133(x98801),x98803))+~P22(f312(f312(f314(x98801),x98802),f312(f168(x98801),x98803)))+E(f312(f165(x98801),f312(f167(x98801),f312(f312(f134(x98801),f312(f190(f854(x98801)),f172(x98801,f312(f312(f8(a846,a846,x98801),a307),f312(f312(f7(x98801,x98801,a846),a309),x98802)),x98803))),x98803))),f172(x98801,f312(f312(f8(a846,a846,x98801),a307),f312(f312(f7(x98801,x98801,a846),a309),x98802)),f312(f165(x98801),x98803)))
% 155.93/155.62 [9968]~P112(x99682)+E(x99681,f2(x99682))+P22(f312(f312(f228(x99682),f2(x99682)),f312(f312(f89(x99682),f312(f312(f240(x99682),x99683),f312(f117(a853),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(x99682),x99681),f312(f117(a853),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)))))))
% 155.93/155.62 [9969]~P112(x99692)+E(x99691,f2(x99692))+P22(f312(f312(f228(x99692),f2(x99692)),f312(f312(f89(x99692),f312(f312(f240(x99692),x99691),f312(f117(a853),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(x99692),x99693),f312(f117(a853),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)))))))
% 155.93/155.62 [10012]~P112(x100121)+P22(f312(f312(f227(x100121),f2(x100121)),x100122))+~P22(f312(f312(f227(x100121),f2(x100121)),f312(f312(f240(x100121),x100122),f312(a126,f312(f312(f90(a853),f312(f117(a853),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)))),x100123)))))
% 155.93/155.62 [5418]~P18(x54181,x54184,x54183)+P18(x54181,x54182,x54183)+~P18(x54181,x54182,x54184)
% 155.93/155.62 [7151]~P36(x71513,x71514,x71511,x71512)+E(x71511,x71512)+~P36(x71513,x71514,x71512,x71511)
% 155.93/155.62 [4893]~E(x48932,f99(x48933,x48931))+P22(f312(x48931,x48932))+~P22(f312(x48931,x48934))
% 155.93/155.62 [6607]~P41(x66072,x66074)+~P41(x66071,x66073)+P41(f860(x66071,x66072),f304(x66071,x66072,x66073,x66074))
% 155.93/155.62 [5070]~P2(x50704,x50701)+~E(f312(x50701,x50702),f312(x50701,x50703))+P22(f312(f312(x50701,x50702),x50703))
% 155.93/155.62 [5238]~P2(x52384,x52381)+E(f312(x52381,x52382),f312(x52381,x52383))+~P22(f312(f312(x52381,x52382),x52383))
% 155.93/155.62 [5324]~P13(x53243,x53244,x53241)+E(f312(x53241,x53242),f312(f72(x53243,x53244),x53242))+~P22(f312(f70(x53243),x53242))
% 155.93/155.62 [5325]~P5(x53253,x53254,x53251)+E(f312(x53251,x53252),f312(f72(x53253,x53254),x53252))+~P22(f312(f70(x53253),x53252))
% 155.93/155.62 [5450]~P2(x54504,x54501)+~P22(f312(f312(x54501,x54503),x54502))+P22(f312(f312(x54501,x54502),x54503))
% 155.93/155.62 [5520]E(x55201,x55202)+~E(f312(f246(x55203,x55204),x55201),f312(f246(x55203,x55204),x55202))+~E(f312(f248(x55203,x55204),x55201),f312(f248(x55203,x55204),x55202))
% 155.93/155.62 [5549]E(x55491,x55492)+~P22(f312(f56(x55493,x55494),x55492))+~P22(f312(f56(x55493,x55494),x55491))
% 155.93/155.62 [5731]~P26(x57312)+E(f217(x57311,x57312,x57313,x57314),f2(x57312))+P22(f312(f70(x57311),x57314))
% 155.93/155.62 [5862]~P22(f312(f300(x58621,x58622),x58624))+P22(f312(f300(x58621,x58622),x58623))+~P22(f312(f312(x58622,x58623),x58624))
% 155.93/155.62 [7792]~P103(x77922)+~P22(f312(f133(x77921),x77924))+P22(f312(f133(x77921),f144(x77921,x77922,x77923,x77924)))
% 155.93/155.62 [8013]~P22(f312(f70(x80132),x80134))+~P22(f312(f70(x80131),x80133))+P22(f312(f70(f859(x80131,x80132)),f298(x80131,x80132,x80133,x80134)))
% 155.93/155.62 [8014]~P22(f312(f133(x80142),x80144))+~P22(f312(f133(x80141),x80143))+P22(f312(f133(f860(x80141,x80142)),f68(x80141,x80142,x80143,x80144)))
% 155.93/155.62 [8018]P22(f312(f312(f314(f854(x80181)),f312(f312(f129(x80181),x80182),x80183)),f157(x80181,x80184)))+~P22(f312(f312(f314(f854(x80181)),x80183),f157(x80181,x80184)))+~P22(f312(f312(f314(f854(x80181)),x80182),f157(x80181,x80184)))
% 155.93/155.62 [8345]P22(f312(x83451,x83452))+~E(x83453,f312(f219(x83454),x83452))+~P22(f312(x83451,f763(x83452,x83451,x83453,x83454)))
% 155.93/155.62 [8356]~P103(x83563)+~P22(f312(f133(x83561),f144(x83561,x83563,x83564,x83562)))+P22(f312(f133(x83561),x83562))
% 155.93/155.62 [8622]~P22(f312(f312(f314(f860(x86221,x86221)),f312(f312(f239(x86221,x86221),x86222),x86224)),f287(x86221,x86223)))+P22(f312(f312(f314(x86221),x86222),f301(x86221,x86223)))+~P22(f312(f312(f314(x86221),x86224),f301(x86221,x86223)))
% 155.93/155.62 [8643]~E(x86434,f312(f219(x86433),x86432))+P22(f312(x86431,x86432))+P22(f312(f312(f314(x86433),f763(x86432,x86431,x86434,x86433)),f218(x86433,x86434)))
% 155.93/155.62 [5052]~P72(x50522)+E(f312(f312(f9(x50521,x50522),x50523),x50524),f87(x50522))+P22(f312(f70(x50521),x50524))
% 155.93/155.62 [5055]~P26(x50552)+E(f312(f312(f6(x50551,x50552),x50553),x50554),f2(x50552))+P22(f312(f70(x50551),x50554))
% 155.93/155.62 [5204]~P27(x52043)+E(x52041,x52042)+~E(f312(f312(f89(x52043),x52044),x52041),f312(f312(f89(x52043),x52044),x52042))
% 155.93/155.62 [5205]~P28(x52053)+E(x52051,x52052)+~E(f312(f312(f89(x52053),x52054),x52051),f312(f312(f89(x52053),x52054),x52052))
% 155.93/155.62 [5207]~P27(x52073)+E(x52071,x52072)+~E(f312(f312(f89(x52073),x52071),x52074),f312(f312(f89(x52073),x52072),x52074))
% 155.93/155.62 [5320]~P31(x53203)+E(x53201,f189(f861(x53202,a846)))+E(f312(f312(f50(x53202,x53203),x53201),f312(f16(x53203,x53202),x53204)),x53204)
% 155.93/155.62 [5321]~P31(x53213)+E(x53211,f189(f861(x53212,a846)))+E(f312(f312(f51(x53212,x53213),x53211),f312(f16(x53213,x53212),x53214)),x53214)
% 155.93/155.62 [5536]~P105(x55363)+E(x55361,x55362)+~E(f283(x55363,x55364,x55361),f312(f312(f289(x55363),x55362),f189(f861(x55363,a846))))
% 155.93/155.62 [5537]~P105(x55373)+E(x55371,x55372)+~E(f283(x55373,x55371,x55372),f312(f312(f289(x55373),x55374),f189(f861(x55373,a846))))
% 155.93/155.62 [5820]P22(f312(x58201,x58202))+~P22(f312(f243(x58203,x58201),x58204))+~P22(f312(f312(f314(x58203),x58202),x58204))
% 155.93/155.62 [5838]P38(x58381,x58382,x58383)+~P38(x58381,x58382,f312(f312(f147(x58381),x58384),x58383))+P22(f312(x58382,x58384))
% 155.93/155.62 [5851]E(x58511,x58512)+~P22(f312(f312(f195(x58513),x58514),x58512))+~P22(f312(f312(f195(x58513),x58514),x58511))
% 155.93/155.62 [5924]P38(x59241,x59242,x59243)+P38(x59241,x59242,x59244)+~P38(x59241,x59242,f312(f312(f129(x59241),x59244),x59243))
% 155.93/155.62 [5943]~P26(x59431)+E(f312(f312(f6(a853,x59431),x59432),f312(f282(a853,x59433),f312(a126,x59434))),f2(x59431))+~P22(f312(f312(f228(a853),x59434),x59433))
% 155.93/155.62 [5947]~P61(x59471)+~E(f54(x59471,x59472,x59473),f54(x59471,x59474,x59473))+E(f54(x59471,f312(f88(x59471),x59472),x59473),f54(x59471,f312(f88(x59471),x59474),x59473))
% 155.93/155.62 [6009]P22(f312(x60091,x60092))+~E(f312(f132(x60093,x60091),x60094),x60094)+~P22(f312(f312(f314(x60093),x60092),f312(f168(x60093),x60094)))
% 155.93/155.62 [6026]~E(f312(f312(f89(a853),x60263),x60262),f312(f312(f89(a853),x60261),x60264))+~P22(f312(f312(f228(a853),x60263),x60264))+P22(f312(f312(f228(a853),x60261),x60262))
% 155.93/155.62 [6030]P38(x60301,x60302,x60303)+~P22(f312(x60302,x60304))+~P22(f312(f312(f314(x60301),x60304),f312(f168(x60301),x60303)))
% 155.93/155.62 [6065]~E(f312(f132(x60651,x60652),x60653),f127(x60651))+~P22(f312(x60652,x60654))+~P22(f312(f312(f314(x60651),x60654),f312(f168(x60651),x60653)))
% 155.93/155.62 [6066]~E(f172(x60663,x60661,x60664),x60664)+P22(f312(x60661,x60662))+~P22(f312(f312(f314(x60663),x60662),f312(f168(x60663),x60664)))
% 155.93/155.62 [6099]~E(x60994,f189(f861(x60992,a846)))+~E(x60993,f189(f861(x60991,a846)))+E(f298(x60991,x60992,x60993,x60994),f189(f861(f859(x60991,x60992),a846)))
% 155.93/155.62 [6243]P22(f312(x62431,x62432))+~P22(f312(f156(x62433,x62431),x62434))+~P22(f312(f312(f314(x62433),x62432),f312(f168(x62433),x62434)))
% 155.93/155.62 [6506]~P26(x65061)+E(f312(f312(f6(a853,x65061),x65062),f283(a853,x65063,f312(a126,x65064))),f2(x65061))+~P22(f312(f312(f228(a853),f312(a126,x65064)),x65063))
% 155.93/155.62 [6648]~P103(x66481)+E(f312(f312(f21(f861(x66481,a846)),f312(f282(x66481,x66482),x66483)),f312(f282(x66481,x66482),x66484)),f312(f282(x66481,x66484),x66483))+~P22(f312(f312(f227(x66481),x66482),x66484))
% 155.93/155.62 [6999]~P22(f312(f312(f314(f854(x69991)),x69994),f157(x69991,x69993)))+P22(f312(f312(f314(x69991),x69992),x69993))+~P22(f312(f312(f314(x69991),x69992),f312(f168(x69991),x69994)))
% 155.93/155.62 [7060]~P72(x70601)+E(f312(f312(f312(f74(x70601,x70602,f90(x70601)),x70603),f87(x70601)),x70604),f312(f312(f9(x70602,x70601),x70603),x70604))+~P22(f312(f70(x70602),x70604))
% 155.93/155.62 [7062]~P26(x70621)+E(f312(f312(f312(f74(x70621,x70622,f89(x70621)),x70623),f2(x70621)),x70624),f312(f312(f6(x70622,x70621),x70623),x70624))+~P22(f312(f70(x70622),x70624))
% 155.93/155.62 [7092]P19(x70921,x70922,x70923,x70924)+~E(f312(f53(x70922),f312(f290(x70921,x70922,x70923),x70924)),f312(f53(x70921),x70924))+~P22(f312(f70(x70921),x70924))
% 155.93/155.62 [7267]~P26(x72671)+E(f312(f312(f89(x72671),f312(x72672,x72673)),f312(f312(f6(a853,x72671),x72672),f284(a853,x72673,x72674))),f312(f312(f6(a853,x72671),x72672),f283(a853,x72673,x72674)))+~P22(f312(f312(f227(a853),x72673),x72674))
% 155.93/155.62 [7278]~P72(x72781)+~P19(x72782,x72781,x72783,x72784)+E(f312(f312(f9(x72781,x72781),f39(x72781)),f312(f290(x72782,x72781,x72783),x72784)),f312(f312(f9(x72782,x72781),x72783),x72784))
% 155.93/155.62 [7279]~P26(x72791)+~P19(x72792,x72791,x72793,x72794)+E(f312(f312(f6(x72791,x72791),f39(x72791)),f312(f290(x72792,x72791,x72793),x72794)),f312(f312(f6(x72792,x72791),x72793),x72794))
% 155.93/155.62 [7330]E(f312(f53(f859(x73301,x73302)),f298(x73301,x73302,x73303,x73304)),f312(f312(f89(a853),f312(f53(x73301),x73303)),f312(f53(x73302),x73304)))+~P22(f312(f70(x73302),x73304))+~P22(f312(f70(x73301),x73303))
% 155.93/155.62 [7414]E(x74141,x74142)+P22(f312(f312(f314(x74143),x74141),f312(f168(x74143),f166(x74143,x74142,x74144))))+~P22(f312(f312(f314(x74143),x74141),f312(f168(x74143),x74144)))
% 155.93/155.62 [7553]~P22(f312(f312(f227(f861(x75531,a846)),x75534),f312(x75533,x75534)))+~P22(f312(f312(f314(x75531),x75532),x75534))+P22(f312(f312(f314(x75531),x75532),f110(f861(x75531,a846),x75533)))
% 155.93/155.62 [7639]~P26(x76391)+E(f312(f312(f89(x76391),f312(f312(f6(a853,x76391),x76392),f312(f282(a853,x76393),x76394))),f312(x76392,x76394)),f312(f312(f6(a853,x76391),x76392),f312(f282(a853,x76393),f312(a126,x76394))))+P22(f312(f312(f228(a853),x76394),x76393))
% 155.93/155.62 [7693]~P19(x76931,x76932,x76933,f235(f861(x76931,a846)))+~P22(f312(f70(x76932),x76934))+P22(f312(f70(x76931),f312(f291(x76931,x76932,x76933),x76934)))
% 155.93/155.62 [7802]P22(f312(f312(f314(f854(x78021)),f312(f312(f147(x78021),x78022),x78023)),f157(x78021,x78024)))+~P22(f312(f312(f314(f854(x78021)),x78023),f157(x78021,x78024)))+~P22(f312(f312(f314(x78021),x78022),x78024))
% 155.93/155.62 [7889]~E(f312(f290(x78893,x78891,x78894),f235(f861(x78893,a846))),f235(f861(x78891,a846)))+P22(f312(f70(x78891),x78892))+~P22(f312(f70(x78893),f312(f291(x78893,x78891,x78894),x78892)))
% 155.93/155.62 [7983]~P19(x79831,x79833,x79834,x79832)+P22(f312(f70(x79831),x79832))+~P22(f312(f70(x79833),f312(f290(x79831,x79833,x79834),x79832)))
% 155.93/155.62 [8004]~E(x80042,x80043)+P22(f312(f312(f314(f860(x80041,x80041)),f312(f312(f239(x80041,x80041),x80042),x80043)),f237(x80041,x80044)))+~P22(f312(f312(f314(x80041),x80042),x80044))
% 155.93/155.62 [8045]~P26(x80451)+E(f312(f312(f89(x80451),f312(f312(f6(a853,x80451),x80452),f283(a853,x80453,x80454))),f312(x80452,f312(a126,x80454))),f312(f312(f6(a853,x80451),x80452),f283(a853,x80453,f312(a126,x80454))))+P22(f312(f312(f228(a853),f312(a126,x80454)),x80453))
% 155.93/155.62 [8109]P22(f312(x81091,x81092))+~P22(f312(x81091,f312(f312(f161(x81093),x81094),f598(x81091,x81094,x81093))))+~P22(f312(f312(f314(x81093),x81092),f312(f168(x81093),x81094)))
% 155.93/155.62 [8254]~P22(f312(f312(f314(x82541),x82542),f301(x82541,x82544)))+P22(f312(f312(f314(f854(x82541)),f312(f312(f147(x82541),x82542),x82543)),f301(f854(x82541),f153(x82541,x82544))))+~P22(f312(f312(f314(f854(x82541)),x82543),f301(f854(x82541),f153(x82541,x82544))))
% 155.93/155.62 [8265]~P19(x82652,x82653,x82654,f699(x82654,x82653,x82652,x82651))+P19(x82652,x82653,x82654,f49(f861(x82652,a846),x82651))+E(x82651,f189(f861(f861(x82652,a846),a846)))
% 155.93/155.62 [8543]E(x85431,x85432)+~P22(f312(f312(f314(f860(x85433,x85433)),f312(f312(f239(x85433,x85433),x85431),x85432)),f287(x85433,x85434)))+P22(f312(f312(f314(x85433),x85431),f312(f238(x85433,x85433),x85434)))
% 155.93/155.62 [8817]P19(x88172,x88173,x88174,f49(f861(x88172,a846),x88171))+E(x88171,f189(f861(f861(x88172,a846),a846)))+P22(f312(f312(f314(f861(x88172,a846)),f699(x88174,x88173,x88172,x88171)),x88171))
% 155.93/155.62 [8958]P22(f312(f70(x89581),x89582))+~P22(f312(f70(x89584),f312(f290(x89581,x89584,x89583),x89582)))+P22(f312(f312(f314(x89581),f578(x89583,x89584,x89582,x89581)),x89582))
% 155.93/155.62 [9131]P22(f312(x91311,x91312))+~P22(f312(x91311,f312(f312(f161(x91313),x91314),f700(x91312,x91311,x91314,x91313))))+~P22(f312(f312(f314(x91313),x91312),f312(f168(x91313),x91314)))
% 155.93/155.62 [9152]E(x91521,x91522)+~P22(f312(f312(f314(f860(x91523,x91523)),f312(f312(f239(x91523,x91523),x91521),x91522)),f287(x91523,x91524)))+P22(f312(f312(f314(f860(x91523,x91523)),f312(f312(f239(x91523,x91523),x91521),x91522)),f312(f312(f267(x91523,x91523,x91523),x91524),f287(x91523,x91524))))
% 155.93/155.62 [9202]~E(f312(f190(f854(x92021)),x92022),f312(f190(f854(x92021)),x92023))+~P22(f312(f312(f314(f860(f854(x92021),f854(x92021))),f312(f312(f239(f854(x92021),f854(x92021)),x92022),x92023)),f143(x92021,x92024)))+P22(f312(f312(f314(f860(f854(x92021),f854(x92021))),f312(f312(f239(f854(x92021),f854(x92021)),x92022),x92023)),f141(x92021,x92024)))
% 155.93/155.62 [9626]~P30(x96261)+E(f312(f312(f6(a853,x96261),f312(f312(f18(a853,x96261,x96261),f312(f312(f8(x96261,f861(x96261,x96261),a853),f21(x96261)),x96262)),f312(f312(f8(a853,x96261,a853),x96262),f312(f312(f7(a853,a853,a853),f89(a853)),f87(a853))))),f283(a853,x96263,x96264)),f2(x96261))+P22(f312(f312(f227(a853),x96263),x96264))
% 155.93/155.62 [9871]~P41(x98712,x98714)+~P19(x98712,x98711,x98713,f235(f861(x98712,a846)))+P41(x98711,f312(f290(f860(x98712,x98712),f860(x98711,x98711),f250(x98712,x98711,x98712,x98711,x98713,x98713)),x98714))
% 155.93/155.62 [10038]~E(f312(f190(f854(x100381)),x100383),f312(f190(f854(x100381)),x100382))+P22(f312(f312(f314(f860(f854(x100381),f854(x100381))),f312(f312(f239(f854(x100381),f854(x100381)),x100382),x100383)),f154(x100381,x100384)))+~P22(f312(f312(f249(x100381,x100381,a846),f312(f312(f7(x100381,f861(f860(x100381,x100381),a846),f861(x100381,a846)),f312(f312(f8(f861(x100381,f861(f861(f860(x100381,x100381),a846),a846)),f861(f861(f860(x100381,x100381),a846),f861(x100381,a846)),x100381),f7(x100381,f861(f860(x100381,x100381),a846),a846)),f312(f312(f8(f861(x100381,f860(x100381,x100381)),f861(x100381,f861(f861(f860(x100381,x100381),a846),a846)),x100381),f312(f8(f860(x100381,x100381),f861(f861(f860(x100381,x100381),a846),a846),x100381),f314(f860(x100381,x100381)))),f239(x100381,x100381)))),x100384)),f591(x100384,x100383,x100382,x100381)))
% 155.93/155.62 [5906]~E(x59064,x59062)+P22(f312(x59061,x59062))+P22(f312(f312(f195(f35(x59061,x59063)),x59062),x59064))
% 155.93/155.62 [5954]~P60(x59541)+~E(x59542,f2(x59541))+E(f312(f47(x59541,f312(f312(f90(x59541),x59542),x59543)),f312(f312(f90(x59541),x59542),x59544)),f2(x59541))
% 155.93/155.62 [6029]E(x60291,f127(x60292))+E(x60293,f312(f312(f21(a853),f312(f190(f854(x60292)),x60291)),f87(a853)))+E(f140(x60292,f312(f312(f155(x60292,x60291),x60293),x60294)),f140(x60292,x60291))
% 155.93/155.62 [6044]~P60(x60442)+E(x60441,f2(x60442))+E(f312(f47(x60442,f312(f312(f90(x60442),x60443),x60441)),f312(f312(f90(x60442),x60444),x60441)),f312(f47(x60442,x60443),x60444))
% 155.93/155.62 [6046]~P60(x60462)+E(x60461,f2(x60462))+E(f312(f47(x60462,f312(f312(f90(x60462),x60461),x60463)),f312(f312(f90(x60462),x60461),x60464)),f312(f47(x60462,x60463),x60464))
% 155.93/155.62 [6057]E(x60571,x60572)+P22(f312(x60573,x60572))+~P22(f312(f312(f312(f289(x60574),x60571),x60573),x60572))
% 155.93/155.62 [6070]~P26(x60701)+~P22(f312(f133(x60702),x60704))+E(f312(f162(x60701),f312(f312(f150(x60702,x60701),x60703),x60704)),f312(f312(f6(x60702,x60701),x60703),f312(f168(x60702),x60704)))
% 155.93/155.62 [6092]~P72(x60922)+~P22(f312(f70(x60921),x60924))+E(f312(f312(f9(x60921,x60922),f312(f16(x60922,x60921),x60923)),x60924),f312(f312(f240(x60922),x60923),f312(f53(x60921),x60924)))
% 155.93/155.62 [6152]~P64(x61522)+E(x61521,f2(x61522))+E(f312(f312(f268(x61522),f312(f312(f90(x61522),x61523),x61521)),f312(f312(f90(x61522),x61524),x61521)),f312(f312(f268(x61522),x61523),x61524))
% 155.93/155.62 [6153]~P64(x61532)+E(x61531,f2(x61532))+E(f312(f312(f268(x61532),f312(f312(f90(x61532),x61531),x61533)),f312(f312(f90(x61532),x61531),x61534)),f312(f312(f268(x61532),x61533),x61534))
% 155.93/155.62 [6216]P22(f312(x62161,x62162))+~E(x62163,f312(f312(f89(a853),x62164),x62162))+~P22(f312(x62161,f312(f312(f21(a853),x62163),x62164)))
% 155.93/155.62 [6296]P21(x62961,x62962,x62963)+P34(x62961,f645(x62963,x62962,x62961),x62964)+~P22(f312(f312(f314(f852(x62961)),x62964),x62962))
% 155.93/155.62 [6298]~P22(f312(x62982,x62983))+~P22(f312(f156(x62981,x62982),x62984))+P22(f312(f156(x62981,x62982),f312(f312(f147(x62981),x62983),x62984)))
% 155.93/155.62 [6336]E(x63361,f127(x63362))+~E(x63363,f312(f312(f21(a853),f312(f190(f854(x63362)),x63361)),f87(a853)))+E(f140(x63362,f312(f312(f155(x63362,x63361),x63363),x63364)),x63364)
% 155.93/155.62 [6358]~P98(x63581)+~P22(f312(f312(f228(x63581),x63582),x63584))+P22(f312(f312(f228(x63581),x63582),f312(f312(f124(x63581),x63583),x63584)))
% 155.93/155.62 [6359]~P98(x63591)+~P22(f312(f312(f228(x63591),x63592),x63593))+P22(f312(f312(f228(x63591),x63592),f312(f312(f124(x63591),x63593),x63594)))
% 155.93/155.62 [6361]~P103(x63611)+~P22(f312(f312(f228(x63611),x63612),x63614))+P22(f312(f312(f228(x63611),x63612),f312(f312(f226(x63611),x63613),x63614)))
% 155.93/155.62 [6363]~P103(x63631)+~P22(f312(f312(f228(x63631),x63632),x63633))+P22(f312(f312(f228(x63631),x63632),f312(f312(f226(x63631),x63633),x63634)))
% 155.93/155.62 [6364]~P98(x63641)+~P22(f312(f312(f227(x63641),x63642),x63644))+P22(f312(f312(f227(x63641),x63642),f312(f312(f124(x63641),x63643),x63644)))
% 155.93/155.62 [6365]~P98(x63651)+~P22(f312(f312(f227(x63651),x63652),x63653))+P22(f312(f312(f227(x63651),x63652),f312(f312(f124(x63651),x63653),x63654)))
% 155.93/155.62 [6367]~P103(x63671)+~P22(f312(f312(f227(x63671),x63672),x63674))+P22(f312(f312(f227(x63671),x63672),f312(f312(f226(x63671),x63673),x63674)))
% 155.93/155.62 [6369]~P103(x63691)+~P22(f312(f312(f227(x63691),x63692),x63693))+P22(f312(f312(f227(x63691),x63692),f312(f312(f226(x63691),x63693),x63694)))
% 155.93/155.62 [6452]~E(f312(f312(f161(x64521),x64522),x64523),x64524)+E(f312(f312(f155(x64521,x64522),x64523),x64524),x64522)+~P22(f312(f312(f228(a853),x64523),f312(f190(f854(x64521)),x64522)))
% 155.93/155.62 [6471]E(x64711,x64712)+P22(f312(x64713,x64711))+~P22(f312(f312(f195(f35(x64713,x64714)),x64711),x64712))
% 155.93/155.62 [6492]P22(f312(x64921,x64922))+~P22(f312(x64923,x64922))+~P22(f312(f312(f227(f861(x64924,a846)),x64923),x64921))
% 155.93/155.62 [6524]~E(f312(f312(f155(x65241,x65242),x65243),x65244),x65242)+E(f312(f312(f161(x65241),x65242),x65243),x65244)+~P22(f312(f312(f228(a853),x65243),f312(f190(f854(x65241)),x65242)))
% 155.93/155.62 [6538]~P22(f312(f156(x65381,x65382),x65384))+~P22(f312(f156(x65381,x65382),x65383))+P22(f312(f156(x65381,x65382),f312(f312(f129(x65381),x65383),x65384)))
% 155.93/155.62 [6636]P34(x66361,x66362,x66363)+~P34(x66361,f312(a126,x66362),f616(x66362,x66364,x66361))+~P22(f312(f312(f314(f852(x66361)),x66363),x66364))
% 155.93/155.62 [6645]E(x66451,f189(f861(x66452,a846)))+E(x66453,f189(f861(x66454,a846)))+~E(f312(f312(f247(x66454,x66452),x66453),f312(f16(f861(x66452,a846),x66454),x66451)),f189(f861(f860(x66454,x66452),a846)))
% 155.93/155.62 [6663]E(x66631,x66632)+P22(f312(f312(f314(x66633),x66631),x66634))+~P22(f312(f312(f314(x66633),x66631),f312(f312(f289(x66633),x66632),x66634)))
% 155.93/155.62 [6679]~P103(x66791)+P22(f312(f312(f228(x66791),x66792),x66793))+~P22(f312(f312(f228(x66791),x66792),f312(f312(f225(x66791),x66794),x66793)))
% 155.93/155.62 [6680]~P103(x66801)+P22(f312(f312(f228(x66801),x66802),x66803))+~P22(f312(f312(f228(x66801),x66802),f312(f312(f225(x66801),x66803),x66804)))
% 155.93/155.62 [6682]~P99(x66821)+P22(f312(f312(f227(x66821),x66822),x66823))+~P22(f312(f312(f227(x66821),x66822),f312(f312(f115(x66821),x66824),x66823)))
% 155.93/155.62 [6684]~P99(x66841)+P22(f312(f312(f227(x66841),x66842),x66843))+~P22(f312(f312(f227(x66841),x66842),f312(f312(f115(x66841),x66843),x66844)))
% 155.93/155.62 [6686]~P103(x66861)+P22(f312(f312(f227(x66861),x66862),x66863))+~P22(f312(f312(f227(x66861),x66862),f312(f312(f225(x66861),x66864),x66863)))
% 155.93/155.62 [6688]~P103(x66881)+P22(f312(f312(f227(x66881),x66882),x66883))+~P22(f312(f312(f227(x66881),x66882),f312(f312(f225(x66881),x66883),x66884)))
% 155.93/155.62 [6706]~E(f312(f312(f161(x67061),x67063),x67064),x67062)+P22(f312(f312(f314(x67061),x67062),f312(f168(x67061),x67063)))+~P22(f312(f312(f228(a853),x67064),f312(f190(f854(x67061)),x67063)))
% 155.93/155.62 [6718]~P103(x67181)+~P33(x67181,f312(f312(f147(x67181),x67182),f312(f312(f147(x67181),x67183),x67184)))+P22(f312(f312(f227(x67181),x67182),x67183))
% 155.93/155.62 [6849]E(x68491,f2(a1))+E(f312(f47(a1,x68492),x68491),x68493)+~P22(f312(f57(x68492,x68491),f312(f312(f239(a1,a1),x68493),x68494)))
% 155.93/155.62 [6897]E(f54(a1,x68972,x68971),x68973)+E(x68971,f2(a1))+~P22(f312(f57(x68972,x68971),f312(f312(f239(a1,a1),x68974),x68973)))
% 155.93/155.62 [7017]P22(f312(f312(f314(x70171),x70172),x70173))+~P22(f312(f312(f314(x70171),x70172),x70174))+~P22(f312(f312(f228(f861(x70171,a846)),x70174),x70173))
% 155.93/155.62 [7021]P22(f312(f312(f314(x70211),x70212),x70213))+~P22(f312(f312(f314(x70211),x70212),x70214))+~P22(f312(f312(f227(f861(x70211,a846)),x70214),x70213))
% 155.93/155.62 [7131]P38(x71311,x71312,x71313)+~P22(f312(x71312,f312(f312(f161(x71311),x71313),x71314)))+~P22(f312(f312(f228(a853),x71314),f312(f190(f854(x71311)),x71313)))
% 155.93/155.62 [7234]~P104(x72342)+~P22(f312(f312(f228(f861(x72341,x72342)),x72343),x72344))+P22(f312(f312(f227(f861(x72341,x72342)),x72343),x72344))
% 155.93/155.62 [7318]~P18(x73181,x73182,x73184)+P18(x73181,x73182,f312(f312(f289(f852(x73181)),x73183),x73184))+~P18(x73181,x73182,f312(f312(f289(f852(x73181)),x73183),f189(f861(f852(x73181),a846))))
% 155.93/155.62 [7361]~P22(f312(f312(f314(x73611),x73612),x73614))+P22(f312(f312(f314(x73611),x73612),f48(f861(x73611,a846),x73613)))+~P22(f312(f312(f314(f861(x73611,a846)),x73614),x73613))
% 155.93/155.62 [7375]P34(x73751,x73752,x73753)+P22(f312(f312(f314(f852(x73751)),f616(x73752,x73754,x73751)),x73754))+~P22(f312(f312(f314(f852(x73751)),x73753),x73754))
% 155.93/155.62 [7392]~P80(x73921)+~P22(f312(f312(f228(x73921),x73923),x73924))+P22(f312(f312(f228(x73921),f312(f312(f89(x73921),x73922),x73923)),f312(f312(f89(x73921),x73922),x73924)))
% 155.93/155.62 [7393]~P81(x73931)+~P22(f312(f312(f228(x73931),x73933),x73934))+P22(f312(f312(f228(x73931),f312(f312(f89(x73931),x73932),x73933)),f312(f312(f89(x73931),x73932),x73934)))
% 155.93/155.62 [7394]~P80(x73941)+~P22(f312(f312(f228(x73941),x73942),x73944))+P22(f312(f312(f228(x73941),f312(f312(f89(x73941),x73942),x73943)),f312(f312(f89(x73941),x73944),x73943)))
% 155.93/155.62 [7395]~P81(x73951)+~P22(f312(f312(f228(x73951),x73952),x73954))+P22(f312(f312(f228(x73951),f312(f312(f89(x73951),x73952),x73953)),f312(f312(f89(x73951),x73954),x73953)))
% 155.93/155.62 [7396]~P81(x73961)+~P22(f312(f312(f227(x73961),x73963),x73964))+P22(f312(f312(f227(x73961),f312(f312(f89(x73961),x73962),x73963)),f312(f312(f89(x73961),x73962),x73964)))
% 155.93/155.62 [7397]~P82(x73971)+~P22(f312(f312(f227(x73971),x73973),x73974))+P22(f312(f312(f227(x73971),f312(f312(f89(x73971),x73972),x73973)),f312(f312(f89(x73971),x73972),x73974)))
% 155.93/155.62 [7398]~P81(x73981)+~P22(f312(f312(f227(x73981),x73982),x73984))+P22(f312(f312(f227(x73981),f312(f312(f89(x73981),x73982),x73983)),f312(f312(f89(x73981),x73984),x73983)))
% 155.93/155.62 [7399]~P82(x73991)+~P22(f312(f312(f227(x73991),x73992),x73994))+P22(f312(f312(f227(x73991),f312(f312(f89(x73991),x73992),x73993)),f312(f312(f89(x73991),x73994),x73993)))
% 155.93/155.62 [7408]~P132(x74081)+~P91(x74081)+E(f312(f312(f89(x74081),f312(f312(f90(x74081),x74082),f312(f117(x74081),x74083))),f312(f312(f90(x74081),x74084),f312(f117(x74081),x74083))),f312(f312(f90(x74081),f312(f312(f89(x74081),x74082),x74084)),f312(f117(x74081),x74083)))
% 155.93/155.62 [7409]~P120(x74091)+~P91(x74091)+E(f312(f312(f21(x74091),f312(f312(f90(x74091),x74092),f312(f117(x74091),x74093))),f312(f312(f90(x74091),x74094),f312(f117(x74091),x74093))),f312(f312(f90(x74091),f312(f312(f21(x74091),x74092),x74094)),f312(f117(x74091),x74093)))
% 155.93/155.62 [7444]~P26(x74441)+E(f312(f312(f89(x74441),f312(x74442,x74443)),f312(f312(f6(a853,x74441),x74442),f283(a853,f312(a126,x74443),x74444))),f312(f312(f6(a853,x74441),x74442),f283(a853,x74443,x74444)))+~P22(f312(f312(f227(a853),x74443),x74444))
% 155.93/155.62 [7456]~P19(x74562,x74561,x74563,f312(f168(x74562),x74564))+~P22(f312(f133(x74562),x74564))+P22(f312(f133(x74561),f312(f312(f150(x74562,x74561),x74563),x74564)))
% 155.93/155.62 [7503]~P22(f312(f312(f228(a853),x75032),x75034))+~P22(f312(f312(f228(a853),x75031),x75033))+P22(f312(f312(f228(a853),f312(f312(f89(a853),x75031),x75032)),f312(f312(f89(a853),x75033),x75034)))
% 155.93/155.62 [7506]~P22(f312(f312(f228(a1),x75061),x75063))+~P22(f312(f312(f227(a1),x75062),x75064))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x75061),x75062)),f312(f312(f89(a1),x75063),x75064)))
% 155.93/155.62 [7507]~P22(f312(f312(f227(a853),x75072),x75074))+~P22(f312(f312(f227(a853),x75071),x75073))+P22(f312(f312(f227(a853),f312(f312(f89(a853),x75071),x75072)),f312(f312(f89(a853),x75073),x75074)))
% 155.93/155.62 [7508]~P22(f312(f312(f227(a853),x75082),x75084))+~P22(f312(f312(f227(a853),x75081),x75083))+P22(f312(f312(f227(a853),f312(f312(f90(a853),x75081),x75082)),f312(f312(f90(a853),x75083),x75084)))
% 155.93/155.62 [7555]P22(f312(f312(f314(x75551),x75552),x75553))+~P22(f312(f312(f314(x75551),x75552),f49(f861(x75551,a846),x75554)))+~P22(f312(f312(f314(f861(x75551,a846)),x75553),x75554))
% 155.93/155.62 [7570]~P22(f312(x75701,f597(x75701,x75703,x75702)))+P22(f312(x75701,f312(f312(f161(x75702),x75703),x75704)))+~P22(f312(f312(f228(a853),x75704),f312(f190(f854(x75702)),x75703)))
% 155.93/155.62 [7576]P22(f312(x75761,x75762))+~P22(f312(f312(f314(x75764),x75762),f312(f168(x75764),x75763)))+P22(f312(f312(f228(a853),f598(x75761,x75763,x75764)),f312(f190(f854(x75764)),x75763)))
% 155.93/155.62 [7595]~P22(f312(f312(f195(x75952),x75953),x75954))+~P22(f312(f312(f195(f35(x75951,x75952)),x75954),x75953))+P22(f312(f312(f195(f35(x75951,x75952)),x75953),x75953))
% 155.93/155.62 [7624]~P104(x76241)+~P22(f312(f312(f227(f861(x76242,x76241)),x76244),x76243))+~P22(f312(f312(f228(f861(x76242,x76241)),x76243),x76244))
% 155.93/155.62 [7670]~P22(f312(x76704,x76702))+~P22(f312(f312(f314(x76701),x76702),x76703))+P22(f312(f312(f314(x76701),x76702),f312(f312(f115(f861(x76701,a846)),x76703),f312(f233(x76701),x76704))))
% 155.93/155.62 [7811]~P22(f312(f312(f314(x78111),x78113),x78114))+~P22(f312(f312(f228(f861(x78111,a846)),x78112),x78114))+P22(f312(f312(f228(f861(x78111,a846)),x78112),f312(f312(f289(x78111),x78113),x78114)))
% 155.93/155.62 [7812]E(f312(f312(f115(f861(x78121,a846)),x78122),x78123),f189(f861(x78121,a846)))+~E(f312(f312(f115(f861(x78121,a846)),f48(f861(x78121,a846),x78124)),x78123),f189(f861(x78121,a846)))+~P22(f312(f312(f314(f861(x78121,a846)),x78122),x78124))
% 155.93/155.62 [7885]P22(f312(f312(f314(x78851),x78852),x78853))+~P22(f312(f312(f227(f861(x78851,a846)),x78853),f312(f312(f289(x78851),x78852),x78854)))+P22(f312(f312(f227(f861(x78851,a846)),x78853),x78854))
% 155.93/155.62 [7905]P22(f312(f312(f314(x79052),f597(x79051,x79053,x79052)),f312(f168(x79052),x79053)))+P22(f312(x79051,f312(f312(f161(x79052),x79053),x79054)))+~P22(f312(f312(f228(a853),x79054),f312(f190(f854(x79052)),x79053)))
% 155.93/155.62 [7913]~P22(f312(f312(f228(f861(x79131,a846)),x79132),x79134))+P22(f312(f312(f228(f861(x79131,a846)),x79132),x79133))+~P22(f312(f312(f228(f861(x79131,a846)),x79134),x79133))
% 155.93/155.62 [7914]~P22(f312(f312(f227(f861(x79141,a846)),x79142),x79144))+P22(f312(f312(f228(f861(x79141,a846)),x79142),x79143))+~P22(f312(f312(f228(f861(x79141,a846)),x79144),x79143))
% 155.93/155.62 [7915]~P22(f312(f312(f227(f861(x79151,a846)),x79154),x79153))+~P22(f312(f312(f228(f861(x79151,a846)),x79152),x79154))+P22(f312(f312(f228(f861(x79151,a846)),x79152),x79153))
% 155.93/155.62 [7916]~P22(f312(f312(f227(f861(x79161,a846)),x79162),x79164))+P22(f312(f312(f227(f861(x79161,a846)),x79162),x79163))+~P22(f312(f312(f227(f861(x79161,a846)),x79164),x79163))
% 155.93/155.62 [7956]~P22(f312(f312(f314(x79561),x79564),x79563))+~P22(f312(f312(f228(f861(x79561,a846)),x79562),f312(f312(f289(x79561),x79564),x79563)))+P22(f312(f312(f228(f861(x79561,a846)),x79562),x79563))
% 155.93/155.62 [7968]~P81(x79681)+P22(f312(f312(f228(x79681),x79682),x79683))+~P22(f312(f312(f228(x79681),f312(f312(f89(x79681),x79684),x79682)),f312(f312(f89(x79681),x79684),x79683)))
% 155.93/155.62 [7970]~P81(x79701)+P22(f312(f312(f228(x79701),x79702),x79703))+~P22(f312(f312(f228(x79701),f312(f312(f89(x79701),x79702),x79704)),f312(f312(f89(x79701),x79703),x79704)))
% 155.93/155.62 [7972]~P81(x79721)+P22(f312(f312(f227(x79721),x79722),x79723))+~P22(f312(f312(f227(x79721),f312(f312(f89(x79721),x79724),x79722)),f312(f312(f89(x79721),x79724),x79723)))
% 155.93/155.62 [7974]~P81(x79741)+P22(f312(f312(f227(x79741),x79742),x79743))+~P22(f312(f312(f227(x79741),f312(f312(f89(x79741),x79742),x79744)),f312(f312(f89(x79741),x79743),x79744)))
% 155.93/155.62 [8025]P22(f312(x80251,x80252))+~E(f312(f312(f134(x80253),f312(f190(f854(x80253)),f172(x80253,x80251,x80254))),x80254),f127(x80253))+~P22(f312(f312(f314(x80253),x80252),f312(f168(x80253),x80254)))
% 155.93/155.62 [8151]P22(f312(x81511,x81512))+~P22(f312(f312(f314(x81513),x81512),f312(f168(x81513),x81514)))+P22(f312(f312(f228(a853),f312(f190(f854(x81513)),f312(f132(x81513,x81511),x81514))),f312(f190(f854(x81513)),x81514)))
% 155.93/155.62 [8280]E(x82801,x82802)+P22(f312(f312(f195(x82803),x82801),f805(x82802,x82801,x82803,x82804)))+~P22(f312(f312(f195(f35(x82804,x82803)),x82801),x82802))
% 155.93/155.62 [8281]E(x82811,x82812)+P22(f312(f312(f195(x82813),x82811),f845(x82812,x82811,x82813,x82814)))+~P22(f312(f312(f195(f35(x82814,x82813)),x82811),x82812))
% 155.93/155.62 [8311]~P22(f312(x83114,x83112))+P22(f312(f312(f195(x83111),x83112),f805(x83113,x83112,x83111,x83114)))+~P22(f312(f312(f195(f35(x83114,x83111)),x83112),x83113))
% 155.93/155.62 [8312]~P22(f312(x83124,x83122))+P22(f312(f312(f195(x83121),x83122),f845(x83123,x83122,x83121,x83124)))+~P22(f312(f312(f195(f35(x83124,x83121)),x83122),x83123))
% 155.93/155.62 [8633]~P22(f312(x86331,f739(x86331,x86333,x86332,x86334)))+P22(f312(x86331,f312(f312(f161(x86332),x86333),x86334)))+~P22(f312(f312(f228(a853),x86334),f312(f190(f854(x86332)),x86333)))
% 155.93/155.62 [8658]~P19(x86584,x86583,x86581,f235(f861(x86584,a846)))+E(f312(x86581,f825(x86582,x86581,x86583,x86584)),x86582)+~P22(f312(f312(f314(x86583),x86582),f312(f290(x86584,x86583,x86581),f235(f861(x86584,a846)))))
% 155.93/155.62 [8721]E(f172(x87211,x87212,x87213),f312(f312(f169(x87211),x87214),x87213))+P22(f312(f312(f228(a853),f683(x87212,x87213,x87211,x87214)),x87214))+P22(f312(f312(f228(a853),x87214),f312(f190(f854(x87211)),x87213)))
% 155.93/155.62 [8724]E(f172(x87241,x87242,x87243),f312(f312(f169(x87241),x87244),x87243))+P22(f312(f312(f228(a853),f683(x87242,x87243,x87241,x87244)),x87244))+P22(f312(x87242,f312(f312(f161(x87241),x87243),x87244)))
% 155.93/155.62 [8753]P22(f312(x87531,x87532))+~P22(f312(f312(f314(x87534),x87532),f312(f168(x87534),x87533)))+P22(f312(f312(f228(a853),f700(x87532,x87531,x87533,x87534)),f312(f190(f854(x87534)),x87533)))
% 155.93/155.62 [8756]E(f172(x87561,x87562,x87563),f312(f312(f169(x87561),x87564),x87563))+P22(f312(f312(f228(a853),x87564),f312(f190(f854(x87561)),x87563)))+P22(f312(f312(f228(a853),f683(x87562,x87563,x87561,x87564)),f312(f190(f854(x87561)),x87563)))
% 155.93/155.62 [8762]E(f172(x87621,x87622,x87623),f312(f312(f169(x87621),x87624),x87623))+P22(f312(x87622,f312(f312(f161(x87621),x87623),x87624)))+P22(f312(f312(f228(a853),f683(x87622,x87623,x87621,x87624)),f312(f190(f854(x87621)),x87623)))
% 155.93/155.62 [8819]~P22(f312(f70(x88191),x88194))+P22(f312(f312(f314(x88191),f525(x88192,x88193,x88194,x88191)),x88194))+P22(f312(f70(f860(x88191,x88193)),f312(f312(f247(x88191,x88193),x88194),x88192)))
% 155.93/155.62 [8854]P22(f312(f312(f314(x88542),f739(x88541,x88543,x88542,x88544)),f312(f168(x88542),x88543)))+P22(f312(x88541,f312(f312(f161(x88542),x88543),x88544)))+~P22(f312(f312(f228(a853),x88544),f312(f190(f854(x88542)),x88543)))
% 155.93/155.62 [8869]E(x88691,x88692)+P22(f312(f312(f195(f35(x88693,x88694)),f805(x88691,x88692,x88694,x88693)),x88691))+~P22(f312(f312(f195(f35(x88693,x88694)),x88692),x88691))
% 155.93/155.62 [8870]E(x88701,x88702)+P22(f312(f312(f195(f35(x88703,x88704)),f845(x88701,x88702,x88704,x88703)),x88701))+~P22(f312(f312(f195(f35(x88703,x88704)),x88702),x88701))
% 155.93/155.62 [8892]~P22(f312(x88921,x88924))+P22(f312(f312(f195(f35(x88921,x88922)),f805(x88923,x88924,x88922,x88921)),x88923))+~P22(f312(f312(f195(f35(x88921,x88922)),x88924),x88923))
% 155.93/155.62 [8893]~P22(f312(x88931,x88934))+P22(f312(f312(f195(f35(x88931,x88932)),f845(x88933,x88934,x88932,x88931)),x88933))+~P22(f312(f312(f195(f35(x88931,x88932)),x88934),x88933))
% 155.93/155.62 [8985]P22(f312(f312(f227(a853),x89854),f312(f190(f854(x89852)),f172(x89852,x89853,x89851))))+P22(f312(f312(f228(a853),f684(x89851,x89852,x89853,x89854)),x89854))+~P22(f312(f312(f227(a853),x89854),f312(f190(f854(x89852)),x89851)))
% 155.93/155.62 [9087]~E(f312(f312(f173(x90871,x90872),x90873),f707(x90874,x90873,x90872,x90871)),f312(f312(f173(x90871,x90872),x90874),f707(x90874,x90873,x90872,x90871)))+E(f312(f173(x90871,x90872),x90873),f312(f173(x90871,x90872),x90874))+~E(f312(f168(x90871),f312(f312(f150(f860(x90871,x90872),x90871),f246(x90871,x90872)),x90873)),f312(f168(x90871),f312(f312(f150(f860(x90871,x90872),x90871),f246(x90871,x90872)),x90874)))
% 155.93/155.62 [9134]E(f172(x91341,x91342,x91343),f312(f312(f169(x91341),x91344),x91343))+~P22(f312(x91342,f312(f312(f161(x91341),x91343),f683(x91342,x91343,x91341,x91344))))+P22(f312(f312(f228(a853),x91344),f312(f190(f854(x91341)),x91343)))
% 155.93/155.62 [9139]E(f172(x91391,x91392,x91393),f312(f312(f169(x91391),x91394),x91393))+~P22(f312(x91392,f312(f312(f161(x91391),x91393),f683(x91392,x91393,x91391,x91394))))+P22(f312(x91392,f312(f312(f161(x91391),x91393),x91394)))
% 155.93/155.62 [9146]~P22(f312(f70(x91461),x91463))+~P22(f312(f70(x91462),f312(x91464,f525(x91464,x91462,x91463,x91461))))+P22(f312(f70(f860(x91461,x91462)),f312(f312(f247(x91461,x91462),x91463),x91464)))
% 155.93/155.62 [9160]~E(f312(f190(f854(x91604)),x91602),f312(f190(f854(x91604)),x91603))+P22(f312(f312(f314(f860(f854(x91604),f854(x91604))),f312(f312(f239(f854(x91604),f854(x91604)),x91603),x91602)),f154(x91604,x91601)))+P22(f312(f312(f228(a853),f602(x91601,x91602,x91603,x91604)),f312(f190(f854(x91604)),x91603)))
% 155.93/155.62 [9215]~P22(f312(x92153,f312(f312(f161(x92152),x92154),f684(x92154,x92152,x92153,x92151))))+P22(f312(f312(f227(a853),x92151),f312(f190(f854(x92152)),f172(x92152,x92153,x92154))))+~P22(f312(f312(f227(a853),x92151),f312(f190(f854(x92152)),x92154)))
% 155.93/155.62 [9289]E(f312(f312(f169(x92891),f603(x92892,x92893,x92894,x92891)),x92893),f312(f312(f169(x92891),f603(x92892,x92893,x92894,x92891)),x92894))+~P22(f312(f312(f314(f860(f854(x92891),f854(x92891))),f312(f312(f239(f854(x92891),f854(x92891)),x92894),x92893)),f143(x92891,x92892)))+P22(f312(f312(f228(a853),f312(f190(f854(x92891)),x92894)),f312(f190(f854(x92891)),x92893)))
% 155.93/155.62 [9345]~P22(f312(f312(f228(a853),f2(a853)),x93453))+~P22(f312(f312(f228(a853),x93454),x93451))+P22(f312(f312(f228(a853),f312(f312(f89(a853),f312(f312(f90(a853),x93451),f54(a853,x93452,x93453))),x93454)),f312(f312(f90(a853),x93451),x93453)))
% 155.93/155.62 [9531]~P104(x95312)+~P22(f312(f312(f227(x95312),f312(x95313,f815(x95314,x95313,x95311,x95312))),f312(x95314,f815(x95314,x95313,x95311,x95312))))+P22(f312(f312(f227(f861(x95311,x95312)),x95313),x95314))
% 155.93/155.62 [9634]~P30(x96341)+E(f312(f312(f6(a853,x96341),f312(f312(f18(a853,x96341,x96341),f312(f312(f8(x96341,f861(x96341,x96341),a853),f21(x96341)),x96342)),f312(f312(f8(a853,x96341,a853),x96342),f312(f312(f7(a853,a853,a853),f89(a853)),f87(a853))))),f283(a853,x96343,x96344)),f312(f312(f21(x96341),f312(x96342,x96343)),f312(x96342,f312(f312(f89(a853),x96344),f87(a853)))))+~P22(f312(f312(f227(a853),x96343),x96344))
% 155.93/155.62 [6709]E(f312(f312(f129(x67091),x67092),x67093),x67094)+~E(x67093,f312(f312(f134(x67091),f312(f190(f854(x67091)),x67092)),x67094))+~E(f312(f312(f169(x67091),f312(f190(f854(x67091)),x67092)),x67094),x67092)
% 155.93/155.62 [6763]~P65(x67632)+E(x67631,f2(x67632))+E(f312(f312(f268(x67632),f312(f312(f240(x67632),x67633),x67634)),f312(f312(f240(x67632),x67631),x67634)),f312(f312(f240(x67632),f312(f312(f268(x67632),x67633),x67631)),x67634))
% 155.93/155.62 [6901]~E(f312(f190(f854(x69011)),x69013),f312(f190(f854(x69012)),x69014))+~P22(f312(f133(x69011),x69013))+E(f179(x69011,x69012,f312(f173(x69011,x69012),f312(f312(f177(x69011,x69012),x69013),x69014))),f312(f168(x69011),x69013))
% 155.93/155.62 [6921]~P99(x69211)+~P22(f312(f312(f228(x69211),x69213),x69214))+P22(f312(f312(f228(x69211),f312(f312(f115(x69211),x69212),x69213)),x69214))
% 155.93/155.62 [6922]~P99(x69221)+~P22(f312(f312(f228(x69221),x69222),x69224))+P22(f312(f312(f228(x69221),f312(f312(f115(x69221),x69222),x69223)),x69224))
% 155.93/155.62 [6924]~P103(x69241)+~P22(f312(f312(f228(x69241),x69243),x69244))+P22(f312(f312(f228(x69241),f312(f312(f225(x69241),x69242),x69243)),x69244))
% 155.93/155.62 [6926]~P103(x69261)+~P22(f312(f312(f228(x69261),x69262),x69264))+P22(f312(f312(f228(x69261),f312(f312(f225(x69261),x69262),x69263)),x69264))
% 155.93/155.62 [6927]~P99(x69271)+~P22(f312(f312(f227(x69271),x69273),x69274))+P22(f312(f312(f227(x69271),f312(f312(f115(x69271),x69272),x69273)),x69274))
% 155.93/155.62 [6928]~P99(x69281)+~P22(f312(f312(f227(x69281),x69282),x69284))+P22(f312(f312(f227(x69281),f312(f312(f115(x69281),x69282),x69283)),x69284))
% 155.93/155.62 [6930]~P103(x69301)+~P22(f312(f312(f227(x69301),x69303),x69304))+P22(f312(f312(f227(x69301),f312(f312(f225(x69301),x69302),x69303)),x69304))
% 155.93/155.62 [6932]~P103(x69321)+~P22(f312(f312(f227(x69321),x69322),x69324))+P22(f312(f312(f227(x69321),f312(f312(f225(x69321),x69322),x69323)),x69324))
% 155.93/155.62 [6951]~P22(f312(x69513,x69514))+~P22(f312(x69512,x69514))+P22(f312(f312(f312(f115(f861(x69511,a846)),x69512),x69513),x69514))
% 155.93/155.62 [7077]P18(x70771,x70772,x70773)+~P18(x70771,x70774,x70773)+~P22(f312(f312(f227(f861(f852(x70771),a846)),x70774),x70772))
% 155.93/155.62 [7078]P18(x70781,x70782,x70783)+~P18(x70781,x70782,x70784)+~P22(f312(f312(f227(f861(f852(x70781),a846)),x70783),x70784))
% 155.93/155.62 [7434]~P26(x74341)+E(f312(f312(f89(x74341),f312(x74342,x74343)),f312(f312(f6(a853,x74341),x74342),f312(f282(a853,f312(a126,x74343)),x74344))),f312(f312(f6(a853,x74341),x74342),f312(f282(a853,x74343),x74344)))+~P22(f312(f312(f228(a853),x74343),x74344))
% 155.93/155.62 [7463]~P103(x74631)+P22(f312(f312(f228(x74631),x74632),x74633))+~P22(f312(f312(f228(x74631),f312(f312(f226(x74631),x74634),x74632)),x74633))
% 155.93/155.62 [7464]~P103(x74641)+P22(f312(f312(f228(x74641),x74642),x74643))+~P22(f312(f312(f228(x74641),f312(f312(f226(x74641),x74642),x74644)),x74643))
% 155.93/155.62 [7466]~P98(x74661)+P22(f312(f312(f227(x74661),x74662),x74663))+~P22(f312(f312(f227(x74661),f312(f312(f124(x74661),x74664),x74662)),x74663))
% 155.93/155.62 [7468]~P98(x74681)+P22(f312(f312(f227(x74681),x74682),x74683))+~P22(f312(f312(f227(x74681),f312(f312(f124(x74681),x74682),x74684)),x74683))
% 155.93/155.62 [7470]~P103(x74701)+P22(f312(f312(f227(x74701),x74702),x74703))+~P22(f312(f312(f227(x74701),f312(f312(f226(x74701),x74704),x74702)),x74703))
% 155.93/155.62 [7472]~P103(x74721)+P22(f312(f312(f227(x74721),x74722),x74723))+~P22(f312(f312(f227(x74721),f312(f312(f226(x74721),x74722),x74724)),x74723))
% 155.93/155.62 [7547]~P22(f312(f312(f314(x75471),x75472),x75474))+P22(f312(f312(f314(x75471),x75472),x75473))+P22(f312(f312(f314(x75471),x75472),f312(f312(f21(f861(x75471,a846)),x75474),x75473)))
% 155.93/155.62 [7631]P22(f312(x76311,x76312))+P22(f312(x76313,x76312))+~P22(f312(f312(f312(f124(f861(x76314,a846)),x76313),x76311),x76312))
% 155.93/155.62 [7642]~P22(f312(f312(f314(x76421),x76422),x76424))+~P22(f312(f312(f314(x76421),x76422),x76423))+P22(f312(f312(f314(x76421),x76422),f312(f312(f115(f861(x76421,a846)),x76423),x76424)))
% 155.93/155.62 [7694]~P98(x76941)+~P22(f312(f70(x76941),x76944))+E(f312(f312(f73(x76941,x76941,f124(x76941)),x76942),f312(f312(f289(x76941),x76943),x76944)),f312(f312(f124(x76941),x76943),f312(f312(f73(x76941,x76941,f124(x76941)),x76942),x76944)))
% 155.93/155.62 [7695]~P99(x76951)+~P22(f312(f70(x76951),x76954))+E(f312(f312(f73(x76951,x76951,f115(x76951)),x76952),f312(f312(f289(x76951),x76953),x76954)),f312(f312(f115(x76951),x76953),f312(f312(f73(x76951,x76951,f115(x76951)),x76952),x76954)))
% 155.93/155.62 [7696]~P103(x76961)+~P22(f312(f70(x76961),x76964))+E(f312(f312(f73(x76961,x76961,f225(x76961)),x76962),f312(f312(f289(x76961),x76963),x76964)),f312(f312(f225(x76961),x76963),f312(f312(f73(x76961,x76961,f225(x76961)),x76962),x76964)))
% 155.93/155.62 [7697]~P103(x76971)+~P22(f312(f70(x76971),x76974))+E(f312(f312(f73(x76971,x76971,f226(x76971)),x76972),f312(f312(f289(x76971),x76973),x76974)),f312(f312(f226(x76971),x76973),f312(f312(f73(x76971,x76971,f226(x76971)),x76972),x76974)))
% 155.93/155.62 [7698]~P132(x76981)+~P91(x76981)+E(f312(f312(f89(x76981),f312(f312(f90(x76981),f312(f117(x76981),x76982)),x76983)),f312(f312(f90(x76981),f312(f117(x76981),x76982)),x76984)),f312(f312(f90(x76981),f312(f117(x76981),x76982)),f312(f312(f89(x76981),x76983),x76984)))
% 155.93/155.62 [7699]~P120(x76991)+~P91(x76991)+E(f312(f312(f21(x76991),f312(f312(f90(x76991),f312(f117(x76991),x76992)),x76993)),f312(f312(f90(x76991),f312(f117(x76991),x76992)),x76994)),f312(f312(f90(x76991),f312(f117(x76991),x76992)),f312(f312(f21(x76991),x76993),x76994)))
% 155.93/155.62 [7809]E(x78091,x78092)+P22(f312(f312(f314(x78093),x78091),f312(f168(x78093),x78094)))+~P22(f312(f312(f314(x78093),x78091),f312(f168(x78093),f312(f312(f147(x78093),x78092),x78094))))
% 155.93/155.62 [7832]~P63(x78321)+~E(f312(f190(f854(x78322)),x78323),f312(f190(f854(x78321)),f64(x78321)))+E(f312(f312(f173(x78321,x78322),f312(f312(f177(x78321,x78322),f64(x78321)),x78323)),x78324),f312(f219(x78322),f672(x78324,x78323,x78322,x78321)))
% 155.93/155.62 [7981]P54(x79811,x79812,x79813)+~P54(x79811,x79812,x79814)+~P22(f312(f312(f227(f861(f860(x79811,x79812),a846)),x79813),x79814))
% 155.93/155.62 [8028]P22(f312(f312(f314(x80281),x80282),x80283))+P22(f312(f312(f314(x80281),x80282),x80284))+~P22(f312(f312(f314(x80281),x80282),f312(f312(f124(f861(x80281,a846)),x80284),x80283)))
% 155.93/155.62 [8039]~P50(x80391,x80394,x80393)+~P22(f312(f312(f314(x80391),x80392),x80394))+P22(f312(f312(f314(f860(x80391,x80391)),f312(f312(f239(x80391,x80391),x80392),x80392)),x80393))
% 155.93/155.62 [8055]~P22(f312(f70(x80552),x80554))+~P22(f312(f70(x80551),x80553))+P22(f312(f70(f860(x80551,x80552)),f312(f312(f247(x80551,x80552),x80553),f312(f16(f861(x80552,a846),x80551),x80554))))
% 155.93/155.62 [8056]~P22(f312(f312(f314(x80561),x80562),x80564))+~P22(f312(f312(f227(f861(x80561,a846)),x80563),x80564))+P22(f312(f312(f227(f861(x80561,a846)),f312(f312(f289(x80561),x80562),x80563)),x80564))
% 155.93/155.62 [8064]~P23(x80642)+~P72(x80642)+E(f312(f312(f9(x80641,x80642),f312(f312(f8(a853,x80642,x80641),f114(x80642)),x80643)),x80644),f312(f114(x80642),f312(f312(f9(x80641,a853),x80643),x80644)))
% 155.93/155.62 [8065]~P111(x80652)+~P72(x80652)+E(f312(f312(f9(x80651,x80652),f312(f312(f8(a1,x80652,x80651),f116(x80652)),x80653)),x80654),f312(f116(x80652),f312(f312(f9(x80651,a1),x80653),x80654)))
% 155.93/155.62 [8089]E(f312(f312(f21(f861(x80891,a846)),x80892),f312(f312(f21(f861(x80891,a846)),x80893),x80894)),x80894)+~P22(f312(f312(f227(f861(x80891,a846)),x80892),x80893))+~P22(f312(f312(f227(f861(x80891,a846)),x80894),x80892))
% 155.93/155.62 [8186]~P22(f312(f70(x81861),x81864))+E(f312(f312(f21(a853),f312(f312(f6(x81861,a853),x81862),x81863)),f312(f312(f6(x81861,a853),x81862),x81864)),f312(f312(f6(x81861,a853),x81862),f312(f312(f21(f861(x81861,a846)),x81863),x81864)))+~P22(f312(f312(f227(f861(x81861,a846)),x81864),x81863))
% 155.93/155.62 [8349]~P3(x83491,x83494,x83493)+~P22(f312(f312(f314(x83491),x83492),x83494))+P22(f312(f312(f314(x83491),x83492),f312(f264(x83491,x83491,x83493),f312(f312(f289(x83491),x83492),f189(f861(x83491,a846))))))
% 155.93/155.62 [8414]~P22(f312(f312(f227(f861(x84141,a846)),x84142),x84143))+~P22(f312(f312(f227(f861(x84141,a846)),x84142),x84144))+P22(f312(f312(f227(f861(x84141,a846)),x84142),f312(f312(f115(f861(x84141,a846)),x84143),x84144)))
% 155.93/155.62 [8514]E(x85141,f189(f861(x85142,a846)))+P22(f312(f70(x85143),x85144))+~P22(f312(f70(f860(x85143,x85142)),f312(f312(f247(x85143,x85142),x85144),f312(f16(f861(x85142,a846),x85143),x85141))))
% 155.93/155.62 [8515]E(x85151,f189(f861(x85152,a846)))+P22(f312(f70(x85153),x85154))+~P22(f312(f70(f860(x85152,x85153)),f312(f312(f247(x85152,x85153),x85151),f312(f16(f861(x85153,a846),x85152),x85154))))
% 155.93/155.62 [8576]P22(f312(f312(f314(x85761),x85762),f301(x85761,x85763)))+~P22(f312(f312(f314(x85761),x85764),f301(x85761,x85763)))+~P22(f312(f312(f314(f860(x85761,x85761)),f312(f312(f239(x85761,x85761),x85762),x85764)),x85763))
% 155.93/155.62 [8628]~P41(x86281,x86284)+P22(f312(f312(f314(f860(x86281,x86281)),f312(f312(f239(x86281,x86281),x86283),x86282)),f287(x86281,x86284)))+P41(x86281,f312(f312(f289(f860(x86281,x86281)),f312(f312(f239(x86281,x86281),x86282),x86283)),x86284))
% 155.93/155.62 [8629]~P57(x86291,x86294)+P22(f312(f312(f314(f860(x86291,x86291)),f312(f312(f239(x86291,x86291),x86293),x86292)),f287(x86291,x86294)))+P57(x86291,f312(f312(f289(f860(x86291,x86291)),f312(f312(f239(x86291,x86291),x86292),x86293)),x86294))
% 155.93/155.62 [8706]~E(x87062,x87063)+~P22(f312(f312(f314(x87061),x87062),f312(f168(x87061),x87064)))+P22(f312(f312(f314(f860(x87061,x87061)),f312(f312(f239(x87061,x87061),x87062),x87063)),f312(f168(f860(x87061,x87061)),f312(f312(f177(x87061,x87061),x87064),x87064))))
% 155.93/155.62 [8729]~P49(f861(x87291,a846),f861(x87291,a846),x87293)+~P22(f312(f312(f314(x87291),x87292),f110(f861(x87291,a846),x87293)))+P22(f312(f312(f314(x87291),x87292),f312(x87293,f312(f312(f124(f861(x87291,a846)),x87294),f110(f861(x87291,a846),x87293)))))
% 155.93/155.62 [8787]~E(x87873,x87874)+P22(f312(f312(f249(x87871,x87871,a846),a309),x87872))+~P22(f312(f312(f314(f860(x87871,x87871)),x87872),f312(f168(f860(x87871,x87871)),f312(f312(f177(x87871,x87871),x87873),x87874))))
% 155.93/155.62 [8810]~P22(f312(x88104,x88102))+P22(f312(f312(f312(f312(a198,x88101),x88102),x88103),f350(x88103,x88102,x88101,x88104)))+~P22(f312(f312(f312(f312(a198,f35(x88104,x88101)),x88102),x88103),x88102))
% 155.93/155.62 [8837]P22(f312(f312(f314(f860(f854(x88371),f854(x88371))),f312(f312(f239(f854(x88371),f854(x88371)),x88372),x88373)),f143(x88371,x88374)))+~E(f312(f312(f169(x88371),f312(f190(f854(x88371)),x88372)),x88373),x88372)+~P22(f312(f312(f228(a853),f312(f190(f854(x88371)),x88372)),f312(f190(f854(x88371)),x88373)))
% 155.93/155.62 [8940]~P22(f312(f70(x89401),x89404))+P22(f312(f312(f314(x89401),f403(x89402,x89403,x89404,x89401)),x89404))+P22(f312(f70(x89403),f312(f312(f50(x89401,f861(x89403,a846)),x89404),x89402)))
% 155.93/155.62 [8941]~P22(f312(f70(x89411),x89414))+P22(f312(f312(f314(x89411),f706(x89412,x89413,x89414,x89411)),x89414))+P22(f312(f70(x89413),f312(f312(f50(x89411,f861(x89413,a846)),x89414),x89412)))
% 155.93/155.62 [9020]P22(f312(f312(f314(f860(x90201,x90201)),x90202),f312(f312(f267(x90201,x90201,x90201),x90203),f287(x90201,x90203))))+~P22(f312(f312(f228(a853),f2(a853)),x90204))+~P22(f312(f312(f314(f860(x90201,x90201)),x90202),f312(f312(f184(f860(x90201,x90201),a846),x90204),x90203)))
% 155.93/155.62 [9028]~P41(x90281,x90282)+~P22(f312(f312(f314(f860(x90281,x90281)),f312(f312(f239(x90281,x90281),x90284),x90283)),x90282))+~P22(f312(f312(f314(f860(x90281,x90281)),f312(f312(f239(x90281,x90281),x90283),x90284)),x90282))
% 155.93/155.62 [9154]~P22(f312(f70(x91541),x91544))+E(f312(f312(f6(x91541,a853),f312(f312(f8(f861(x91542,a846),a853,x91541),f53(x91542)),x91543)),x91544),f312(f53(f860(x91541,x91542)),f312(f312(f247(x91541,x91542),x91544),x91543)))+P22(f312(f312(f314(x91541),f527(x91543,x91542,x91544,x91541)),x91544))
% 155.93/155.62 [9156]~P22(f312(f133(x91561),x91562))+P22(f312(f133(x91561),f312(f312(f155(x91561,x91562),x91563),x91564)))+P22(f312(f312(f314(x91561),x91564),f312(f312(f21(f861(x91561,a846)),f312(f168(x91561),x91562)),f312(f312(f289(x91561),f312(f312(f161(x91561),x91562),x91563)),f189(f861(x91561,a846))))))
% 155.93/155.62 [9174]~P22(f312(f70(x91742),x91743))+~P22(f312(f70(x91741),f312(x91744,f403(x91744,x91741,x91743,x91742))))+P22(f312(f70(x91741),f312(f312(f50(x91742,f861(x91741,a846)),x91743),x91744)))
% 155.93/155.62 [9175]~P22(f312(f70(x91752),x91753))+~P22(f312(f70(x91751),f312(x91754,f706(x91754,x91751,x91753,x91752))))+P22(f312(f70(x91751),f312(f312(f50(x91752,f861(x91751,a846)),x91753),x91754)))
% 155.93/155.62 [9251]~P22(f312(f312(f314(f860(x92511,x92511)),x92512),f312(f312(f267(x92511,x92511,x92511),x92514),f287(x92511,x92514))))+P22(f312(f312(f314(f860(x92511,x92511)),x92512),f312(f312(f267(x92511,x92511,x92511),x92513),f287(x92511,x92513))))+~P22(f312(f312(f227(f861(f860(x92511,x92511),a846)),x92514),x92513))
% 155.93/155.62 [9257]E(f312(f312(f169(x92571),f603(x92574,x92573,x92572,x92571)),x92573),f312(f312(f169(x92571),f603(x92574,x92573,x92572,x92571)),x92572))+~P22(f312(f312(f314(f860(f854(x92571),f854(x92571))),f312(f312(f239(f854(x92571),f854(x92571)),x92572),x92573)),f143(x92571,x92574)))+E(f312(f312(f169(x92571),f312(f190(f854(x92571)),x92572)),x92573),x92572)
% 155.93/155.62 [9274]~P22(f312(f70(x92741),x92744))+E(f312(f312(f6(x92741,a853),f312(f312(f8(f861(x92742,a846),a853,x92741),f53(x92742)),x92743)),x92744),f312(f53(f860(x92741,x92742)),f312(f312(f247(x92741,x92742),x92744),x92743)))+~P22(f312(f70(x92742),f312(x92743,f527(x92743,x92742,x92744,x92741))))
% 155.93/155.62 [9278]~E(f312(f190(f854(x92781)),x92783),f312(f190(f854(x92781)),x92782))+P22(f312(f312(f314(f860(f854(x92781),f854(x92781))),f312(f312(f239(f854(x92781),f854(x92781)),x92782),x92783)),f154(x92781,x92784)))+P22(f312(f312(f314(f860(x92781,x92781)),f591(x92784,x92783,x92782,x92781)),f312(f168(f860(x92781,x92781)),f312(f312(f177(x92781,x92781),x92782),x92783))))
% 155.93/155.62 [9357]~P22(f312(f312(f314(f860(f854(x93571),f854(x93571))),f312(f312(f239(f854(x93571),f854(x93571)),x93572),x93573)),f143(x93571,x93574)))+E(f312(f312(f169(x93571),f312(f190(f854(x93571)),x93572)),x93573),x93572)+P22(f312(f312(f228(a853),f603(x93574,x93573,x93572,x93571)),f312(f312(f225(a853),f312(f190(f854(x93571)),x93572)),f312(f190(f854(x93571)),x93573))))
% 155.93/155.62 [9358]E(f312(f173(x93581,x93582),x93583),f312(f173(x93581,x93582),x93584))+~E(f312(f168(x93581),f312(f312(f150(f860(x93581,x93582),x93581),f246(x93581,x93582)),x93583)),f312(f168(x93581),f312(f312(f150(f860(x93581,x93582),x93581),f246(x93581,x93582)),x93584)))+P22(f312(f312(f314(x93581),f707(x93583,x93584,x93582,x93581)),f312(f168(x93581),f312(f312(f150(f860(x93581,x93582),x93581),f246(x93581,x93582)),x93584))))
% 155.93/155.62 [9371]~P22(f312(x93711,x93714))+P22(f312(f312(f312(f312(a198,f35(x93711,x93712)),f350(x93713,x93714,x93712,x93711)),x93713),x93714))+~P22(f312(f312(f312(f312(a198,f35(x93711,x93712)),x93714),x93713),x93714))
% 155.93/155.62 [9376]~P22(f312(f312(f314(f860(f854(x93761),f854(x93761))),f312(f312(f239(f854(x93761),f854(x93761)),x93762),x93763)),f143(x93761,x93764)))+P22(f312(f312(f228(a853),f312(f190(f854(x93761)),x93762)),f312(f190(f854(x93761)),x93763)))+P22(f312(f312(f228(a853),f603(x93764,x93763,x93762,x93761)),f312(f312(f225(a853),f312(f190(f854(x93761)),x93762)),f312(f190(f854(x93761)),x93763))))
% 155.93/155.62 [9669]~P22(f312(f312(f312(x96691,f351(x96691,x96694,x96693,x96692)),f352(x96691,x96694,x96693,x96692)),f353(x96691,x96694,x96693,x96692)))+P22(f312(f312(f312(x96691,x96692),x96693),x96694))+~P22(f312(f300(f860(f861(a1,f857(f854(a308))),f860(a1,a1)),a297),f312(f312(f239(f861(a1,f857(f854(a308))),f860(a1,a1)),x96692),f312(f312(f239(a1,a1),x96693),x96694))))
% 155.93/155.62 [9747]P22(f312(f312(f312(x97471,x97472),x97473),x97474))+P22(f312(f300(f860(f861(a1,f857(f854(a308))),f860(a1,a1)),a297),f312(f312(f239(f861(a1,f857(f854(a308))),f860(a1,a1)),f351(x97471,x97474,x97473,x97472)),f312(f312(f239(a1,a1),f352(x97471,x97474,x97473,x97472)),f353(x97471,x97474,x97473,x97472)))))+~P22(f312(f300(f860(f861(a1,f857(f854(a308))),f860(a1,a1)),a297),f312(f312(f239(f861(a1,f857(f854(a308))),f860(a1,a1)),x97472),f312(f312(f239(a1,a1),x97473),x97474))))
% 155.93/155.62 [9786]~P22(f312(f312(f314(f860(f854(x97861),f854(x97861))),f312(f312(f239(f854(x97861),f854(x97861)),x97862),x97863)),f143(x97861,x97864)))+E(f312(f312(f169(x97861),f312(f190(f854(x97861)),x97862)),x97863),x97862)+P22(f312(f312(f314(f860(x97861,x97861)),f312(f312(f239(x97861,x97861),f312(f312(f161(x97861),x97862),f603(x97864,x97863,x97862,x97861))),f312(f312(f161(x97861),x97863),f603(x97864,x97863,x97862,x97861)))),x97864))
% 155.93/155.62 [9789]~P22(f312(f312(f314(f860(f854(x97891),f854(x97891))),f312(f312(f239(f854(x97891),f854(x97891)),x97892),x97893)),f143(x97891,x97894)))+P22(f312(f312(f228(a853),f312(f190(f854(x97891)),x97892)),f312(f190(f854(x97891)),x97893)))+P22(f312(f312(f314(f860(x97891,x97891)),f312(f312(f239(x97891,x97891),f312(f312(f161(x97891),x97892),f603(x97894,x97893,x97892,x97891))),f312(f312(f161(x97891),x97893),f603(x97894,x97893,x97892,x97891)))),x97894))
% 155.93/155.62 [9848]~E(f312(f190(f854(x98481)),x98482),f312(f190(f854(x98481)),x98483))+P22(f312(f312(f314(f860(f854(x98481),f854(x98481))),f312(f312(f239(f854(x98481),f854(x98481)),x98482),x98483)),f154(x98481,x98484)))+~P22(f312(f312(f314(f860(x98481,x98481)),f312(f312(f239(x98481,x98481),f312(f312(f161(x98481),x98482),f602(x98484,x98483,x98482,x98481))),f312(f312(f161(x98481),x98483),f602(x98484,x98483,x98482,x98481)))),x98484))
% 155.93/155.62 [9987]~P26(x99871)+~P22(f312(f70(x99872),x99874))+E(f312(f162(x99871),f312(f312(f150(x99872,x99871),x99873),f99(f854(x99872),f312(f312(f18(f854(x99872),a846,a846),f312(f312(f8(a846,f861(a846,a846),f854(x99872)),a310),f312(f312(f7(f854(x99872),f861(x99872,a846),a846),f312(f312(f8(f861(x99872,a846),f861(f861(x99872,a846),a846),f854(x99872)),a309),f168(x99872))),x99874))),f133(x99872))))),f217(x99872,x99871,x99873,x99874))
% 155.93/155.62 [7202]~P60(x72022)+E(x72021,f2(x72022))+E(f312(f47(x72022,f312(f312(f89(x72022),x72023),f312(f312(f90(x72022),x72024),x72021))),x72021),f312(f312(f89(x72022),x72024),f312(f47(x72022,x72023),x72021)))
% 155.93/155.62 [7203]~P60(x72032)+E(x72031,f2(x72032))+E(f312(f47(x72032,f312(f312(f89(x72032),x72033),f312(f312(f90(x72032),x72031),x72034))),x72031),f312(f312(f89(x72032),x72034),f312(f47(x72032,x72033),x72031)))
% 155.93/155.62 [7280]~P64(x72802)+E(x72801,f2(x72802))+E(f312(f312(f268(x72802),f312(f312(f89(x72802),x72803),f312(f312(f90(x72802),x72804),x72801))),x72801),f312(f312(f89(x72802),x72804),f312(f312(f268(x72802),x72803),x72801)))
% 155.93/155.62 [7511]~P64(x75112)+E(x75111,f2(x75112))+E(f312(f312(f268(x75112),f312(f312(f89(x75112),x75113),f312(f312(f90(x75112),x75114),x75111))),x75111),f312(f312(f89(x75112),f312(f312(f268(x75112),x75113),x75111)),x75114))
% 155.93/155.62 [7512]~P65(x75122)+E(x75121,f2(x75122))+E(f312(f312(f268(x75122),f312(f312(f89(x75122),x75123),f312(f312(f90(x75122),x75121),x75124))),x75121),f312(f312(f89(x75122),f312(f312(f268(x75122),x75123),x75121)),x75124))
% 155.93/155.62 [7513]~P65(x75132)+E(x75131,f2(x75132))+E(f312(f312(f268(x75132),f312(f312(f21(x75132),x75133),f312(f312(f90(x75132),x75131),x75134))),x75131),f312(f312(f21(x75132),f312(f312(f268(x75132),x75133),x75131)),x75134))
% 155.93/155.62 [8215]~P22(f312(f156(x82151,x82153),x82154))+~P22(f312(f156(x82151,x82152),x82154))+P22(f312(f156(x82151,f312(f312(f115(f861(x82151,a846)),x82152),x82153)),x82154))
% 155.93/155.62 [8590]~E(f312(f312(f267(x85901,x85901,x85901),x85902),x85904),f189(f861(f860(x85901,x85901),a846)))+~E(f312(f312(f267(x85901,x85901,x85901),x85902),x85903),f189(f861(f860(x85901,x85901),a846)))+E(f312(f312(f267(x85901,x85901,x85901),x85902),f312(f312(f124(f861(f860(x85901,x85901),a846)),x85903),x85904)),f189(f861(f860(x85901,x85901),a846)))
% 155.93/155.62 [8707]~P22(f312(f312(f227(f861(x87071,a846)),x87073),x87074))+~P22(f312(f312(f227(f861(x87071,a846)),x87072),x87074))+P22(f312(f312(f227(f861(x87071,a846)),f312(f312(f124(f861(x87071,a846)),x87072),x87073)),x87074))
% 155.93/155.62 [9081]~P22(f312(f70(x90811),x90814))+~P22(f312(f70(x90811),x90813))+E(f312(f312(f21(a853),f312(f312(f89(a853),f312(f312(f6(x90811,a853),x90812),x90813)),f312(f312(f6(x90811,a853),x90812),x90814))),f312(f312(f6(x90811,a853),x90812),f312(f312(f115(f861(x90811,a846)),x90813),x90814))),f312(f312(f6(x90811,a853),x90812),f312(f312(f124(f861(x90811,a846)),x90813),x90814)))
% 155.93/155.62 [9169]~P22(f312(f312(f314(x91691),x91693),x91692))+~P22(f312(f312(f227(f861(x91691,a846)),x91692),f312(f312(f289(x91691),x91693),x91694)))+P22(f312(f312(f227(f861(x91691,a846)),f312(f312(f21(f861(x91691,a846)),x91692),f312(f312(f289(x91691),x91693),f189(f861(x91691,a846))))),x91694))
% 155.93/155.62 [9329]~P22(f312(f312(f314(x93291),x93293),x93292))+P22(f312(f312(f227(f861(x93291,a846)),x93292),f312(f312(f289(x93291),x93293),x93294)))+~P22(f312(f312(f227(f861(x93291,a846)),f312(f312(f21(f861(x93291,a846)),x93292),f312(f312(f289(x93291),x93293),f189(f861(x93291,a846))))),x93294))
% 155.93/155.62 [9418]~P22(f312(f312(f228(a853),x94182),x94184))+~P22(f312(f312(f227(a853),x94181),x94183))+P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),f312(f312(f239(a853,a853),x94181),x94182)),f312(f312(f239(a853,a853),x94183),x94184))),a45))
% 155.93/155.62 [9419]~P22(f312(f312(f227(a853),x94192),x94194))+~P22(f312(f312(f227(a853),x94191),x94193))+P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),f312(f312(f239(a853,a853),x94191),x94192)),f312(f312(f239(a853,a853),x94193),x94194))),a79))
% 155.93/155.62 [9705]~P22(f312(f312(f314(f854(x97051)),x97054),f157(x97051,x97053)))+~P22(f312(f312(f314(f854(x97051)),x97054),f157(x97051,x97052)))+P22(f312(f156(x97051,f312(f312(f115(f861(x97051,a846)),f312(f312(f7(x97051,f861(x97051,a846),a846),f314(x97051)),x97052)),f312(f312(f7(x97051,f861(x97051,a846),a846),f314(x97051)),x97053))),x97054))
% 155.93/155.62 [9813]~P19(x98131,f861(f861(x98131,a846),a846),f312(f312(f7(x98131,f861(f860(x98131,x98131),a846),f861(f861(x98131,a846),a846)),f312(f312(f8(f861(x98131,a846),f861(f861(f860(x98131,x98131),a846),f861(f861(x98131,a846),a846)),x98131),f69(x98131)),f312(f312(f7(x98131,f861(x98131,a846),f861(x98131,a846)),f289(x98131)),f189(f861(x98131,a846))))),x98133),x98132)+~P22(f312(f312(f314(x98131),x98134),x98132))+E(f312(f312(f21(f861(f861(x98131,a846),a846)),f312(f312(f69(x98131),x98132),x98133)),f312(f312(f69(x98131),f312(f312(f289(x98131),x98134),f189(f861(x98131,a846)))),x98133)),f312(f312(f69(x98131),f312(f312(f21(f861(x98131,a846)),x98132),f312(f312(f289(x98131),x98134),f189(f861(x98131,a846))))),x98133))
% 155.93/155.62 [9952]~P50(x99521,x99522,x99524)+~P22(f312(f312(f314(f860(x99521,x99521)),x99523),x99524))+P22(f312(f312(f249(x99521,x99521,a846),f312(f312(f7(x99521,f861(x99521,a846),f861(x99521,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x99521,a846),f861(x99521,a846)),x99521),f8(a846,a846,x99521)),f312(f312(f8(a846,f861(a846,a846),x99521),a310),f312(f312(f7(x99521,f861(x99521,a846),a846),f314(x99521)),x99522)))),f312(f312(f7(x99521,f861(x99521,a846),a846),f314(x99521)),x99522))),x99523))
% 155.93/155.62 [9965]P22(f312(f70(x99651),x99652))+~P22(f312(f70(x99653),f312(f290(x99651,x99653,x99654),x99652)))+~P22(f312(f70(x99651),f312(f233(x99651),f312(f312(f18(x99651,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99651),a310),f312(f312(f7(x99651,f861(x99651,a846),a846),f314(x99651)),x99652))),f312(f312(f7(x99651,x99653,a846),f312(f312(f8(x99653,f861(x99653,a846),x99651),a309),x99654)),f312(x99654,f578(x99654,x99653,x99652,x99651)))))))
% 155.93/155.62 [7963]~P65(x79632)+E(x79631,f2(x79632))+E(f312(f312(f268(x79632),f312(f312(f89(x79632),f312(f312(f90(x79632),x79631),x79633)),x79634)),x79631),f312(f312(f89(x79632),x79633),f312(f312(f268(x79632),x79634),x79631)))
% 155.93/155.62 [7964]~P65(x79642)+E(x79641,f2(x79642))+E(f312(f312(f268(x79642),f312(f312(f21(x79642),f312(f312(f90(x79642),x79641),x79643)),x79644)),x79641),f312(f312(f21(x79642),x79643),f312(f312(f268(x79642),x79644),x79641)))
% 155.93/155.62 [8868]~E(f312(f312(f267(x88681,x88681,x88681),x88683),x88684),f189(f861(f860(x88681,x88681),a846)))+~E(f312(f312(f267(x88681,x88681,x88681),x88682),x88684),f189(f861(f860(x88681,x88681),a846)))+E(f312(f312(f267(x88681,x88681,x88681),f312(f312(f124(f861(f860(x88681,x88681),a846)),x88682),x88683)),x88684),f189(f861(f860(x88681,x88681),a846)))
% 155.93/155.62 [9896]~P138(x98961)+~P138(x98962)+E(f312(f312(f296(x98961),f312(f312(f7(x98961,a113,f857(f854(a308))),f312(f312(f8(f861(x98962,f857(f854(a308))),f861(a113,f857(f854(a308))),x98961),f296(x98962)),f312(f312(f8(f861(x98962,f860(x98961,x98962)),f861(x98962,f857(f854(a308))),x98961),f312(f8(f860(x98961,x98962),f857(f854(a308)),x98962),x98963)),f239(x98961,x98962)))),x98964)),x98964),f312(f312(f296(f860(x98961,x98962)),x98963),x98964))
% 155.93/155.62 [9618]~P22(f312(f156(x96181,x96183),x96184))+~P22(f312(f156(x96181,x96182),x96184))+P22(f312(f156(x96181,f312(f312(f18(x96181,a846,a846),f312(f312(f8(a846,f861(a846,a846),x96181),a310),x96182)),x96183)),x96184))
% 155.93/155.62 [9888]P22(f312(x98881,f560(x98882,x98883,x98881,x98884)))+~P22(f312(f70(x98884),f312(f233(x98884),x98881)))+P22(f312(f70(x98883),f312(f233(x98883),f312(f312(f8(f861(x98884,a846),a846,x98883),f96(x98884)),f312(f312(f8(f861(x98884,a846),f861(x98884,a846),x98883),f312(f18(x98884,a846,a846),f312(f312(f8(a846,f861(a846,a846),x98884),a310),x98881))),x98882)))))
% 155.93/155.62 [9907]~P22(f312(f70(x99072),f312(f233(x99072),x99073)))+~P22(f312(f70(x99071),f312(f233(x99071),f312(f312(f7(x99071,x99072,a846),x99074),f560(x99074,x99071,x99073,x99072)))))+P22(f312(f70(x99071),f312(f233(x99071),f312(f312(f8(f861(x99072,a846),a846,x99071),f96(x99072)),f312(f312(f8(f861(x99072,a846),f861(x99072,a846),x99071),f312(f18(x99072,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99072),a310),x99073))),x99074)))))
% 155.93/155.62 [7653]~P36(x76531,x76532,x76533,x76535)+P36(x76531,x76532,x76533,x76534)+~P36(x76531,x76532,x76535,x76534)
% 155.93/155.62 [6432]E(x64321,x64322)+~E(f312(x64323,x64321),f312(x64323,x64322))+~P19(x64324,x64325,x64323,f235(f861(x64324,a846)))
% 155.93/155.62 [6596]~E(f312(x65963,x65965),f192(x65962))+~E(f312(x65964,x65965),f192(x65962))+E(f312(f180(x65961,x65962,x65963,x65964),x65965),f192(x65962))
% 155.93/155.62 [7314]E(x73141,x73142)+~P19(x73143,x73144,x73145,f235(f861(x73143,a846)))+~E(f312(f290(x73143,x73144,x73145),x73141),f312(f290(x73143,x73144,x73145),x73142))
% 155.93/155.62 [7455]~P36(x74554,x74555,x74551,x74553)+E(f312(x74551,x74552),f312(x74553,x74552))+~P22(f312(f312(f314(x74554),x74552),f179(x74554,x74555,x74551)))
% 155.93/155.62 [7564]P19(x75642,x75643,f829(x75644,x75643,x75642,x75641),x75641)+~E(f312(f290(x75643,x75642,x75645),x75644),x75641)+E(x75641,f189(f861(x75642,a846)))
% 155.93/155.62 [8101]~P22(f312(f312(x81013,x81012),x81015))+~P22(f312(f312(x81013,x81014),x81012))+P22(f312(f312(f314(x81011),x81012),f277(x81011,x81013,x81014,x81015)))
% 155.93/155.62 [8102]~P22(f312(f312(x81023,x81022),x81025))+~P22(f312(f312(x81023,x81024),x81022))+P22(f312(f312(f314(x81021),x81022),f274(x81021,x81023,x81024,x81025)))
% 155.93/155.62 [8667]~P19(x86671,x86673,x86675,f235(f861(x86671,a846)))+~P19(x86673,x86672,x86674,f235(f861(x86673,a846)))+P19(x86671,x86672,f312(f82(x86673,x86672,x86671,x86674),x86675),f235(f861(x86671,a846)))
% 155.93/155.62 [9229]P22(f312(f312(f314(f860(x92291,x92291)),f312(f312(f239(x92291,x92291),x92292),x92293)),f287(x92291,x92294)))+~P22(f312(f312(f314(f860(x92291,x92291)),f312(f312(f239(x92291,x92291),x92292),x92295)),f287(x92291,x92294)))+~P22(f312(f312(f314(f860(x92291,x92291)),f312(f312(f239(x92291,x92291),x92295),x92293)),f287(x92291,x92294)))
% 155.93/155.62 [9264]~P103(x92642)+~P22(f312(f133(x92641),x92645))+P22(f312(f133(x92641),f146(x92641,x92642,x92643,x92644,x92645)))
% 155.93/155.62 [5290]~E(x52902,f127(x52901))+E(f312(f312(f129(x52901),x52902),x52903),f312(f312(f147(x52901),x52904),x52905))+~E(x52903,f312(f312(f147(x52901),x52904),x52905))
% 155.93/155.62 [5291]~E(x52912,f127(x52911))+E(f312(f312(f129(x52911),x52912),x52913),f312(f312(f147(x52911),x52914),x52915))+~E(f312(f312(f147(x52911),x52914),x52915),x52913)
% 155.93/155.62 [6393]~E(f312(f190(f854(x63931)),x63935),f312(f190(f854(x63932)),x63934))+E(f312(f312(f150(f860(x63931,x63932),x63932),f248(x63931,x63932)),x63933),x63934)+~E(f312(f312(f177(x63931,x63932),x63935),x63934),x63933)
% 155.93/155.62 [6394]~E(f312(f190(f854(x63941)),x63944),f312(f190(f854(x63942)),x63945))+E(f312(f312(f150(f860(x63941,x63942),x63941),f246(x63941,x63942)),x63943),x63944)+~E(f312(f312(f177(x63941,x63942),x63944),x63945),x63943)
% 155.93/155.62 [6854]~P103(x68541)+~P33(x68541,f312(f312(f150(x68542,x68541),x68543),x68545))+P33(x68541,f312(f312(f150(x68542,x68541),x68543),f312(f132(x68542,x68544),x68545)))
% 155.93/155.62 [6907]~P22(f312(x69073,x69075))+~P22(f312(f312(x69072,x69074),x69075))+P22(f312(f312(f103(x69071,x69072,x69073),x69074),x69075))
% 155.93/155.62 [7006]~P103(x70061)+P33(x70061,f312(f312(f150(x70062,x70061),x70063),f166(x70062,x70064,x70065)))+~P33(x70061,f312(f312(f150(x70062,x70061),x70063),x70065))
% 155.93/155.62 [7027]~P54(x70273,x70272,x70275)+~P54(x70271,x70273,x70274)+P54(x70271,x70272,f312(f312(f267(x70271,x70273,x70272),x70274),x70275))
% 155.93/155.62 [7121]E(x71211,x71212)+~P19(x71213,x71214,x71215,f235(f861(x71213,a846)))+~E(f312(f312(f150(x71213,x71214),x71215),x71211),f312(f312(f150(x71213,x71214),x71215),x71212))
% 155.93/155.62 [7265]~P22(f312(f312(f228(a853),x72651),f312(x72653,x72655)))+P22(f312(f312(f228(a853),x72651),f151(x72652,x72653,x72654)))+~P22(f312(f312(f314(x72652),x72655),f312(f168(x72652),x72654)))
% 155.93/155.62 [7266]~P22(f312(f312(f227(a853),x72661),f312(x72663,x72665)))+P22(f312(f312(f227(a853),x72661),f151(x72662,x72663,x72664)))+~P22(f312(f312(f314(x72662),x72665),f312(f168(x72662),x72664)))
% 155.93/155.62 [7669]~P105(x76691)+P22(f312(f312(f227(f861(x76691,a846)),f283(x76691,x76692,x76693)),f283(x76691,x76694,x76695)))+P22(f312(f312(f227(x76691),x76692),x76693))
% 155.93/155.62 [7692]~P31(x76921)+P22(f312(f312(f227(x76921),f312(f312(f51(x76922,x76921),x76923),x76924)),f312(x76924,x76925)))+~P22(f312(f312(f314(x76922),x76925),x76923))
% 155.93/155.62 [7760]~P19(x77601,x77602,x77604,x77603)+E(f312(f86(x77601,x77602,x77603,x77604),f312(x77604,x77605)),x77605)+~P22(f312(f312(f314(x77601),x77605),x77603))
% 155.93/155.62 [7951]~P22(f312(x79511,x79515))+P22(f312(x79511,f806(x79511,x79512,x79513,x79514)))+~P22(f312(f312(f314(x79514),x79515),x79513))
% 155.93/155.62 [7952]~P22(f312(x79521,x79525))+P22(f312(x79521,f806(x79521,x79522,x79523,x79524)))+~P22(f312(f312(f314(x79524),x79525),x79522))
% 155.93/155.62 [8052]P22(f312(f70(x80521),x80522))+~P22(f312(f70(x80523),x80524))+~P22(f312(f312(f227(f861(x80521,a846)),x80522),f312(f290(x80523,x80521,x80525),x80524)))
% 155.93/155.62 [8218]E(x82181,x82182)+~P19(x82183,x82184,x82185,f312(f312(f124(f861(x82183,a846)),f312(f168(x82183),x82181)),f312(f168(x82183),x82182)))+~E(f312(f312(f150(x82183,x82184),x82185),x82181),f312(f312(f150(x82183,x82184),x82185),x82182))
% 155.93/155.62 [8274]~P105(x82741)+~P22(f312(f312(f228(f861(x82741,a846)),f283(x82741,x82744,x82745)),f283(x82741,x82742,x82743)))+P22(f312(f312(f227(x82741),x82742),x82743))
% 155.93/155.62 [8347]~P19(x83471,x83474,x83475,f235(f861(x83471,a846)))+~P22(f312(f312(f314(x83474),f312(x83475,x83472)),f312(f290(x83471,x83474,x83475),x83473)))+P22(f312(f312(f314(x83471),x83472),x83473))
% 155.93/155.62 [8426]P22(f312(x84261,x84262))+~P22(f312(x84261,f809(x84261,x84263,x84264,x84265)))+~P22(f312(f312(f314(x84265),x84262),x84264))
% 155.93/155.62 [8427]P22(f312(x84271,x84272))+~P22(f312(x84271,f809(x84271,x84273,x84274,x84275)))+~P22(f312(f312(f314(x84275),x84272),x84273))
% 155.93/155.62 [8704]~P19(x87042,x87043,x87041,x87044)+E(f312(x87041,f312(f86(x87042,x87043,x87044,x87041),x87045)),x87045)+~P22(f312(f312(f314(x87043),x87045),f312(f290(x87042,x87043,x87041),x87044)))
% 155.93/155.62 [8805]E(x88051,f127(x88052))+E(f312(f312(f147(x88052),x88053),f621(x88054,x88053,x88055,x88051,x88052)),x88051)+~E(f312(f312(f129(x88052),x88051),x88055),f312(f312(f147(x88052),x88053),x88054))
% 155.93/155.62 [8806]E(x88061,f127(x88062))+E(f312(f312(f147(x88062),x88063),f622(x88064,x88061,x88065,x88063,x88062)),x88061)+~E(f312(f312(f129(x88062),x88061),x88064),f312(f312(f147(x88062),x88063),x88065))
% 155.93/155.62 [8823]E(f312(f312(f147(x88232),x88233),f621(x88234,x88233,x88231,x88235,x88232)),x88235)+~E(f312(f312(f129(x88232),x88235),x88231),f312(f312(f147(x88232),x88233),x88234))+E(x88231,f312(f312(f147(x88232),x88233),x88234))
% 155.93/155.62 [8824]E(f312(f312(f147(x88241),x88242),f622(x88244,x88245,x88243,x88242,x88241)),x88245)+~E(f312(f312(f129(x88241),x88245),x88244),f312(f312(f147(x88241),x88242),x88243))+E(f312(f312(f147(x88241),x88242),x88243),x88244)
% 155.93/155.62 [8910]~E(f312(f290(x89103,x89102,x89104),f235(f861(x89103,a846))),f235(f861(x89102,a846)))+~E(f312(f290(x89101,x89103,x89105),f235(f861(x89101,a846))),f235(f861(x89103,a846)))+E(f312(f290(x89101,x89102,f312(f82(x89103,x89102,x89101,x89104),x89105)),f235(f861(x89101,a846))),f235(f861(x89102,a846)))
% 155.93/155.62 [9271]E(x92711,f127(x92712))+~E(f312(f312(f129(x92712),x92711),x92713),f312(f312(f147(x92712),x92715),x92714))+E(f312(f312(f129(x92712),f622(x92713,x92711,x92714,x92715,x92712)),x92713),x92714)
% 155.93/155.62 [9272]E(x92721,f127(x92722))+~E(f312(f312(f129(x92722),x92721),x92725),f312(f312(f147(x92722),x92724),x92723))+E(f312(f312(f129(x92722),f621(x92723,x92724,x92725,x92721,x92722)),x92725),x92723)
% 155.93/155.62 [9279]E(f312(f312(f129(x92792),f621(x92794,x92793,x92791,x92795,x92792)),x92791),x92794)+~E(f312(f312(f129(x92792),x92795),x92791),f312(f312(f147(x92792),x92793),x92794))+E(x92791,f312(f312(f147(x92792),x92793),x92794))
% 155.93/155.62 [9280]~E(f312(f312(f129(x92801),x92805),x92804),f312(f312(f147(x92801),x92802),x92803))+E(f312(f312(f129(x92801),f622(x92804,x92805,x92803,x92802,x92801)),x92804),x92803)+E(f312(f312(f147(x92801),x92802),x92803),x92804)
% 155.93/155.62 [9281]E(f312(f312(f129(x92811),x92815),f624(x92813,x92812,x92814,x92815,x92811)),x92812)+E(f312(f312(f129(x92811),x92812),f623(x92813,x92812,x92814,x92815,x92811)),x92815)+~E(f312(f312(f129(x92811),x92815),x92814),f312(f312(f129(x92811),x92812),x92813))
% 155.93/155.62 [9314]~P103(x93141)+P33(x93141,f312(f312(f150(x93142,x93141),x93143),f146(x93142,x93141,x93143,x93144,x93145)))+~P33(x93141,f312(f312(f150(x93142,x93141),x93143),x93145))
% 155.93/155.62 [9326]~P58(x93265,x93261,x93264,x93263)+P22(f312(f312(x93261,x93262),f514(x93263,x93264,x93261,x93265,x93262)))+~P22(f312(f312(f314(x93265),x93262),x93264))
% 155.93/155.62 [9430]~P22(f312(f312(f314(f860(x94301,x94301)),f312(f312(f239(x94301,x94301),x94305),x94303)),f287(x94301,x94304)))+P22(f312(f312(f314(f860(x94301,x94301)),f312(f312(f239(x94301,x94301),x94302),x94303)),f312(f312(f267(x94301,x94301,x94301),x94304),f287(x94301,x94304))))+~P22(f312(f312(f314(f860(x94301,x94301)),f312(f312(f239(x94301,x94301),x94302),x94305)),f312(f312(f267(x94301,x94301,x94301),x94304),f287(x94301,x94304))))
% 155.93/155.62 [9431]~P22(f312(f312(f314(f860(x94311,x94311)),f312(f312(f239(x94311,x94311),x94312),x94315)),f287(x94311,x94314)))+P22(f312(f312(f314(f860(x94311,x94311)),f312(f312(f239(x94311,x94311),x94312),x94313)),f312(f312(f267(x94311,x94311,x94311),x94314),f287(x94311,x94314))))+~P22(f312(f312(f314(f860(x94311,x94311)),f312(f312(f239(x94311,x94311),x94315),x94313)),f312(f312(f267(x94311,x94311,x94311),x94314),f287(x94311,x94314))))
% 155.93/155.62 [9434]P22(f312(f312(f314(f860(f854(x94341),f854(x94341))),f312(f312(f239(f854(x94341),f854(x94341)),x94342),x94343)),f154(x94341,f287(x94341,x94344))))+~P22(f312(f312(f314(f860(f854(x94341),f854(x94341))),f312(f312(f239(f854(x94341),f854(x94341)),x94342),x94345)),f154(x94341,f287(x94341,x94344))))+~P22(f312(f312(f314(f860(f854(x94341),f854(x94341))),f312(f312(f239(f854(x94341),f854(x94341)),x94345),x94343)),f154(x94341,f287(x94341,x94344))))
% 155.93/155.62 [9439]E(f312(f312(f129(x94391),x94392),f623(x94393,x94392,x94394,x94395,x94391)),x94395)+E(f312(f312(f129(x94391),f624(x94393,x94392,x94394,x94395,x94391)),x94393),x94394)+~E(f312(f312(f129(x94391),x94392),x94393),f312(f312(f129(x94391),x94395),x94394))
% 155.93/155.62 [9440]E(f312(f312(f129(x94401),x94402),f624(x94403,x94404,x94405,x94402,x94401)),x94404)+E(f312(f312(f129(x94401),f623(x94403,x94404,x94405,x94402,x94401)),x94405),x94403)+~E(f312(f312(f129(x94401),x94402),x94405),f312(f312(f129(x94401),x94404),x94403))
% 155.93/155.62 [9494]P22(f312(f312(f314(f860(x94941,x94941)),f312(f312(f239(x94941,x94941),x94942),x94943)),f312(f312(f267(x94941,x94941,x94941),x94944),f287(x94941,x94944))))+~P22(f312(f312(f314(f860(x94941,x94941)),f312(f312(f239(x94941,x94941),x94942),x94945)),f312(f312(f267(x94941,x94941,x94941),x94944),f287(x94941,x94944))))+~P22(f312(f312(f314(f860(x94941,x94941)),f312(f312(f239(x94941,x94941),x94945),x94943)),f312(f312(f267(x94941,x94941,x94941),x94944),f287(x94941,x94944))))
% 155.93/155.62 [9520]P39(x95201,x95202,x95203,x95204,x95205)+~E(f312(f190(f854(x95201)),x95204),f312(f190(f854(x95202)),x95205))+~P22(f312(f312(f249(x95201,x95202,a846),x95203),f686(x95205,x95204,x95203,x95202,x95201)))
% 155.93/155.62 [9521]P39(x95211,x95212,x95213,x95214,x95215)+~E(f312(f190(f854(x95211)),x95214),f312(f190(f854(x95212)),x95215))+~P22(f312(f312(f249(x95211,x95212,a846),x95213),f695(x95213,x95215,x95214,x95212,x95211)))
% 155.93/155.62 [9525]E(f312(f312(f129(x95251),f623(x95252,x95253,x95254,x95255,x95251)),x95254),x95252)+~E(f312(f312(f129(x95251),x95253),x95252),f312(f312(f129(x95251),x95255),x95254))+E(f312(f312(f129(x95251),f624(x95252,x95253,x95254,x95255,x95251)),x95252),x95254)
% 155.93/155.62 [9536]~P103(x95362)+E(f312(f312(f145(x95361,x95362,x95363),x95364),x95365),f312(f312(f147(x95361),x95364),x95365))+P22(f312(f312(f314(x95361),f722(x95364,x95363,x95365,x95361,x95362)),f312(f168(x95361),x95365)))
% 155.93/155.62 [9541]~P58(x95411,x95414,x95413,x95412)+~P22(f312(f312(f314(x95411),x95415),x95413))+P22(f312(f312(f314(x95411),f514(x95412,x95413,x95414,x95411,x95415)),x95412))
% 155.93/155.62 [9660]~P22(f312(f312(f314(f860(f861(x96601,a846),f861(x96601,a846))),f312(f312(f239(f861(x96601,a846),f861(x96601,a846)),x96604),x96603)),f303(x96601,x96602)))+~P22(f312(f312(f314(x96601),x96605),x96604))+P22(f312(f312(f314(x96601),f742(x96602,x96603,x96604,x96601,x96605)),x96603))
% 155.93/155.62 [9672]~P103(x96722)+E(f312(f312(f145(x96721,x96722,x96723),x96724),x96725),f312(f312(f147(x96721),x96724),x96725))+~P22(f312(f312(f227(x96722),f312(x96723,x96724)),f312(x96723,f722(x96724,x96723,x96725,x96721,x96722))))
% 155.93/155.62 [9865]P39(x98651,x98652,x98653,x98654,x98655)+~E(f312(f190(f854(x98651)),x98654),f312(f190(f854(x98652)),x98655))+~P22(f312(f312(x98653,f312(f312(f161(x98651),x98654),f696(x98655,x98654,x98653,x98652,x98651))),f312(f312(f161(x98652),x98655),f696(x98655,x98654,x98653,x98652,x98651))))
% 155.93/155.62 [9866]P39(x98661,x98662,x98663,x98664,x98665)+~E(f312(f190(f854(x98661)),x98664),f312(f190(f854(x98662)),x98665))+~P22(f312(f312(x98663,f312(f312(f161(x98661),x98664),f713(x98663,x98665,x98662,x98664,x98661))),f312(f312(f161(x98662),x98665),f713(x98663,x98665,x98662,x98664,x98661))))
% 155.93/155.62 [6461]~P12(x64612,x64615,x64611)+~P22(f312(f70(x64612),x64614))+E(f312(x64611,f312(f312(f289(x64612),x64613),x64614)),f312(f312(f73(x64612,x64612,x64615),x64613),x64614))
% 155.93/155.62 [6462]~E(x64623,x64624)+~E(x64622,x64625)+E(f312(f312(f289(x64621),x64622),f312(f312(f289(x64621),x64623),f189(f861(x64621,a846)))),f312(f312(f289(x64621),x64624),f312(f312(f289(x64621),x64625),f189(f861(x64621,a846)))))
% 155.93/155.62 [6475]P22(f312(x64752,x64755))+E(f172(x64751,x64752,f312(f312(f129(x64751),x64753),x64754)),f172(x64751,x64752,x64753))+~P22(f312(f312(f314(x64751),x64755),f312(f168(x64751),x64753)))
% 155.93/155.62 [6509]E(f312(x65091,x65092),f189(f861(x65093,a846)))+~E(f312(f312(f50(x65094,f861(x65093,a846)),x65095),x65091),f189(f861(x65093,a846)))+~P22(f312(f312(f314(x65094),x65092),x65095))
% 155.93/155.62 [6510]E(f312(x65101,x65102),f235(f861(x65103,a846)))+~E(f312(f312(f51(x65104,f861(x65103,a846)),x65105),x65101),f235(f861(x65103,a846)))+~P22(f312(f312(f314(x65104),x65102),x65105))
% 155.93/155.62 [6803]~P22(f312(f312(f195(x68031),x68033),x68035))+~P22(f312(f312(f195(x68032),x68035),x68034))+P22(f312(f312(f195(f36(x68031,x68032)),x68033),x68034))
% 155.93/155.62 [7014]~E(x70142,x70144)+~P136(x70141)+E(f312(f312(f89(x70141),f312(f312(f90(x70141),x70142),x70143)),f312(f312(f90(x70141),x70144),x70145)),f312(f312(f89(x70141),f312(f312(f90(x70141),x70142),x70145)),f312(f312(f90(x70141),x70144),x70143)))
% 155.93/155.62 [7076]~P31(x70761)+~P22(f312(f312(f314(x70764),x70763),x70765))+P22(f312(f312(f227(x70761),f312(x70762,x70763)),f312(f312(f50(x70764,x70761),x70765),x70762)))
% 155.93/155.62 [7126]~P104(x71261)+P22(f312(f312(f227(x71261),f312(x71262,x71263)),f312(x71264,x71263)))+~P22(f312(f312(f227(f861(x71265,x71261)),x71262),x71264))
% 155.93/155.62 [7235]E(x72351,x72352)+E(x72353,x72351)+~E(f312(f312(f289(x72354),x72351),f312(f312(f289(x72354),x72355),f189(f861(x72354,a846)))),f312(f312(f289(x72354),x72352),f312(f312(f289(x72354),x72353),f189(f861(x72354,a846)))))
% 155.93/155.62 [7236]E(x72361,x72362)+E(x72363,x72361)+~E(f312(f312(f289(x72364),x72363),f312(f312(f289(x72364),x72362),f189(f861(x72364,a846)))),f312(f312(f289(x72364),x72365),f312(f312(f289(x72364),x72361),f189(f861(x72364,a846)))))
% 155.93/155.62 [7237]E(x72371,x72372)+E(x72371,x72373)+~E(f312(f312(f289(x72374),x72373),f312(f312(f289(x72374),x72372),f189(f861(x72374,a846)))),f312(f312(f289(x72374),x72375),f312(f312(f289(x72374),x72371),f189(f861(x72374,a846)))))
% 155.93/155.62 [7238]E(x72381,x72382)+E(x72381,x72383)+~E(f312(f312(f289(x72384),x72381),f312(f312(f289(x72384),x72385),f189(f861(x72384,a846)))),f312(f312(f289(x72384),x72382),f312(f312(f289(x72384),x72383),f189(f861(x72384,a846)))))
% 155.93/155.62 [7769]P19(x77691,x77692,x77693,x77694)+~P19(x77691,x77692,x77693,x77695)+~P22(f312(f312(f227(f861(x77691,a846)),x77694),x77695))
% 155.93/155.62 [7775]~P22(f312(f312(f227(a853),x77755),x77753))+~P22(f312(f312(f312(f312(a198,x77751),x77752),x77755),x77754))+P22(f312(f312(f312(f312(a198,x77751),x77752),x77753),x77754))
% 155.93/155.62 [7865]P22(f312(x78651,x78652))+~P22(f312(f312(f195(x78654),x78652),x78655))+P22(f312(f312(f195(f33(x78651,x78653,x78654)),x78652),x78655))
% 155.93/155.62 [7892]~P22(f312(x78921,x78924))+~P22(f312(f312(f195(x78922),x78924),x78925))+P22(f312(f312(f195(f33(x78921,x78922,x78923)),x78924),x78925))
% 155.93/155.62 [7941]E(x79411,x79412)+~E(f312(f290(x79413,x79414,x79415),x79411),f312(f290(x79413,x79414,x79415),x79412))+~P19(x79413,x79414,x79415,f312(f312(f124(f861(x79413,a846)),x79411),x79412))
% 155.93/155.62 [8017]P22(f312(x80172,x80174))+E(f312(f312(f134(x80171),f312(f190(f854(x80171)),f172(x80171,x80172,x80173))),x80173),f312(f312(f147(x80171),x80174),x80175))+~E(f312(f312(f129(x80171),f172(x80171,x80172,x80173)),f312(f312(f147(x80171),x80174),x80175)),x80173)
% 155.93/155.62 [8049]~P19(x80491,x80492,x80493,x80495)+~P19(x80491,x80492,x80493,x80494)+P19(x80491,x80492,x80493,f312(f312(f115(f861(x80491,a846)),x80494),x80495))
% 155.93/155.62 [8159]~P26(x81591)+E(f312(f312(f89(x81591),f312(x81592,x81593)),f312(f162(x81591),f312(f312(f150(x81594,x81591),x81592),f166(x81594,x81593,x81595)))),f312(f162(x81591),f312(f312(f150(x81594,x81591),x81592),x81595)))+~P22(f312(f312(f314(x81594),x81593),f312(f168(x81594),x81595)))
% 155.93/155.62 [8253]~P103(x82531)+~P33(x82531,f312(f312(f150(x82532,x82531),x82533),x82535))+P33(x82531,f312(f312(f150(x82532,x82531),x82533),f312(f312(f145(x82532,x82531,x82533),x82534),x82535)))
% 155.93/155.62 [8330]P22(f312(x83301,x83302))+P22(f312(f312(f195(x83303),x83302),x83304))+~P22(f312(f312(f195(f33(x83301,x83305,x83303)),x83302),x83304))
% 155.93/155.62 [8341]~P31(x83411)+P22(f312(f312(f227(x83411),f312(f312(f50(x83412,x83411),x83413),x83414)),f312(f312(f50(x83412,x83411),x83415),x83414)))+~P22(f312(f312(f227(f861(x83412,a846)),x83413),x83415))
% 155.93/155.62 [8342]~P31(x83421)+P22(f312(f312(f227(x83421),f312(f312(f51(x83422,x83421),x83423),x83424)),f312(f312(f51(x83422,x83421),x83425),x83424)))+~P22(f312(f312(f227(f861(x83422,a846)),x83425),x83423))
% 155.93/155.62 [8355]~P22(f312(x83554,x83552))+P22(f312(f312(f195(x83551),x83552),x83553))+~P22(f312(f312(f195(f33(x83554,x83551,x83555)),x83552),x83553))
% 155.93/155.62 [8381]~P103(x83813)+P22(f312(f133(x83811),x83812))+~P22(f312(f133(x83811),f312(f312(f145(x83811,x83813,x83814),x83815),x83812)))
% 155.93/155.62 [8391]P22(f312(f312(f195(x83911),x83912),x83913))+P22(f312(f312(f195(x83914),x83912),x83913))+~P22(f312(f312(f195(f33(x83915,x83911,x83914)),x83912),x83913))
% 155.93/155.62 [8523]~P103(x85231)+~P22(f312(f312(f314(x85232),x85233),f312(f168(x85232),x85234)))+~P22(f312(f133(x85232),f312(f312(f145(x85232,x85231,x85235),x85233),x85234)))
% 155.93/155.62 [8600]~P103(x86001)+P33(x86001,f312(f312(f150(x86002,x86001),x86003),x86004))+~P33(x86001,f312(f312(f150(x86002,x86001),x86003),f312(f312(f145(x86002,x86001,x86003),x86005),x86004)))
% 155.93/155.62 [8693]~P103(x86932)+E(f312(f312(f145(x86931,x86932,x86933),x86934),x86935),f146(x86931,x86932,x86933,x86934,x86935))+P22(f312(f312(f314(x86932),f312(x86933,x86934)),f312(f290(x86931,x86932,x86933),f312(f168(x86931),x86935))))
% 155.93/155.62 [8765]~P103(x87652)+E(f146(x87651,x87652,x87653,x87654,x87655),x87655)+~P22(f312(f312(f314(x87652),f312(x87653,x87654)),f312(f290(x87651,x87652,x87653),f312(f168(x87651),x87655))))
% 155.93/155.62 [8781]~P19(x87812,x87811,x87813,x87815)+P22(f312(f312(f228(f861(x87811,a846)),f312(f290(x87812,x87811,x87813),x87814)),f312(f290(x87812,x87811,x87813),x87815)))+~P22(f312(f312(f228(f861(x87812,a846)),x87814),x87815))
% 155.93/155.62 [8951]~P19(x89511,x89512,x89513,f235(f861(x89511,a846)))+~P22(f312(f312(f227(f861(x89512,a846)),x89514),f312(f290(x89511,x89512,x89513),x89515)))+P22(f312(f312(f227(f861(x89511,a846)),f312(f291(x89511,x89512,x89513),x89514)),x89515))
% 155.93/155.62 [8970]~E(f312(f290(x89703,x89701,x89704),f235(f861(x89703,a846))),f235(f861(x89701,a846)))+P22(f312(f312(f227(f861(x89701,a846)),x89702),f312(f290(x89703,x89701,x89704),x89705)))+~P22(f312(f312(f227(f861(x89703,a846)),f312(f291(x89703,x89701,x89704),x89702)),x89705))
% 155.93/155.62 [8993]~E(f312(f219(x89932),x89934),f312(f312(f173(x89931,x89932),x89935),x89933))+~P22(f312(f133(x89931),f312(f312(f150(f860(x89931,x89932),x89931),f246(x89931,x89932)),x89935)))+P22(f312(f312(f314(f860(x89931,x89932)),f312(f312(f239(x89931,x89932),x89933),x89934)),f312(f168(f860(x89931,x89932)),x89935)))
% 155.93/155.62 [9073]~P19(x90731,x90734,x90735,f235(f861(x90731,a846)))+~P22(f312(f312(f227(f861(x90734,a846)),f312(f290(x90731,x90734,x90735),x90732)),f312(f290(x90731,x90734,x90735),x90733)))+P22(f312(f312(f227(f861(x90731,a846)),x90732),x90733))
% 155.93/155.62 [9140]E(f312(f219(x91401),x91402),f312(f312(f173(x91403,x91401),x91404),x91405))+~P22(f312(f133(x91403),f312(f312(f150(f860(x91403,x91401),x91403),f246(x91403,x91401)),x91404)))+~P22(f312(f312(f314(f860(x91403,x91401)),f312(f312(f239(x91403,x91401),x91405),x91402)),f312(f168(f860(x91403,x91401)),x91404)))
% 155.93/155.62 [9142]E(f312(f312(f173(x91421,x91422),x91423),x91424),f312(f219(x91422),x91425))+~P22(f312(f133(x91421),f312(f312(f150(f860(x91421,x91422),x91421),f246(x91421,x91422)),x91423)))+~P22(f312(f312(f314(f860(x91421,x91422)),f312(f312(f239(x91421,x91422),x91424),x91425)),f312(f168(f860(x91421,x91422)),x91423)))
% 155.93/155.62 [9198]~P25(x91981)+~E(f312(x91983,f665(x91983,x91984,x91985,x91982,x91981)),f2(x91981))+E(f312(f162(x91981),f312(f312(f150(x91982,x91981),x91983),f312(f132(x91982,x91984),x91985))),f312(f162(x91981),f312(f312(f150(x91982,x91981),x91983),x91985)))
% 155.93/155.62 [9464]~P25(x94641)+~P22(f312(x94644,f665(x94643,x94644,x94645,x94642,x94641)))+E(f312(f162(x94641),f312(f312(f150(x94642,x94641),x94643),f312(f132(x94642,x94644),x94645))),f312(f162(x94641),f312(f312(f150(x94642,x94641),x94643),x94645)))
% 155.93/155.62 [9539]~P31(x95395)+P22(f312(f312(f314(x95391),f636(x95392,x95393,x95391,x95394,x95395)),x95393))+P22(f312(f312(f227(x95395),x95394),f312(f312(f51(x95391,x95395),x95393),x95392)))
% 155.93/155.62 [9542]~P25(x95421)+E(f312(f162(x95421),f312(f312(f150(x95422,x95421),x95423),f312(f132(x95422,x95424),x95425))),f312(f162(x95421),f312(f312(f150(x95422,x95421),x95423),x95425)))+P22(f312(f312(f314(x95422),f665(x95423,x95424,x95425,x95422,x95421)),f312(f168(x95422),x95425)))
% 155.93/155.62 [9584]P39(x95841,x95842,x95843,x95844,x95845)+~E(f312(f190(f854(x95842)),x95845),f312(f190(f854(x95841)),x95844))+P22(f312(f312(f228(a853),f696(x95845,x95844,x95843,x95842,x95841)),f312(f190(f854(x95841)),x95844)))
% 155.93/155.62 [9585]P39(x95851,x95852,x95853,x95854,x95855)+~E(f312(f190(f854(x95852)),x95855),f312(f190(f854(x95851)),x95854))+P22(f312(f312(f228(a853),f713(x95853,x95855,x95852,x95854,x95851)),f312(f190(f854(x95851)),x95854)))
% 155.93/155.62 [9673]~P31(x96731)+~P22(f312(f312(f227(x96731),x96732),f312(x96735,f636(x96735,x96734,x96733,x96732,x96731))))+P22(f312(f312(f227(x96731),x96732),f312(f312(f51(x96733,x96731),x96734),x96735)))
% 155.93/155.62 [9703]~P72(x97031)+~P22(f312(f70(x97032),x97035))+E(f312(f312(f312(f74(x97031,x97032,f90(x97031)),f312(f312(f18(x97032,x97031,x97031),f312(f312(f8(x97031,f861(x97031,x97031),x97032),f90(x97031)),x97033)),x97034)),f87(x97031)),x97035),f312(f312(f90(x97031),f312(f312(f312(f74(x97031,x97032,f90(x97031)),x97033),f87(x97031)),x97035)),f312(f312(f312(f74(x97031,x97032,f90(x97031)),x97034),f87(x97031)),x97035)))
% 155.93/155.62 [9767]~P22(f312(f312(f314(f860(f861(x97671,a846),f861(x97671,a846))),f312(f312(f239(f861(x97671,a846),f861(x97671,a846)),x97675),x97674)),f303(x97671,x97673)))+~P22(f312(f312(f314(x97671),x97672),x97675))+P22(f312(f312(f314(f860(x97671,x97671)),f312(f312(f239(x97671,x97671),x97672),f742(x97673,x97674,x97675,x97671,x97672))),x97673))
% 155.93/155.62 [9906]~P22(f312(f312(f314(f860(f854(x99061),f854(x99061))),f312(f312(f239(f854(x99061),f854(x99061)),f312(f312(f129(x99061),x99065),x99062)),f312(f312(f129(x99061),x99065),x99063))),f143(x99061,x99064)))+P22(f312(f312(f314(f860(f854(x99061),f854(x99061))),f312(f312(f239(f854(x99061),f854(x99061)),x99062),x99063)),f143(x99061,x99064)))+P22(f312(f312(f314(f860(x99061,x99061)),f312(f312(f239(x99061,x99061),f629(x99064,x99063,x99062,x99065,x99061)),f629(x99064,x99063,x99062,x99065,x99061))),x99064))
% 155.93/155.62 [7055]~E(f312(f190(f854(x70551)),x70553),f312(f190(f854(x70552)),x70554))+E(f312(f312(f173(x70551,x70552),f312(f312(f177(x70551,x70552),x70553),x70554)),x70555),f192(x70552))+P22(f312(f312(f314(x70551),x70555),f312(f168(x70551),x70553)))
% 155.93/155.62 [7129]~E(x71293,x71295)+E(f312(f312(f161(x71291),f312(f312(f155(x71291,x71292),x71293),x71294)),x71295),x71294)+~P22(f312(f312(f228(a853),x71293),f312(f190(f854(x71291)),x71292)))
% 155.93/155.62 [7228]~E(f312(f312(f129(x72281),x72282),x72284),f312(f312(f129(x72281),x72283),x72285))+E(f312(f312(f169(x72281),f312(f190(f854(x72281)),x72282)),x72283),x72282)+P22(f312(f312(f227(a853),f312(f190(f854(x72281)),x72283)),f312(f190(f854(x72281)),x72282)))
% 155.93/155.62 [7247]~E(x72475,x72472)+P22(f312(x72471,x72472))+P22(f312(f312(f312(f312(a198,f35(x72471,x72473)),x72472),x72474),x72475))
% 155.93/155.62 [7732]~E(f312(f312(f129(x77321),x77322),x77324),f312(f312(f129(x77321),x77323),x77325))+E(f312(f312(f169(x77321),f312(f190(f854(x77321)),x77322)),x77323),x77322)+~P22(f312(f312(f227(a853),f312(f190(f854(x77321)),x77322)),f312(f190(f854(x77321)),x77323)))
% 155.93/155.62 [7756]~P22(f312(f70(x77561),f312(x77564,x77565)))+~P22(f312(f312(f314(x77562),x77565),x77563))+P22(f312(f70(x77561),f312(f312(f51(x77562,f861(x77561,a846)),x77563),x77564)))
% 155.93/155.62 [7803]~E(f312(f190(f854(x78031)),x78032),f312(f190(f854(x78033)),x78034))+~E(f312(f312(f173(x78031,x78033),f312(f312(f177(x78031,x78033),x78032),x78034)),x78035),f192(x78033))+~P22(f312(f312(f314(x78031),x78035),f312(f168(x78031),x78032)))
% 155.93/155.62 [7926]~P50(x79261,x79263,x79265)+~P50(x79261,x79262,x79264)+P50(x79261,f312(f312(f124(f861(x79261,a846)),x79262),x79263),f312(f312(f124(f861(f860(x79261,x79261),a846)),x79264),x79265))
% 155.93/155.62 [7927]~P50(x79271,x79273,x79275)+~P50(x79271,x79272,x79274)+P50(x79271,f312(f312(f115(f861(x79271,a846)),x79272),x79273),f312(f312(f115(f861(f860(x79271,x79271),a846)),x79274),x79275))
% 155.93/155.62 [8010]E(x80101,x80102)+P22(f312(x80103,x80101))+~P22(f312(f312(f312(f312(a198,f35(x80103,x80104)),x80101),x80105),x80102))
% 155.93/155.62 [8289]E(f312(f312(f239(x82891,x82892),f312(f312(f161(x82891),x82893),x82894)),f312(f312(f161(x82892),x82895),x82894)),f312(f312(f161(f860(x82891,x82892)),f312(f312(f177(x82891,x82892),x82893),x82895)),x82894))+~P22(f312(f312(f228(a853),x82894),f312(f190(f854(x82891)),x82893)))+~P22(f312(f312(f228(a853),x82894),f312(f190(f854(x82892)),x82895)))
% 155.93/155.62 [8455]~P50(x84551,x84553,x84554)+P22(f312(f312(f314(x84551),x84552),x84553))+~P22(f312(f312(f314(f860(x84551,x84551)),f312(f312(f239(x84551,x84551),x84555),x84552)),x84554))
% 155.93/155.62 [8456]~P50(x84561,x84563,x84564)+P22(f312(f312(f314(x84561),x84562),x84563))+~P22(f312(f312(f314(f860(x84561,x84561)),f312(f312(f239(x84561,x84561),x84562),x84565)),x84564))
% 155.93/155.62 [8457]~P3(x84571,x84573,x84574)+P22(f312(f312(f314(x84571),x84572),x84573))+~P22(f312(f312(f314(f860(x84571,x84571)),f312(f312(f239(x84571,x84571),x84575),x84572)),x84574))
% 155.93/155.62 [8458]~P3(x84581,x84583,x84584)+P22(f312(f312(f314(x84581),x84582),x84583))+~P22(f312(f312(f314(f860(x84581,x84581)),f312(f312(f239(x84581,x84581),x84582),x84585)),x84584))
% 155.93/155.62 [8714]~P3(x87141,x87145,x87142)+E(f312(f264(x87141,x87141,x87142),f312(f312(f289(x87141),x87143),f189(f861(x87141,a846)))),f312(f264(x87141,x87141,x87142),f312(f312(f289(x87141),x87144),f189(f861(x87141,a846)))))+~P22(f312(f312(f314(f860(x87141,x87141)),f312(f312(f239(x87141,x87141),x87143),x87144)),x87142))
% 155.93/155.62 [8793]~P22(f312(f312(f312(f312(a198,x87932),x87933),x87934),x87935))+~P22(f312(f312(f312(f312(a198,f35(x87931,x87932)),x87935),x87934),x87933))+P22(f312(f312(f312(f312(a198,f35(x87931,x87932)),x87933),x87934),x87933))
% 155.93/155.62 [8907]P22(f312(x89071,x89072))+~P22(f312(f312(f314(x89073),x89072),x89075))+P22(f312(f312(f314(x89073),f809(x89071,x89074,x89075,x89073)),f312(f312(f124(f861(x89073,a846)),x89075),x89074)))
% 155.93/155.62 [8908]P22(f312(x89081,x89082))+~P22(f312(f312(f314(x89083),x89082),x89084))+P22(f312(f312(f314(x89083),f809(x89081,x89084,x89085,x89083)),f312(f312(f124(f861(x89083,a846)),x89085),x89084)))
% 155.93/155.62 [8916]~P22(f312(x89162,x89165))+~P22(f312(f312(f314(x89161),x89165),x89164))+P22(f312(f312(f314(x89161),f806(x89162,x89163,x89164,x89161)),f312(f312(f124(f861(x89161,a846)),x89164),x89163)))
% 155.93/155.62 [8917]~P22(f312(x89172,x89175))+~P22(f312(f312(f314(x89171),x89175),x89173))+P22(f312(f312(f314(x89171),f806(x89172,x89173,x89174,x89171)),f312(f312(f124(f861(x89171,a846)),x89174),x89173)))
% 155.93/155.62 [8932]~P22(f312(f312(f227(f861(x89321,a846)),x89325),x89323))+~P22(f312(f312(f227(f861(x89321,a846)),x89322),x89324))+P22(f312(f312(f227(f861(x89321,a846)),f312(f312(f21(f861(x89321,a846)),x89322),x89323)),f312(f312(f21(f861(x89321,a846)),x89324),x89325)))
% 155.93/155.62 [8933]~P22(f312(f312(f227(f861(x89331,a846)),x89333),x89335))+~P22(f312(f312(f227(f861(x89331,a846)),x89332),x89334))+P22(f312(f312(f227(f861(x89331,a846)),f312(f312(f124(f861(x89331,a846)),x89332),x89333)),f312(f312(f124(f861(x89331,a846)),x89334),x89335)))
% 155.93/155.62 [8934]~P22(f312(f312(f227(f861(x89341,a846)),x89343),x89345))+~P22(f312(f312(f227(f861(x89341,a846)),x89342),x89344))+P22(f312(f312(f227(f861(x89341,a846)),f312(f312(f115(f861(x89341,a846)),x89342),x89343)),f312(f312(f115(f861(x89341,a846)),x89344),x89345)))
% 155.93/155.62 [9019]~E(f312(f190(f854(x90191)),x90193),f312(f190(f854(x90192)),x90194))+E(f312(f312(f173(x90191,x90192),f312(f312(f177(x90191,x90192),x90193),x90194)),x90195),f312(f219(x90192),f590(x90195,x90194,x90192,x90193,x90191)))+~P22(f312(f312(f314(x90191),x90195),f312(f168(x90191),x90193)))
% 155.93/155.62 [9023]P22(f312(f312(f314(f860(x90231,x90231)),f312(f312(f239(x90231,x90231),x90232),x90233)),f306(x90231,x90234,x90235)))+~P22(f312(f312(f227(a853),f312(x90234,x90232)),f312(x90234,x90233)))+~P22(f312(f312(f314(f860(x90231,x90231)),f312(f312(f239(x90231,x90231),x90232),x90233)),x90235))
% 155.93/155.62 [9208]P22(f312(f312(f314(f860(x92081,x92081)),f312(f312(f239(x92081,x92081),x92082),x92083)),f287(x92081,x92084)))+~P22(f312(f312(f314(f860(x92081,x92081)),f312(f312(f239(x92081,x92081),x92082),x92085)),f287(x92081,x92084)))+~P22(f312(f312(f314(f860(x92081,x92081)),f312(f312(f239(x92081,x92081),x92085),x92083)),x92084))
% 155.93/155.62 [9209]P22(f312(f312(f314(f860(x92091,x92091)),f312(f312(f239(x92091,x92091),x92092),x92093)),f287(x92091,x92094)))+~P22(f312(f312(f314(f860(x92091,x92091)),f312(f312(f239(x92091,x92091),x92095),x92093)),f287(x92091,x92094)))+~P22(f312(f312(f314(f860(x92091,x92091)),f312(f312(f239(x92091,x92091),x92092),x92095)),x92094))
% 155.93/155.62 [9302]E(x93021,x93022)+E(f312(a126,f766(x93023,x93024,x93021,x93022,x93025)),x93024)+~P22(f312(f312(f314(f860(x93025,x93025)),f312(f312(f239(x93025,x93025),x93022),x93021)),f312(f312(f184(f860(x93025,x93025),a846),x93024),x93023)))
% 155.93/155.62 [9303]E(x93031,x93032)+E(f312(a126,f768(x93033,x93034,x93031,x93032,x93035)),x93034)+~P22(f312(f312(f314(f860(x93035,x93035)),f312(f312(f239(x93035,x93035),x93032),x93031)),f312(f312(f184(f860(x93035,x93035),a846),x93034),x93033)))
% 155.93/155.62 [9304]E(x93041,f2(a853))+E(f312(a126,f766(x93042,x93041,x93043,x93044,x93045)),x93041)+~P22(f312(f312(f314(f860(x93045,x93045)),f312(f312(f239(x93045,x93045),x93044),x93043)),f312(f312(f184(f860(x93045,x93045),a846),x93041),x93042)))
% 155.93/155.62 [9305]E(x93051,f2(a853))+E(f312(a126,f768(x93052,x93051,x93053,x93054,x93055)),x93051)+~P22(f312(f312(f314(f860(x93055,x93055)),f312(f312(f239(x93055,x93055),x93054),x93053)),f312(f312(f184(f860(x93055,x93055),a846),x93051),x93052)))
% 155.93/155.62 [9322]P22(f312(f312(f314(f860(x93221,x93221)),f312(f312(f239(x93221,x93221),x93222),x93223)),f312(f312(f267(x93221,x93221,x93221),x93224),f287(x93221,x93224))))+~P22(f312(f312(f314(f860(x93221,x93221)),f312(f312(f239(x93221,x93221),x93222),x93225)),x93224))+~P22(f312(f312(f314(f860(x93221,x93221)),f312(f312(f239(x93221,x93221),x93225),x93223)),x93224))
% 155.93/155.62 [9330]~P22(f312(f312(f314(f860(x93301,x93301)),f312(f312(f239(x93301,x93301),x93302),x93305)),f287(x93301,x93304)))+P22(f312(f312(f314(f860(x93301,x93301)),f312(f312(f239(x93301,x93301),x93302),x93303)),f312(f312(f267(x93301,x93301,x93301),x93304),f287(x93301,x93304))))+~P22(f312(f312(f314(f860(x93301,x93301)),f312(f312(f239(x93301,x93301),x93305),x93303)),x93304))
% 155.93/155.62 [9367]~P3(x93671,x93675,x93672)+~P22(f312(f312(f314(f860(x93671,x93671)),f312(f312(f239(x93671,x93671),x93673),x93674)),x93672))+P22(f312(f312(f227(f861(x93671,a846)),f312(f264(x93671,x93671,x93672),f312(f312(f289(x93671),x93673),f189(f861(x93671,a846))))),f312(f264(x93671,x93671,x93672),f312(f312(f289(x93671),x93674),f189(f861(x93671,a846))))))
% 155.93/155.62 [9389]E(x93891,x93892)+P22(f312(f312(f312(f312(a198,x93893),x93891),x93894),f341(x93892,x93894,x93891,x93893,x93895)))+~P22(f312(f312(f312(f312(a198,f35(x93895,x93893)),x93891),x93894),x93892))
% 155.93/155.62 [9390]E(x93901,x93902)+P22(f312(f312(f312(f312(a198,x93903),x93901),x93904),f386(x93902,x93904,x93901,x93903,x93905)))+~P22(f312(f312(f312(f312(a198,f35(x93905,x93903)),x93901),x93904),x93902))
% 155.93/155.62 [9395]~P22(f312(x93955,x93952))+P22(f312(f312(f312(f312(a198,x93951),x93952),x93953),f341(x93954,x93953,x93952,x93951,x93955)))+~P22(f312(f312(f312(f312(a198,f35(x93955,x93951)),x93952),x93953),x93954))
% 155.93/155.62 [9396]~P22(f312(x93965,x93962))+P22(f312(f312(f312(f312(a198,x93961),x93962),x93963),f386(x93964,x93963,x93962,x93961,x93965)))+~P22(f312(f312(f312(f312(a198,f35(x93965,x93961)),x93962),x93963),x93964))
% 155.93/155.62 [9423]P22(f312(f312(f314(f860(x94231,x94231)),f312(f312(f239(x94231,x94231),x94232),x94233)),f312(f312(f267(x94231,x94231,x94231),x94234),f287(x94231,x94234))))+~P22(f312(f312(f314(f860(x94231,x94231)),f312(f312(f239(x94231,x94231),x94232),x94235)),f312(f312(f267(x94231,x94231,x94231),x94234),f287(x94231,x94234))))+~P22(f312(f312(f314(f860(x94231,x94231)),f312(f312(f239(x94231,x94231),x94235),x94233)),x94234))
% 155.93/155.62 [9424]P22(f312(f312(f314(f860(x94241,x94241)),f312(f312(f239(x94241,x94241),x94242),x94243)),f312(f312(f267(x94241,x94241,x94241),x94244),f287(x94241,x94244))))+~P22(f312(f312(f314(f860(x94241,x94241)),f312(f312(f239(x94241,x94241),x94245),x94243)),f312(f312(f267(x94241,x94241,x94241),x94244),f287(x94241,x94244))))+~P22(f312(f312(f314(f860(x94241,x94241)),f312(f312(f239(x94241,x94241),x94242),x94245)),x94244))
% 155.93/155.62 [9473]~P22(f312(f75(x94731,x94731,x94734,x94732,x94733),x94735))+P22(f312(f312(f314(x94731),x94732),x94733))+P22(f312(f71(x94731,x94734,f312(f312(f289(x94731),x94732),x94733)),x94735))
% 155.93/155.62 [9514]~E(f312(f290(x95143,x95142,x95145),x95144),x95141)+E(x95141,f189(f861(x95142,a846)))+P22(f312(f312(f227(f861(x95143,a846)),f312(f290(x95142,x95143,f829(x95144,x95143,x95142,x95141)),x95141)),x95144))
% 155.93/155.62 [9554]~P31(x95545)+P22(f312(f312(f314(x95541),f409(x95542,x95543,x95544,x95541,x95545)),x95544))+P22(f312(f312(f227(x95545),f312(f312(f50(x95541,x95545),x95544),x95543)),x95542))
% 155.93/155.62 [9605]P39(x96051,x96052,x96053,x96054,x96055)+~E(f312(f190(f854(x96051)),x96054),f312(f190(f854(x96052)),x96055))+P22(f312(f312(f314(f860(x96051,x96052)),f686(x96055,x96054,x96053,x96052,x96051)),f312(f168(f860(x96051,x96052)),f312(f312(f177(x96051,x96052),x96054),x96055))))
% 155.93/155.62 [9606]P39(x96061,x96062,x96063,x96064,x96065)+~E(f312(f190(f854(x96061)),x96064),f312(f190(f854(x96062)),x96065))+P22(f312(f312(f314(f860(x96061,x96062)),f695(x96063,x96065,x96064,x96062,x96061)),f312(f168(f860(x96061,x96062)),f312(f312(f177(x96061,x96062),x96064),x96065))))
% 155.93/155.62 [9734]E(x97341,x97342)+P22(f312(f312(f312(f312(a198,f35(x97343,x97344)),f341(x97341,x97345,x97342,x97344,x97343)),x97345),x97341))+~P22(f312(f312(f312(f312(a198,f35(x97343,x97344)),x97342),x97345),x97341))
% 155.93/155.62 [9735]E(x97351,x97352)+P22(f312(f312(f312(f312(a198,f35(x97353,x97354)),f386(x97351,x97355,x97352,x97354,x97353)),x97355),x97351))+~P22(f312(f312(f312(f312(a198,f35(x97353,x97354)),x97352),x97355),x97351))
% 155.93/155.62 [9737]~P22(f312(x97371,x97375))+P22(f312(f312(f312(f312(a198,f35(x97371,x97372)),f341(x97373,x97374,x97375,x97372,x97371)),x97374),x97373))+~P22(f312(f312(f312(f312(a198,f35(x97371,x97372)),x97375),x97374),x97373))
% 155.93/155.62 [9738]~P22(f312(x97381,x97385))+P22(f312(f312(f312(f312(a198,f35(x97381,x97382)),f386(x97383,x97384,x97385,x97382,x97381)),x97384),x97383))+~P22(f312(f312(f312(f312(a198,f35(x97381,x97382)),x97385),x97384),x97383))
% 155.93/155.62 [9745]E(x97451,x97452)+P22(f312(f312(f314(f860(x97453,x97453)),f312(f312(f239(x97453,x97453),x97451),f767(x97454,x97455,x97452,x97451,x97453))),x97454))+~P22(f312(f312(f314(f860(x97453,x97453)),f312(f312(f239(x97453,x97453),x97451),x97452)),f312(f312(f184(f860(x97453,x97453),a846),x97455),x97454)))
% 155.93/155.62 [9746]E(x97461,f2(a853))+P22(f312(f312(f314(f860(x97462,x97462)),f312(f312(f239(x97462,x97462),x97463),f767(x97464,x97461,x97465,x97463,x97462))),x97464))+~P22(f312(f312(f314(f860(x97462,x97462)),f312(f312(f239(x97462,x97462),x97463),x97465)),f312(f312(f184(f860(x97462,x97462),a846),x97461),x97464)))
% 155.93/155.62 [9792]~P31(x97921)+~P22(f312(f312(f227(x97921),f312(x97924,f409(x97925,x97924,x97923,x97922,x97921))),x97925))+P22(f312(f312(f227(x97921),f312(f312(f50(x97922,x97921),x97923),x97924)),x97925))
% 155.93/155.62 [9835]E(x98351,x98352)+P22(f312(f312(f314(f860(x98353,x98353)),f312(f312(f239(x98353,x98353),f769(x98354,x98355,x98351,x98352,x98353)),x98351)),x98354))+~P22(f312(f312(f314(f860(x98353,x98353)),f312(f312(f239(x98353,x98353),x98352),x98351)),f312(f312(f184(f860(x98353,x98353),a846),x98355),x98354)))
% 155.93/155.62 [9836]E(x98361,f2(a853))+P22(f312(f312(f314(f860(x98362,x98362)),f312(f312(f239(x98362,x98362),f769(x98363,x98361,x98364,x98365,x98362)),x98364)),x98363))+~P22(f312(f312(f314(f860(x98362,x98362)),f312(f312(f239(x98362,x98362),x98365),x98364)),f312(f312(f184(f860(x98362,x98362),a846),x98361),x98363)))
% 155.93/155.62 [9840]E(x98401,x98402)+P22(f312(f312(f314(f860(x98403,x98403)),f312(f312(f239(x98403,x98403),x98401),f769(x98404,x98405,x98402,x98401,x98403))),f312(f312(f184(f860(x98403,x98403),a846),f768(x98404,x98405,x98402,x98401,x98403)),x98404)))+~P22(f312(f312(f314(f860(x98403,x98403)),f312(f312(f239(x98403,x98403),x98401),x98402)),f312(f312(f184(f860(x98403,x98403),a846),x98405),x98404)))
% 155.93/155.62 [9841]E(x98411,f2(a853))+P22(f312(f312(f314(f860(x98412,x98412)),f312(f312(f239(x98412,x98412),x98413),f769(x98414,x98411,x98415,x98413,x98412))),f312(f312(f184(f860(x98412,x98412),a846),f768(x98414,x98411,x98415,x98413,x98412)),x98414)))+~P22(f312(f312(f314(f860(x98412,x98412)),f312(f312(f239(x98412,x98412),x98413),x98415)),f312(f312(f184(f860(x98412,x98412),a846),x98411),x98414)))
% 155.93/155.62 [9897]E(x98971,x98972)+P22(f312(f312(f314(f860(x98973,x98973)),f312(f312(f239(x98973,x98973),f767(x98974,x98975,x98971,x98972,x98973)),x98971)),f312(f312(f184(f860(x98973,x98973),a846),f766(x98974,x98975,x98971,x98972,x98973)),x98974)))+~P22(f312(f312(f314(f860(x98973,x98973)),f312(f312(f239(x98973,x98973),x98972),x98971)),f312(f312(f184(f860(x98973,x98973),a846),x98975),x98974)))
% 155.93/155.62 [9898]E(x98981,f2(a853))+P22(f312(f312(f314(f860(x98982,x98982)),f312(f312(f239(x98982,x98982),f767(x98983,x98981,x98984,x98985,x98982)),x98984)),f312(f312(f184(f860(x98982,x98982),a846),f766(x98983,x98981,x98984,x98985,x98982)),x98983)))+~P22(f312(f312(f314(f860(x98982,x98982)),f312(f312(f239(x98982,x98982),x98985),x98984)),f312(f312(f184(f860(x98982,x98982),a846),x98981),x98983)))
% 155.93/155.62 [9930]~P26(x99302)+~P22(f312(f70(x99301),x99305))+E(f312(f312(f6(x99301,x99302),f312(f312(f7(x99301,x99302,x99302),f312(f312(f18(x99301,x99302,f861(x99302,x99302)),f312(f312(f8(a846,f861(x99302,f861(x99302,x99302)),x99301),f108(x99302)),f312(f312(f7(x99301,f861(x99301,a846),a846),f314(x99301)),x99303))),x99304)),f2(x99302))),x99305),f312(f312(f6(x99301,x99302),x99304),f312(f312(f115(f861(x99301,a846)),x99305),x99303)))
% 155.93/155.62 [8520]~P72(x85201)+~P22(f312(f70(x85204),x85205))+E(f312(f312(f90(x85201),f312(x85202,x85203)),f312(f312(f9(x85204,x85201),x85202),f312(f312(f21(f861(x85204,a846)),x85205),f312(f312(f289(x85204),x85203),f189(f861(x85204,a846)))))),f312(f312(f9(x85204,x85201),x85202),f312(f312(f289(x85204),x85203),x85205)))
% 155.93/155.62 [8521]~P26(x85211)+~P22(f312(f70(x85214),x85215))+E(f312(f312(f89(x85211),f312(x85212,x85213)),f312(f312(f6(x85214,x85211),x85212),f312(f312(f21(f861(x85214,a846)),x85215),f312(f312(f289(x85214),x85213),f189(f861(x85214,a846)))))),f312(f312(f6(x85214,x85211),x85212),f312(f312(f289(x85214),x85213),x85215)))
% 155.93/155.62 [8833]~P103(x88332)+~P33(x88332,f312(f165(x88332),f312(f312(f150(x88331,x88332),x88334),x88335)))+E(f312(f132(x88331,f312(f312(f8(x88332,a846,x88331),f312(f228(x88332),x88333)),x88334)),x88335),f172(x88331,f312(f312(f8(x88332,a846,x88331),f312(f228(x88332),x88333)),x88334),x88335))
% 155.93/155.62 [8858]~P26(x88581)+E(f312(f312(f89(x88581),f312(f312(f6(a853,x88581),x88582),f283(a853,x88583,x88584))),f312(f312(f6(a853,x88581),x88582),f283(a853,f312(f312(f89(a853),x88584),f87(a853)),f312(f312(f89(a853),x88584),x88585)))),f312(f312(f6(a853,x88581),x88582),f283(a853,x88583,f312(f312(f89(a853),x88584),x88585))))+~P22(f312(f312(f227(a853),x88583),f312(f312(f89(a853),x88584),f87(a853))))
% 155.93/155.62 [8859]~P22(f312(f312(f314(x88591),x88594),x88595))+~P22(f312(f312(f227(f861(x88591,a846)),f312(f168(x88591),x88592)),x88595))+P22(f312(f312(f227(f861(x88591,a846)),f312(f168(x88591),f312(f312(f155(x88591,x88592),x88593),x88594))),x88595))
% 155.93/155.62 [9083]~P31(x90832)+~P22(f312(f70(x90831),x90835))+E(f312(f312(f73(x90831,x90832,f312(f312(f8(x90832,f861(x90832,x90832),x90831),f124(x90832)),x90833)),x90834),x90835),f312(f312(f124(x90832),x90834),f312(f312(f50(x90831,x90832),x90835),x90833)))
% 155.93/155.62 [9084]~P31(x90842)+~P22(f312(f70(x90841),x90845))+E(f312(f312(f73(x90841,x90842,f312(f312(f8(x90842,f861(x90842,x90842),x90841),f115(x90842)),x90843)),x90844),x90845),f312(f312(f115(x90842),x90844),f312(f312(f51(x90841,x90842),x90845),x90843)))
% 155.93/155.62 [9132]E(f312(x91321,x91322),f312(x91321,x91323))+P22(f312(f312(f228(a853),f312(x91321,x91322)),f312(x91321,x91323)))+~P22(f312(f312(f314(f860(x91324,x91324)),f312(f312(f239(x91324,x91324),x91322),x91323)),f149(x91324,f312(f312(f147(f861(x91324,a853)),x91321),x91325))))
% 155.93/155.62 [9163]~E(f312(x91634,x91632),f312(x91634,x91633))+~P22(f312(f312(f314(f860(x91631,x91631)),f312(f312(f239(x91631,x91631),x91632),x91633)),f149(x91631,x91635)))+P22(f312(f312(f314(f860(x91631,x91631)),f312(f312(f239(x91631,x91631),x91632),x91633)),f149(x91631,f312(f312(f147(f861(x91631,a853)),x91634),x91635))))
% 155.93/155.62 [9187]~P19(x91871,x91872,x91873,x91875)+P19(x91871,x91872,x91873,f312(f312(f289(x91871),x91874),x91875))+P22(f312(f312(f314(x91872),f312(x91873,x91874)),f312(f290(x91871,x91872,x91873),f312(f312(f21(f861(x91871,a846)),x91875),f312(f312(f289(x91871),x91874),f189(f861(x91871,a846)))))))
% 155.93/155.62 [9191]P22(f312(x91912,x91915))+~P22(f312(f312(f314(x91911),x91915),f312(f168(x91911),x91913)))+E(f312(f312(f134(x91911),f312(f190(f854(x91911)),f172(x91911,x91912,f312(f312(f129(x91911),x91913),x91914)))),f312(f312(f129(x91911),x91913),x91914)),f312(f312(f129(x91911),f312(f312(f134(x91911),f312(f190(f854(x91911)),f172(x91911,x91912,x91913))),x91913)),x91914))
% 155.93/155.62 [9194]~P22(f312(f312(f314(f860(x91941,x91941)),f312(f312(f239(x91941,x91941),x91942),x91943)),f149(x91941,x91945)))+~P22(f312(f312(f227(a853),f312(x91944,x91942)),f312(x91944,x91943)))+P22(f312(f312(f314(f860(x91941,x91941)),f312(f312(f239(x91941,x91941),x91942),x91943)),f149(x91941,f312(f312(f147(f861(x91941,a853)),x91944),x91945))))
% 155.93/155.62 [9255]P22(f312(f312(f314(f860(x92554,x92554)),f312(f312(f239(x92554,x92554),x92552),x92553)),f149(x92554,x92555)))+P22(f312(f312(f228(a853),f312(x92551,x92552)),f312(x92551,x92553)))+~P22(f312(f312(f314(f860(x92554,x92554)),f312(f312(f239(x92554,x92554),x92552),x92553)),f149(x92554,f312(f312(f147(f861(x92554,a853)),x92551),x92555))))
% 155.93/155.62 [9399]~P22(f312(f312(f314(f860(f854(x93991),f854(x93991))),f312(f312(f239(f854(x93991),f854(x93991)),x93992),x93994)),f154(x93991,x93995)))+~P22(f312(f312(f228(a853),x93993),f312(f190(f854(x93991)),x93992)))+P22(f312(f312(f314(f860(x93991,x93991)),f312(f312(f239(x93991,x93991),f312(f312(f161(x93991),x93992),x93993)),f312(f312(f161(x93991),x93994),x93993))),x93995))
% 155.93/155.62 [9627]E(x96271,f2(a1))+~P22(f312(f57(x96273,x96271),f312(f312(f239(a1,a1),x96274),x96275)))+P22(f312(f57(f312(f312(f90(a1),x96272),x96273),x96271),f312(f312(f239(a1,a1),f312(f312(f89(a1),f312(f312(f90(a1),x96272),x96274)),f312(f47(a1,f312(f312(f90(a1),x96272),x96275)),x96271))),f54(a1,f312(f312(f90(a1),x96272),x96275),x96271))))
% 155.93/155.62 [9629]~P22(f312(f312(f228(a853),f2(a853)),x96293))+~P22(f312(f56(x96292,x96293),f312(f312(f239(a853,a853),x96294),x96295)))+P22(f312(f56(f312(f312(f90(a853),x96291),x96292),x96293),f312(f312(f239(a853,a853),f312(f312(f89(a853),f312(f312(f90(a853),x96291),x96294)),f312(f47(a853,f312(f312(f90(a853),x96291),x96295)),x96293))),f54(a853,f312(f312(f90(a853),x96291),x96295),x96293))))
% 155.93/155.62 [9953]~P26(x99532)+~P22(f312(f70(x99531),x99534))+E(f312(f312(f6(x99531,x99532),x99533),f312(f233(x99531),f312(f312(f18(x99531,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99531),a310),f312(f312(f7(x99531,f861(x99531,a846),a846),f314(x99531)),x99534))),f312(f312(f7(x99531,f861(x99531,a846),a846),f314(x99531)),x99535)))),f312(f312(f6(x99531,x99532),f312(f312(f7(x99531,x99532,x99532),f312(f312(f18(x99531,x99532,f861(x99532,x99532)),f312(f312(f8(a846,f861(x99532,f861(x99532,x99532)),x99531),f108(x99532)),f312(f312(f7(x99531,f861(x99531,a846),a846),f314(x99531)),x99535))),x99533)),f2(x99532))),x99534))
% 155.93/155.62 [8141]~E(f312(f312(f129(x81411),x81412),x81415),f312(f312(f129(x81411),x81413),x81414))+E(f312(f312(f129(x81411),f312(f312(f134(x81411),f312(f190(f854(x81411)),x81412)),x81413)),x81414),x81415)+P22(f312(f312(f227(a853),f312(f190(f854(x81411)),x81413)),f312(f190(f854(x81411)),x81412)))
% 155.93/155.62 [8346]~E(f312(f312(f129(x83462),x83463),x83461),f312(f312(f129(x83462),x83464),x83465))+E(x83461,f312(f312(f129(x83462),f312(f312(f134(x83462),f312(f190(f854(x83462)),x83463)),x83464)),x83465))+~P22(f312(f312(f227(a853),f312(f190(f854(x83462)),x83463)),f312(f190(f854(x83462)),x83464)))
% 155.93/155.62 [8437]~E(f312(f312(f89(a853),f312(f312(f90(a853),x84373),x84374)),x84371),f312(f312(f89(a853),f312(f312(f90(a853),x84372),x84374)),x84375))+~P22(f312(f312(f227(a853),x84373),x84372))+E(x84371,f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x84372),x84373)),x84374)),x84375))
% 155.93/155.62 [8438]~E(f312(f312(f89(a853),f312(f312(f90(a853),x84381),x84383)),x84384),f312(f312(f89(a853),f312(f312(f90(a853),x84382),x84383)),x84385))+~P22(f312(f312(f227(a853),x84382),x84381))+E(f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x84381),x84382)),x84383)),x84384),x84385)
% 155.93/155.62 [8593]E(f312(f312(f89(a853),f312(f312(f90(a853),x85931),x85932)),x85933),f312(f312(f89(a853),f312(f312(f90(a853),x85934),x85932)),x85935))+~P22(f312(f312(f227(a853),x85934),x85931))+~E(x85935,f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x85931),x85934)),x85932)),x85933))
% 155.93/155.62 [8594]E(f312(f312(f89(a853),f312(f312(f90(a853),x85941),x85942)),x85943),f312(f312(f89(a853),f312(f312(f90(a853),x85944),x85942)),x85945))+~P22(f312(f312(f227(a853),x85944),x85941))+~E(f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x85941),x85944)),x85942)),x85943),x85945)
% 155.93/155.62 [9449]~P64(x94492)+~P22(f312(f70(x94491),x94495))+E(f312(f312(f9(x94491,x94492),f312(f312(f18(x94491,x94492,x94492),f312(f312(f8(x94492,f861(x94492,x94492),x94491),f268(x94492)),x94493)),x94494)),x94495),f312(f312(f268(x94492),f312(f312(f9(x94491,x94492),x94493),x94495)),f312(f312(f9(x94491,x94492),x94494),x94495)))
% 155.93/155.62 [9569]~E(f770(x95695,x95694,x95693,x95692,x95691),f771(x95695,x95694,x95693,x95692,x95691))+P22(f312(f312(f314(f860(x95691,x95691)),f312(f312(f239(x95691,x95691),x95692),x95693)),f287(x95691,x95694)))+~P22(f312(f312(f314(f860(x95691,x95691)),f312(f312(f239(x95691,x95691),x95692),x95693)),f287(x95691,f312(f312(f124(f861(f860(x95691,x95691),a846)),x95694),x95695))))
% 155.93/155.62 [9570]~E(f772(x95705,x95704,x95703,x95702,x95701),f773(x95705,x95704,x95703,x95702,x95701))+P22(f312(f312(f314(f860(x95701,x95701)),f312(f312(f239(x95701,x95701),x95702),x95703)),f287(x95701,x95704)))+~P22(f312(f312(f314(f860(x95701,x95701)),f312(f312(f239(x95701,x95701),x95702),x95703)),f287(x95701,f312(f312(f124(f861(f860(x95701,x95701),a846)),x95704),x95705))))
% 155.93/155.62 [9778]P22(f312(f312(f314(f860(x97781,x97781)),f312(f312(f239(x97781,x97781),x97782),f773(x97785,x97784,x97783,x97782,x97781))),f287(x97781,x97784)))+P22(f312(f312(f314(f860(x97781,x97781)),f312(f312(f239(x97781,x97781),x97782),x97783)),f287(x97781,x97784)))+~P22(f312(f312(f314(f860(x97781,x97781)),f312(f312(f239(x97781,x97781),x97782),x97783)),f287(x97781,f312(f312(f124(f861(f860(x97781,x97781),a846)),x97784),x97785))))
% 155.93/155.62 [9862]P22(f312(f312(f314(f860(x98621,x98621)),f312(f312(f239(x98621,x98621),f771(x98625,x98624,x98623,x98622,x98621)),x98623)),f287(x98621,x98624)))+P22(f312(f312(f314(f860(x98621,x98621)),f312(f312(f239(x98621,x98621),x98622),x98623)),f287(x98621,x98624)))+~P22(f312(f312(f314(f860(x98621,x98621)),f312(f312(f239(x98621,x98621),x98622),x98623)),f287(x98621,f312(f312(f124(f861(f860(x98621,x98621),a846)),x98624),x98625))))
% 155.93/155.62 [9904]P22(f312(f312(f314(f860(x99041,x99041)),f312(f312(f239(x99041,x99041),x99042),x99043)),f287(x99041,x99044)))+P22(f312(f312(f314(f860(x99041,x99041)),f312(f312(f239(x99041,x99041),f770(x99045,x99044,x99043,x99042,x99041)),f771(x99045,x99044,x99043,x99042,x99041))),x99045))+~P22(f312(f312(f314(f860(x99041,x99041)),f312(f312(f239(x99041,x99041),x99042),x99043)),f287(x99041,f312(f312(f124(f861(f860(x99041,x99041),a846)),x99044),x99045))))
% 155.93/155.62 [9905]P22(f312(f312(f314(f860(x99051,x99051)),f312(f312(f239(x99051,x99051),x99052),x99053)),f287(x99051,x99054)))+P22(f312(f312(f314(f860(x99051,x99051)),f312(f312(f239(x99051,x99051),f773(x99055,x99054,x99053,x99052,x99051)),f772(x99055,x99054,x99053,x99052,x99051))),x99055))+~P22(f312(f312(f314(f860(x99051,x99051)),f312(f312(f239(x99051,x99051),x99052),x99053)),f287(x99051,f312(f312(f124(f861(f860(x99051,x99051),a846)),x99054),x99055))))
% 155.93/155.62 [10026]~P22(f312(f312(f314(f860(f854(x100261),f854(x100261))),f312(f312(f239(f854(x100261),f854(x100261)),x100264),x100265)),f154(x100261,x100262)))+~P22(f312(f312(f314(f860(x100261,x100261)),x100263),f312(f168(f860(x100261,x100261)),f312(f312(f177(x100261,x100261),x100264),x100265))))+P22(f312(f312(f249(x100261,x100261,a846),f312(f312(f7(x100261,f861(f860(x100261,x100261),a846),f861(x100261,a846)),f312(f312(f8(f861(x100261,f861(f861(f860(x100261,x100261),a846),a846)),f861(f861(f860(x100261,x100261),a846),f861(x100261,a846)),x100261),f7(x100261,f861(f860(x100261,x100261),a846),a846)),f312(f312(f8(f861(x100261,f860(x100261,x100261)),f861(x100261,f861(f861(f860(x100261,x100261),a846),a846)),x100261),f312(f8(f860(x100261,x100261),f861(f861(f860(x100261,x100261),a846),a846),x100261),f314(f860(x100261,x100261)))),f239(x100261,x100261)))),x100262)),x100263))
% 155.93/155.62 [9477]~P22(f312(f312(f227(a853),x94773),x94772))+~P22(f312(f312(f228(a853),f312(f312(f89(a853),f312(f312(f90(a853),x94773),x94774)),x94771)),f312(f312(f89(a853),f312(f312(f90(a853),x94772),x94774)),x94775)))+P22(f312(f312(f228(a853),x94771),f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x94772),x94773)),x94774)),x94775)))
% 155.93/155.62 [9478]~P22(f312(f312(f227(a853),x94783),x94782))+~P22(f312(f312(f227(a853),f312(f312(f89(a853),f312(f312(f90(a853),x94783),x94784)),x94781)),f312(f312(f89(a853),f312(f312(f90(a853),x94782),x94784)),x94785)))+P22(f312(f312(f227(a853),x94781),f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x94782),x94783)),x94784)),x94785)))
% 155.93/155.62 [9498]~P22(f312(f312(f227(a853),x94981),x94984))+P22(f312(f312(f228(a853),f312(f312(f89(a853),f312(f312(f90(a853),x94981),x94982)),x94983)),f312(f312(f89(a853),f312(f312(f90(a853),x94984),x94982)),x94985)))+~P22(f312(f312(f228(a853),x94983),f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x94984),x94981)),x94982)),x94985)))
% 155.93/155.62 [9499]~P22(f312(f312(f227(a853),x94991),x94994))+P22(f312(f312(f227(a853),f312(f312(f89(a853),f312(f312(f90(a853),x94991),x94992)),x94993)),f312(f312(f89(a853),f312(f312(f90(a853),x94994),x94992)),x94995)))+~P22(f312(f312(f227(a853),x94993),f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x94994),x94991)),x94992)),x94995)))
% 155.93/155.62 [9603]~P22(f312(f312(f227(a853),x96032),x96031))+~P22(f312(f312(f228(a853),f312(f312(f89(a853),f312(f312(f90(a853),x96031),x96033)),x96034)),f312(f312(f89(a853),f312(f312(f90(a853),x96032),x96033)),x96035)))+P22(f312(f312(f228(a853),f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x96031),x96032)),x96033)),x96034)),x96035))
% 155.93/155.62 [9604]~P22(f312(f312(f227(a853),x96042),x96041))+~P22(f312(f312(f227(a853),f312(f312(f89(a853),f312(f312(f90(a853),x96041),x96043)),x96044)),f312(f312(f89(a853),f312(f312(f90(a853),x96042),x96043)),x96045)))+P22(f312(f312(f227(a853),f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x96041),x96042)),x96043)),x96044)),x96045))
% 155.93/155.62 [9657]~P22(f312(f312(f227(a853),x96574),x96571))+P22(f312(f312(f228(a853),f312(f312(f89(a853),f312(f312(f90(a853),x96571),x96572)),x96573)),f312(f312(f89(a853),f312(f312(f90(a853),x96574),x96572)),x96575)))+~P22(f312(f312(f228(a853),f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x96571),x96574)),x96572)),x96573)),x96575))
% 155.93/155.62 [9658]~P22(f312(f312(f227(a853),x96584),x96581))+P22(f312(f312(f227(a853),f312(f312(f89(a853),f312(f312(f90(a853),x96581),x96582)),x96583)),f312(f312(f89(a853),f312(f312(f90(a853),x96584),x96582)),x96585)))+~P22(f312(f312(f227(a853),f312(f312(f89(a853),f312(f312(f90(a853),f312(f312(f21(a853),x96581),x96584)),x96582)),x96583)),x96585))
% 155.93/155.62 [9889]~P9(x98891,x98892,x98895,x98893)+~P22(f312(f312(f314(f860(x98891,x98891)),x98894),x98895))+P22(f312(f312(f249(x98891,x98891,a846),f312(f312(f7(x98891,f861(x98891,x98892),f861(x98891,a846)),f312(f312(f8(f861(x98892,a846),f861(f861(x98891,x98892),f861(x98891,a846)),x98891),f8(x98892,a846,x98891)),f312(f312(f8(x98892,f861(x98892,a846),x98891),a309),x98893))),x98893)),x98894))
% 155.93/155.62 [9911]~P105(x99111)+~P49(x99111,f861(x99112,a846),x99113)+P49(x99111,f861(x99112,a846),f312(f312(f7(x99111,f861(x99112,a846),f861(x99112,a846)),f312(f312(f8(f861(x99112,a846),f861(f861(x99112,a846),f861(x99112,a846)),x99111),f124(f861(x99112,a846))),f312(f312(f7(x99111,f861(x99112,a846),f861(x99112,a846)),f312(f312(f8(f861(x99112,a846),f861(f861(x99112,a846),f861(x99112,a846)),x99111),f124(f861(x99112,a846))),x99113)),x99114))),x99115))
% 155.93/155.62 [6700]~E(f312(x67004,x67005),f192(x67002))+E(f312(f180(x67001,x67002,x67003,x67004),x67005),f312(f219(x67002),x67006))+~E(f312(x67003,x67005),f312(f219(x67002),x67006))
% 155.93/155.62 [6792]~E(f312(x67923,x67926),f192(x67921))+E(f312(f221(f857(x67921),x67922,f192(x67921),x67923),f312(x67924,x67925)),f192(x67921))+~E(f312(x67924,x67925),f312(f219(x67922),x67926))
% 155.93/155.62 [7374]E(f312(x73741,x73742),f192(x73743))+~E(f312(f180(x73745,x73743,x73746,x73741),x73742),f312(f219(x73743),x73744))+E(f312(x73741,x73742),f312(f219(x73743),x73744))
% 155.93/155.62 [7407]~E(f312(f180(x74076,x74073,x74075,x74071),x74072),f312(f219(x74073),x74074))+E(f312(x74071,x74072),f312(f219(x74073),x74074))+E(f312(x74075,x74072),f312(f219(x74073),x74074))
% 155.93/155.62 [8302]~P14(x83026,x83021,x83022,x83024)+E(f312(f82(x83021,x83021,x83021,f312(x83022,x83023)),f312(x83024,x83025)),f312(f82(x83021,x83021,x83021,f312(x83024,x83025)),f312(x83022,x83023)))+~P22(f312(f70(x83026),x83025))
% 155.93/155.62 [8726]~P19(x87261,x87263,x87265,x87266)+~P19(x87263,x87262,x87264,f312(f290(x87261,x87263,x87265),x87266))+P19(x87261,x87262,f312(f82(x87263,x87262,x87261,x87264),x87265),x87266)
% 155.93/155.62 [9287]~P22(f312(f312(x92873,x92872),x92876))+~P22(f312(f312(x92874,x92875),x92872))+P22(f312(f312(f314(x92871),x92872),f278(x92871,x92873,x92874,x92875,x92876)))
% 155.93/155.62 [9288]~P22(f312(f312(x92884,x92882),x92886))+~P22(f312(f312(x92883,x92885),x92882))+P22(f312(f312(f314(x92881),x92882),f275(x92881,x92883,x92884,x92885,x92886)))
% 155.93/155.62 [9400]E(x94001,x94002)+E(x94003,x94004)+~P22(f312(f312(f314(f860(f854(x94005),f854(x94005))),f312(f312(f239(f854(x94005),f854(x94005)),f312(f312(f147(x94005),x94003),x94001)),f312(f312(f147(x94005),x94004),x94002))),f153(x94005,x94006)))
% 155.93/155.62 [9409]~E(x94092,x94094)+P22(f312(f312(f314(f860(f854(x94091),f854(x94091))),f312(f312(f239(f854(x94091),f854(x94091)),f312(f312(f147(x94091),x94092),x94093)),f312(f312(f147(x94091),x94094),x94095))),f141(x94091,x94096)))+~P22(f312(f312(f314(f860(f854(x94091),f854(x94091))),f312(f312(f239(f854(x94091),f854(x94091)),x94093),x94095)),f141(x94091,x94096)))
% 155.93/155.62 [9410]~E(x94102,x94104)+P22(f312(f312(f314(f860(f854(x94101),f854(x94101))),f312(f312(f239(f854(x94101),f854(x94101)),f312(f312(f147(x94101),x94102),x94103)),f312(f312(f147(x94101),x94104),x94105))),f143(x94101,x94106)))+~P22(f312(f312(f314(f860(f854(x94101),f854(x94101))),f312(f312(f239(f854(x94101),f854(x94101)),x94103),x94105)),f143(x94101,x94106)))
% 155.93/155.62 [9411]~E(x94112,x94114)+P22(f312(f312(f314(f860(f854(x94111),f854(x94111))),f312(f312(f239(f854(x94111),f854(x94111)),f312(f312(f147(x94111),x94112),x94113)),f312(f312(f147(x94111),x94114),x94115))),f153(x94111,x94116)))+~P22(f312(f312(f314(f860(f854(x94111),f854(x94111))),f312(f312(f239(f854(x94111),f854(x94111)),x94113),x94115)),f153(x94111,x94116)))
% 155.93/155.62 [9412]~E(x94122,x94124)+P22(f312(f312(f314(f860(f854(x94121),f854(x94121))),f312(f312(f239(f854(x94121),f854(x94121)),f312(f312(f129(x94121),x94122),x94123)),f312(f312(f129(x94121),x94124),x94125))),f153(x94121,x94126)))+~P22(f312(f312(f314(f860(f854(x94121),f854(x94121))),f312(f312(f239(f854(x94121),f854(x94121)),x94123),x94125)),f153(x94121,x94126)))
% 155.93/155.62 [9413]~E(x94133,x94135)+P22(f312(f312(f314(f860(f854(x94131),f854(x94131))),f312(f312(f239(f854(x94131),f854(x94131)),f312(f312(f129(x94131),x94132),x94133)),f312(f312(f129(x94131),x94134),x94135))),f153(x94131,x94136)))+~P22(f312(f312(f314(f860(f854(x94131),f854(x94131))),f312(f312(f239(f854(x94131),f854(x94131)),x94132),x94134)),f153(x94131,x94136)))
% 155.93/155.62 [9465]E(x94651,x94652)+P22(f312(f312(f314(f860(f854(x94653),f854(x94653))),f312(f312(f239(f854(x94653),f854(x94653)),x94651),x94652)),f153(x94653,x94654)))+~P22(f312(f312(f314(f860(f854(x94653),f854(x94653))),f312(f312(f239(f854(x94653),f854(x94653)),f312(f312(f147(x94653),x94655),x94651)),f312(f312(f147(x94653),x94656),x94652))),f153(x94653,x94654)))
% 155.93/155.62 [9607]~E(x96073,x96075)+P22(f312(f312(f314(f860(f854(x96071),f854(x96071))),f312(f312(f239(f854(x96071),f854(x96071)),f312(f312(f129(x96071),x96072),f312(f312(f147(x96071),x96073),f127(x96071)))),f312(f312(f129(x96071),x96074),f312(f312(f147(x96071),x96075),f127(x96071))))),f153(x96071,x96076)))+~P22(f312(f312(f314(f860(f854(x96071),f854(x96071))),f312(f312(f239(f854(x96071),f854(x96071)),x96072),x96074)),f153(x96071,x96076)))
% 155.93/155.62 [9624]E(f312(x96241,x96242),f192(x96243))+~E(f312(f221(f857(x96246),x96243,f192(x96246),x96244),f312(x96241,x96242)),f192(x96246))+E(f312(x96244,f551(x96242,x96241,x96244,x96245,x96246,x96243)),f192(x96246))
% 155.93/155.62 [9625]E(f312(x96251,x96252),f192(x96253))+~E(f312(f221(f857(x96256),x96253,f192(x96256),x96254),f312(x96251,x96252)),f192(x96256))+E(f312(f219(x96253),f551(x96252,x96251,x96254,x96255,x96256,x96253)),f312(x96251,x96252))
% 155.93/155.62 [9661]E(x96611,x96612)+E(x96613,x96614)+~P22(f312(f312(f314(f860(f854(x96615),f854(x96615))),f312(f312(f239(f854(x96615),f854(x96615)),f312(f312(f129(x96615),x96613),f312(f312(f147(x96615),x96611),f127(x96615)))),f312(f312(f129(x96615),x96614),f312(f312(f147(x96615),x96612),f127(x96615))))),f153(x96615,x96616)))
% 155.93/155.62 [9685]E(x96851,x96852)+~P22(f312(f312(f314(f860(f854(x96853),f854(x96853))),f312(f312(f239(f854(x96853),f854(x96853)),f312(f312(f129(x96853),x96851),f312(f312(f147(x96853),x96855),f127(x96853)))),f312(f312(f129(x96853),x96852),f312(f312(f147(x96853),x96856),f127(x96853))))),f153(x96853,x96854)))+P22(f312(f312(f314(f860(f854(x96853),f854(x96853))),f312(f312(f239(f854(x96853),f854(x96853)),x96851),x96852)),f153(x96853,x96854)))
% 155.93/155.62 [9719]~P22(f312(f312(f314(f860(f861(x97191,a846),f861(x97191,a846))),f312(f312(f239(f861(x97191,a846),f861(x97191,a846)),x97192),x97194)),f303(x97191,x97196)))+~P22(f312(f312(f314(f860(f861(x97191,a846),f861(x97191,a846))),f312(f312(f239(f861(x97191,a846),f861(x97191,a846)),x97193),x97195)),f303(x97191,x97196)))+P22(f312(f312(f314(f860(f861(x97191,a846),f861(x97191,a846))),f312(f312(f239(f861(x97191,a846),f861(x97191,a846)),f312(f312(f124(f861(x97191,a846)),x97192),x97193)),f312(f312(f124(f861(x97191,a846)),x97194),x97195))),f303(x97191,x97196)))
% 155.93/155.62 [5181]~E(f312(x51813,x51816),x51815)+~E(x51814,f312(f219(x51811),x51816))+E(f312(f312(f193(x51811,x51812),x51813),x51814),f312(f219(x51812),x51815))
% 155.93/155.62 [5591]~E(f312(f312(f129(x55911),x55916),x55913),x55915)+E(f312(f312(f129(x55911),x55912),x55913),f312(f312(f147(x55911),x55914),x55915))+~E(x55912,f312(f312(f147(x55911),x55914),x55916))
% 155.93/155.62 [5592]~E(f312(f312(f129(x55921),x55926),x55923),x55925)+E(f312(f312(f129(x55921),x55922),x55923),f312(f312(f129(x55921),x55924),x55925))+~E(x55922,f312(f312(f129(x55921),x55924),x55926))
% 155.93/155.62 [5594]E(f312(f312(f129(x55941),x55942),x55943),f312(f312(f147(x55941),x55944),x55945))+~E(f312(f312(f147(x55941),x55944),x55946),x55942)+~E(x55945,f312(f312(f129(x55941),x55946),x55943))
% 155.93/155.62 [5596]~E(f312(f312(f129(x55961),x55962),x55966),x55964)+E(f312(f312(f129(x55961),x55962),x55963),f312(f312(f129(x55961),x55964),x55965))+~E(x55963,f312(f312(f129(x55961),x55966),x55965))
% 155.93/155.62 [6694]E(f312(x66941,x66942),f312(x66943,x66942))+~E(f312(f312(f150(x66944,x66945),x66941),x66946),f312(f312(f150(x66944,x66945),x66943),x66946))+~P22(f312(f312(f314(x66944),x66942),f312(f168(x66944),x66946)))
% 155.93/155.62 [7079]~P14(x70794,x70795,x70796,x70791)+E(f312(f312(x70791,x70792),x70793),f312(f312(f73(x70794,x70795,x70796),x70793),x70792))+~P22(f312(f70(x70794),x70792))
% 155.93/155.62 [7143]~E(x71432,f312(x71434,x71436))+~P22(f312(f312(f314(x71433),x71436),x71435))+P22(f312(f312(f314(x71431),x71432),f312(f290(x71433,x71431,x71434),x71435)))
% 155.93/155.62 [7144]~E(f312(x71444,x71442),x71446)+~P22(f312(f312(f314(x71443),x71446),x71445))+P22(f312(f312(f314(x71441),x71442),f312(f291(x71441,x71443,x71444),x71445)))
% 155.93/155.62 [7586]~P37(x75861,x75862,x75864,x75866)+P37(x75861,x75862,f312(f312(f147(x75861),x75863),x75864),f312(f312(f147(x75861),x75865),x75866))+~P22(f312(f312(x75862,x75863),x75865))
% 155.93/155.62 [8601]~P56(x86014,x86015,x86011,x86012,x86016)+E(f312(x86011,f312(x86012,x86013)),x86013)+~P22(f312(f312(f314(x86015),x86013),x86016))
% 155.93/155.62 [9402]E(x94021,x94022)+E(f312(f190(f854(x94023)),x94024),f312(f190(f854(x94023)),x94025))+~P22(f312(f312(f314(f860(f854(x94023),f854(x94023))),f312(f312(f239(f854(x94023),f854(x94023)),f312(f312(f147(x94023),x94021),x94024)),f312(f312(f147(x94023),x94022),x94025))),f141(x94023,x94026)))
% 155.93/155.62 [9468]E(f312(f190(f854(x94681)),x94682),f312(f190(f854(x94681)),x94683))+P22(f312(f312(f314(f860(f854(x94681),f854(x94681))),f312(f312(f239(f854(x94681),f854(x94681)),x94682),x94683)),f141(x94681,x94684)))+~P22(f312(f312(f314(f860(f854(x94681),f854(x94681))),f312(f312(f239(f854(x94681),f854(x94681)),f312(f312(f147(x94681),x94685),x94682)),f312(f312(f147(x94681),x94686),x94683))),f141(x94681,x94684)))
% 155.93/155.62 [9491]~P22(f312(f312(f314(f860(x94911,x94911)),f312(f312(f239(x94911,x94911),x94912),x94914)),f287(x94911,x94916)))+P22(f312(f312(f314(f860(f854(x94911),f854(x94911))),f312(f312(f239(f854(x94911),f854(x94911)),f312(f312(f147(x94911),x94912),x94913)),f312(f312(f147(x94911),x94914),x94915))),f287(f854(x94911),f153(x94911,x94916))))+~P22(f312(f312(f314(f860(f854(x94911),f854(x94911))),f312(f312(f239(f854(x94911),f854(x94911)),x94913),x94915)),f287(f854(x94911),f153(x94911,x94916))))
% 155.93/155.62 [9667]~P22(f312(x96672,x96676))+~E(f312(f132(x96671,x96672),x96673),f312(f312(f147(x96671),x96674),x96675))+~P22(f312(f312(f314(x96671),x96676),f312(f168(x96671),f728(x96675,x96674,x96673,x96672,x96671))))
% 155.93/155.62 [9668]~P22(f312(x96684,x96686))+~E(f312(f312(f147(x96681),x96682),x96683),f312(f132(x96681,x96684),x96685))+~P22(f312(f312(f314(x96681),x96686),f312(f168(x96681),f730(x96685,x96684,x96683,x96682,x96681))))
% 155.93/155.62 [9980]~P26(x99802)+E(f312(f312(f6(x99801,x99802),f312(f312(f8(f861(x99803,a846),x99802,x99801),f312(f6(x99803,x99802),x99804)),f312(f312(f8(f861(x99803,a846),f861(x99803,a846),x99801),f233(x99803)),f312(f312(f8(f861(x99803,a846),f861(x99803,a846),x99801),f312(f18(x99803,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99803),a310),f312(f312(f7(x99803,f861(x99803,a846),a846),f314(x99803)),x99805)))),f312(f7(x99803,x99801,a846),f312(f312(f8(x99801,f861(x99801,a846),x99803),a309),x99806)))))),f312(f290(x99803,x99801,x99806),x99805)),f312(f312(f6(x99803,x99802),x99804),x99805))+~P22(f312(f70(x99803),x99805))
% 155.93/155.62 [6747]~P103(x67473)+P22(f312(x67472,x67475))+E(f312(f132(x67471,x67472),f312(f312(f145(x67471,x67473,x67474),x67475),x67476)),f312(f132(x67471,x67472),x67476))
% 155.93/155.62 [6749]P22(f312(x67491,x67492))+~E(f163(x67493,x67491,x67494),f312(f312(f239(f854(x67493),f854(x67493)),x67495),x67496))+~P22(f312(f312(f314(x67493),x67492),f312(f168(x67493),x67495)))
% 155.93/155.62 [6790]~P22(f312(x67902,x67906))+~E(f163(x67901,x67902,x67903),f312(f312(f239(f854(x67901),f854(x67901)),x67904),x67905))+~P22(f312(f312(f314(x67901),x67906),f312(f168(x67901),x67905)))
% 155.93/155.62 [7451]~P11(x74511,x74512,x74513)+~P22(f312(f70(x74511),x74516))+E(f312(f312(f73(x74511,x74512,x74513),x74514),f312(f312(f289(x74511),x74515),x74516)),f312(f312(f73(x74511,x74512,x74513),f312(f312(x74513,x74515),x74514)),x74516))
% 155.93/155.62 [7502]~P103(x75022)+~P22(f312(f312(f227(x75022),f312(x75023,x75024)),f312(x75023,x75025)))+E(f312(f312(f145(x75021,x75022,x75023),x75024),f312(f312(f147(x75021),x75025),x75026)),f312(f312(f147(x75021),x75024),f312(f312(f147(x75021),x75025),x75026)))
% 155.93/155.62 [7615]E(x76151,x76152)+~E(f312(f312(f247(x76153,x76154),x76151),f312(f16(f861(x76154,a846),x76153),x76155)),f312(f312(f247(x76153,x76154),x76152),f312(f16(f861(x76154,a846),x76153),x76155)))+~P22(f312(f312(f314(x76154),x76156),x76155))
% 155.93/155.62 [7682]~P11(x76821,x76822,x76823)+~P22(f312(f70(x76821),x76826))+E(f312(f312(f73(x76821,x76822,x76823),x76824),f312(f312(f289(x76821),x76825),x76826)),f312(f312(x76823,x76825),f312(f312(f73(x76821,x76822,x76823),x76824),x76826)))
% 155.93/155.62 [7861]~P15(x78612,x78615,x78616,x78611)+~P22(f312(f70(x78612),x78614))+E(f312(x78611,f312(f312(f289(x78612),x78613),x78614)),f312(f82(x78615,x78615,x78615,f312(x78611,x78614)),f312(x78616,x78613)))
% 155.93/155.62 [7898]~P103(x78982)+P22(f312(f312(f227(x78982),f312(x78983,x78984)),f312(x78983,x78985)))+E(f312(f312(f145(x78981,x78982,x78983),x78984),f312(f312(f147(x78981),x78985),x78986)),f312(f312(f147(x78981),x78985),f312(f312(f145(x78981,x78982,x78983),x78984),x78986)))
% 155.93/155.62 [8041]~E(f312(f190(f854(x80411)),x80415),f312(f190(f854(x80412)),x80416))+~E(f312(f190(f854(x80411)),x80413),f312(f190(f854(x80412)),x80414))+E(f312(f312(f129(f860(x80411,x80412)),f312(f312(f177(x80411,x80412),x80413),x80414)),f312(f312(f177(x80411,x80412),x80415),x80416)),f312(f312(f177(x80411,x80412),f312(f312(f129(x80411),x80413),x80415)),f312(f312(f129(x80412),x80414),x80416)))
% 155.93/155.62 [8156]~E(x81562,f312(f290(x81563,x81561,x81564),x81566))+P22(f312(f312(f227(f861(x81561,a846)),x81562),f312(f290(x81563,x81561,x81564),x81565)))+~P22(f312(f312(f227(f861(x81563,a846)),x81566),x81565))
% 155.93/155.62 [8261]~P103(x82615)+E(f312(x82611,x82612),f312(x82611,x82613))+E(f312(f312(f145(x82614,x82615,x82611),x82612),f312(f312(f145(x82614,x82615,x82611),x82613),x82616)),f312(f312(f145(x82614,x82615,x82611),x82613),f312(f312(f145(x82614,x82615,x82611),x82612),x82616)))
% 155.93/155.62 [8295]~P19(x82953,x82951,x82954,x82955)+P19(x82953,x82951,f312(f312(f312(f81(x82953,x82951),x82954),x82956),x82952),x82955)+P22(f312(f312(f314(x82951),x82952),f312(f290(x82953,x82951,x82954),x82955)))
% 155.93/155.62 [8447]~P22(f312(f312(f314(x84472),x84474),f312(x84476,x84473)))+~P22(f312(f312(f314(x84471),x84473),x84475))+P22(f312(f312(f314(f860(x84471,x84472)),f312(f312(f239(x84471,x84472),x84473),x84474)),f312(f312(f247(x84471,x84472),x84475),x84476)))
% 155.93/155.62 [8905]~P72(x89052)+~P19(x89054,x89051,x89055,x89056)+E(f312(f312(f9(x89051,x89052),x89053),f312(f290(x89054,x89051,x89055),x89056)),f312(f312(f9(x89054,x89052),f312(f82(x89051,x89052,x89054,x89053),x89055)),x89056))
% 155.93/155.62 [8906]~P26(x89062)+~P19(x89064,x89061,x89065,x89066)+E(f312(f312(f6(x89061,x89062),x89063),f312(f290(x89064,x89061,x89065),x89066)),f312(f312(f6(x89064,x89062),f312(f82(x89061,x89062,x89064,x89063),x89065)),x89066))
% 155.93/155.62 [8953]~P39(x89532,x89535,x89531,x89533,x89536)+P22(f312(f312(x89531,f312(f312(f161(x89532),x89533),x89534)),f312(f312(f161(x89535),x89536),x89534)))+~P22(f312(f312(f228(a853),x89534),f312(f190(f854(x89535)),x89536)))
% 155.93/155.62 [8954]~P39(x89542,x89545,x89541,x89543,x89546)+P22(f312(f312(x89541,f312(f312(f161(x89542),x89543),x89544)),f312(f312(f161(x89545),x89546),x89544)))+~P22(f312(f312(f228(a853),x89544),f312(f190(f854(x89542)),x89543)))
% 155.93/155.62 [9153]~E(f312(f312(f312(a201,x91535),f40(x91531)),f312(f312(a202,x91534),x91531)),f312(f312(f312(a201,x91536),f40(x91531)),f312(f312(a202,x91534),x91531)))+~P22(f312(f312(f195(x91533),f312(f312(f312(a201,x91534),f40(x91531)),f312(x91532,x91534))),x91536))+P22(f312(f312(f195(f32(x91531,x91532,x91533)),x91534),f312(f312(f312(a201,x91535),f40(x91531)),f312(f312(a202,x91534),x91531))))
% 155.93/155.62 [9159]~P14(x91593,x91591,x91596,x91592)+~P22(f312(f70(x91593),x91594))+E(f312(f82(x91591,x91591,x91591,f312(x91592,f312(f312(f21(f861(x91593,a846)),x91594),f312(f312(f289(x91593),x91595),f189(f861(x91593,a846)))))),f312(x91596,x91595)),f312(x91592,f312(f312(f289(x91593),x91595),x91594)))
% 155.93/155.62 [9173]~P22(f312(f312(f314(x91735),x91733),x91736))+P22(f312(f312(f314(x91731),f312(x91732,x91733)),f110(f861(x91731,a846),x91734)))+~P22(f312(f312(f227(f861(x91731,a846)),f312(f290(x91735,x91731,x91732),x91736)),f312(x91734,f312(f290(x91735,x91731,x91732),x91736))))
% 155.93/155.62 [9564]~E(f312(f312(f312(a201,f312(f312(a203,x95645),f312(a202,x95644))),x95641),f312(f312(a202,x95645),a25)),f312(f312(f312(a201,f312(f312(a203,x95646),f312(a202,x95644))),x95641),f312(f312(a202,x95646),a25)))+~P22(f312(f312(f195(f312(a27,x95642)),f312(f312(f312(a201,f312(f312(a203,x95644),a204)),f40(a26)),f312(x95643,x95644))),x95646))+P22(f312(f312(f195(f31(x95641,x95642,x95643)),x95644),f312(f312(f312(a201,f312(f312(a203,x95645),f312(a202,x95644))),x95641),f312(f312(a202,x95645),a25))))
% 155.93/155.62 [9758]~E(f312(f290(x97582,x97584,x97586),f235(f861(x97582,a846))),f235(f861(x97584,a846)))+~E(f312(f290(x97581,x97583,x97585),f235(f861(x97581,a846))),f235(f861(x97583,a846)))+E(f312(f290(f860(x97581,x97582),f860(x97583,x97584),f250(x97581,x97583,x97582,x97584,x97585,x97586)),f235(f861(f860(x97581,x97582),a846))),f235(f861(f860(x97583,x97584),a846)))
% 155.93/155.62 [9811]~P19(x98113,x98114,x98115,f312(x98116,f708(x98116,x98115,x98114,x98113,x98112,x98111)))+P19(x98113,x98114,x98115,f312(f312(f51(x98112,f861(x98113,a846)),x98111),x98116))+E(x98111,f189(f861(x98112,a846)))
% 155.93/155.62 [9870]P19(x98706,x98705,x98704,f312(f312(f51(x98702,f861(x98706,a846)),x98701),x98703))+E(x98701,f189(f861(x98702,a846)))+P22(f312(f312(f314(x98702),f708(x98703,x98704,x98705,x98706,x98702,x98701)),x98701))
% 155.93/155.62 [9876]P22(f312(f312(f314(x98761),f733(x98762,x98763,x98764,x98765,x98766,x98761)),x98766))+P22(f312(f312(f227(f861(f860(x98761,x98764),a846)),f312(f312(f247(x98761,x98764),x98766),x98763)),f312(f312(f247(x98761,x98764),x98765),x98762)))+~P22(f312(f312(f227(f861(x98761,a846)),x98766),x98765))
% 155.93/155.62 [9917]P18(x99176,x99175,f312(f312(f289(f852(x99176)),f312(f312(f312(f100(x99176),x99171),x99173),x99172)),f189(f861(f852(x99176),a846))))+~P18(x99176,x99175,f312(f312(f289(f852(x99176)),f312(f312(f312(f100(x99176),x99174),x99173),x99172)),f189(f861(f852(x99176),a846))))+P22(f312(f312(x99171,f697(x99171,x99172,x99173,x99174,x99175,x99176)),f710(x99171,x99172,x99173,x99174,x99175,x99176)))
% 155.93/155.62 [9918]P18(x99186,x99185,f312(f312(f289(f852(x99186)),f312(f312(f312(f100(x99186),x99184),x99183),x99182)),f189(f861(f852(x99186),a846))))+~P18(x99186,x99185,f312(f312(f289(f852(x99186)),f312(f312(f312(f100(x99186),x99184),x99183),x99181)),f189(f861(f852(x99186),a846))))+P22(f312(f312(x99181,f718(x99182,x99181,x99183,x99184,x99185,x99186)),f731(x99182,x99181,x99183,x99184,x99185,x99186)))
% 155.93/155.62 [9957]~P18(x99571,x99572,f312(f312(f289(f852(x99571)),f312(f312(f312(f100(x99571),x99573),x99574),x99576)),f189(f861(f852(x99571),a846))))+P18(x99571,x99572,f312(f312(f289(f852(x99571)),f312(f312(f312(f100(x99571),x99573),x99574),x99575)),f189(f861(f852(x99571),a846))))+~P22(f312(f312(x99575,f718(x99575,x99576,x99574,x99573,x99572,x99571)),f731(x99575,x99576,x99574,x99573,x99572,x99571)))
% 155.93/155.62 [9958]~P18(x99581,x99582,f312(f312(f289(f852(x99581)),f312(f312(f312(f100(x99581),x99586),x99584),x99585)),f189(f861(f852(x99581),a846))))+P18(x99581,x99582,f312(f312(f289(f852(x99581)),f312(f312(f312(f100(x99581),x99583),x99584),x99585)),f189(f861(f852(x99581),a846))))+~P22(f312(f312(x99586,f697(x99583,x99585,x99584,x99586,x99582,x99581)),f710(x99583,x99585,x99584,x99586,x99582,x99581)))
% 155.93/155.62 [9992]~P22(f312(f312(f227(f861(x99922,a846)),f312(x99924,f733(x99926,x99924,x99922,x99925,x99923,x99921))),f312(x99926,f733(x99926,x99924,x99922,x99925,x99923,x99921))))+~P22(f312(f312(f227(f861(x99921,a846)),x99923),x99925))+P22(f312(f312(f227(f861(f860(x99921,x99922),a846)),f312(f312(f247(x99921,x99922),x99923),x99924)),f312(f312(f247(x99921,x99922),x99925),x99926)))
% 155.93/155.62 [7636]~P22(f312(x76361,x76365))+~P22(f312(x76366,x76364))+P22(f312(x76361,f312(f248(x76362,x76363),f312(f312(f239(x76362,x76363),x76364),x76365))))
% 155.93/155.62 [7637]~P22(f312(x76371,x76374))+~P22(f312(x76376,x76375))+P22(f312(x76371,f312(f246(x76372,x76373),f312(f312(f239(x76372,x76373),x76374),x76375))))
% 155.93/155.62 [7659]~E(f312(f190(f854(x76591)),x76593),f312(f190(f854(x76594)),x76595))+~E(f312(f312(f173(x76591,x76594),f312(f312(f177(x76591,x76594),x76593),x76595)),x76592),f312(f219(x76594),x76596))+P22(f312(f312(f314(x76591),x76592),f312(f168(x76591),x76593)))
% 155.93/155.63 [7687]~P22(f312(f312(x76874,x76876),x76875))+~P22(f312(f312(f314(x76871),x76876),x76873))+P22(f312(f312(f312(f50(x76871,f861(x76872,a846)),x76873),x76874),x76875))
% 155.93/155.63 [7987]~P22(f312(f312(f314(x79871),x79872),f312(x79875,x79876)))+~P22(f312(f312(f314(x79873),x79876),x79874))+P22(f312(f312(f314(x79871),x79872),f312(f312(f50(x79873,f861(x79871,a846)),x79874),x79875)))
% 155.93/155.63 [8033]P22(f312(f312(x80331,x80332),x80333))+~P22(f312(f312(x80334,x80332),x80333))+~P22(f312(f312(f227(f861(x80335,f861(x80336,a846))),x80334),x80331))
% 155.93/155.63 [8180]P22(f312(f312(x81801,x81802),x81803))+~P22(f312(f312(f314(x81804),x81802),x81805))+~P22(f312(f312(f312(f51(x81804,f861(x81806,a846)),x81805),x81801),x81803))
% 155.93/155.63 [8319]P22(f312(f312(f314(x83191),x83192),f312(x83193,x83194)))+~P22(f312(f312(f314(x83195),x83194),x83196))+~P22(f312(f312(f314(x83191),x83192),f312(f312(f51(x83195,f861(x83191,a846)),x83196),x83193)))
% 155.93/155.63 [8519]~P22(f312(f312(f312(f312(a198,x85191),x85193),x85194),x85196))+~P22(f312(f312(f312(f312(a198,x85192),x85196),x85194),x85195))+P22(f312(f312(f312(f312(a198,f36(x85191,x85192)),x85193),x85194),x85195))
% 155.93/155.63 [8583]~P9(x85834,x85835,x85836,x85831)+E(f312(x85831,x85832),f312(x85831,x85833))+~P22(f312(f312(f314(f860(x85834,x85834)),f312(f312(f239(x85834,x85834),x85832),x85833)),x85836))
% 155.93/155.63 [8614]P22(f312(f312(f227(f861(x86141,a846)),x86142),f312(x86143,x86144)))+~P22(f312(f312(f314(x86145),x86144),x86146))+~P22(f312(f312(f227(f861(x86141,a846)),x86142),f312(f312(f51(x86145,f861(x86141,a846)),x86146),x86143)))
% 155.93/155.63 [8644]~P54(x86443,x86444,f312(f265(x86444,x86443),x86445))+E(x86441,f189(f861(x86442,a846)))+E(f312(f312(f51(x86442,f861(x86443,a846)),x86441),f312(f312(f8(f861(x86444,a846),f861(x86443,a846),x86442),f264(x86444,x86443,x86445)),x86446)),f312(f264(x86444,x86443,x86445),f312(f312(f51(x86442,f861(x86444,a846)),x86441),x86446)))
% 155.93/155.63 [8717]P22(f312(f312(f314(x87171),x87172),f312(f264(x87173,x87171,x87174),x87175)))+~P22(f312(f312(f314(x87173),x87176),x87175))+~P22(f312(f312(f314(f860(x87173,x87171)),f312(f312(f239(x87173,x87171),x87176),x87172)),x87174))
% 155.93/155.63 [8832]P22(f312(x88321,x88322))+~P22(f312(f312(f312(f312(a198,x88324),x88322),x88325),x88326))+P22(f312(f312(f312(f312(a198,f33(x88321,x88323,x88324)),x88322),x88325),x88326))
% 155.93/155.63 [8849]~P22(f312(x88491,x88494))+~P22(f312(f312(f312(f312(a198,x88492),x88494),x88495),x88496))+P22(f312(f312(f312(f312(a198,f33(x88491,x88492,x88493)),x88494),x88495),x88496))
% 155.93/155.63 [9025]P22(f312(f312(f227(f861(x90251,a846)),f312(f264(x90252,x90251,x90253),x90254)),f312(f264(x90252,x90251,x90255),x90256)))+~P22(f312(f312(f227(f861(x90252,a846)),x90254),x90256))+~P22(f312(f312(f227(f861(f860(x90252,x90251),a846)),x90253),x90255))
% 155.93/155.63 [9110]P22(f312(x91101,x91102))+P22(f312(f312(f312(f312(a198,x91103),x91102),x91104),x91105))+~P22(f312(f312(f312(f312(a198,f33(x91101,x91106,x91103)),x91102),x91104),x91105))
% 155.93/155.63 [9115]~P22(f312(x91155,x91152))+P22(f312(f312(f312(f312(a198,x91151),x91152),x91153),x91154))+~P22(f312(f312(f312(f312(a198,f33(x91155,x91151,x91156)),x91152),x91153),x91154))
% 155.93/155.63 [9166]P22(f312(f312(f312(f312(a198,x91661),x91662),x91663),x91664))+P22(f312(f312(f312(f312(a198,x91665),x91662),x91663),x91664))+~P22(f312(f312(f312(f312(a198,f33(x91666,x91661,x91665)),x91662),x91663),x91664))
% 155.93/155.63 [9210]~P22(f312(f312(f314(x92102),x92106),x92104))+~P22(f312(f312(f227(f861(x92101,a846)),x92103),x92105))+P22(f312(f312(f227(f861(f860(x92101,x92102),a846)),f312(f312(f247(x92101,x92102),x92103),f312(f16(f861(x92102,a846),x92101),x92104))),f312(f312(f247(x92101,x92102),x92105),f312(f16(f861(x92102,a846),x92101),x92104))))
% 155.93/155.63 [9222]~P39(x92221,x92222,x92223,x92225,x92226)+P22(f312(f312(f249(x92221,x92222,a846),x92223),x92224))+~P22(f312(f312(f314(f860(x92221,x92222)),x92224),f312(f168(f860(x92221,x92222)),f312(f312(f177(x92221,x92222),x92225),x92226))))
% 155.93/155.63 [9355]~E(x93553,x93555)+P22(f312(f312(f314(f860(f854(x93551),f854(x93551))),f312(f312(f239(f854(x93551),f854(x93551)),f312(f312(f147(x93551),x93552),x93553)),f312(f312(f147(x93551),x93554),x93555))),f153(x93551,x93556)))+~P22(f312(f312(f314(f860(x93551,x93551)),f312(f312(f239(x93551,x93551),x93552),x93554)),x93556))
% 155.93/155.63 [9359]~E(f312(f190(f854(x93591)),x93595),f312(f190(f854(x93592)),x93596))+E(f182(x93591,x93592,f183(x93591,x93592,x93593,f312(f312(f21(f861(x93591,a846)),x93594),f312(f168(x93591),x93595))),x93595,x93596),f183(x93591,x93592,f182(x93591,x93592,x93593,x93595,x93596),x93594))+~P22(f312(f312(f227(f861(x93591,a846)),f312(f168(x93591),x93595)),x93594))
% 155.93/155.63 [9360]~E(f312(f190(f854(x93601)),x93603),f312(f190(f854(x93601)),x93605))+P22(f312(f312(f314(f860(f854(x93601),f854(x93601))),f312(f312(f239(f854(x93601),f854(x93601)),f312(f312(f147(x93601),x93602),x93603)),f312(f312(f147(x93601),x93604),x93605))),f141(x93601,x93606)))+~P22(f312(f312(f314(f860(x93601,x93601)),f312(f312(f239(x93601,x93601),x93602),x93604)),x93606))
% 155.93/155.63 [9392]P22(f312(f312(f314(f860(x93921,x93921)),f312(f312(f239(x93921,x93921),x93922),x93923)),f312(f312(f184(f860(x93921,x93921),a846),f312(a126,x93924)),x93925)))+~P22(f312(f312(f314(f860(x93921,x93921)),f312(f312(f239(x93921,x93921),x93926),x93923)),x93925))+~P22(f312(f312(f314(f860(x93921,x93921)),f312(f312(f239(x93921,x93921),x93922),x93926)),f312(f312(f184(f860(x93921,x93921),a846),x93924),x93925)))
% 155.93/155.63 [9393]P22(f312(f312(f314(f860(x93931,x93931)),f312(f312(f239(x93931,x93931),x93932),x93933)),f312(f312(f184(f860(x93931,x93931),a846),f312(a126,x93934)),x93935)))+~P22(f312(f312(f314(f860(x93931,x93931)),f312(f312(f239(x93931,x93931),x93932),x93936)),x93935))+~P22(f312(f312(f314(f860(x93931,x93931)),f312(f312(f239(x93931,x93931),x93936),x93933)),f312(f312(f184(f860(x93931,x93931),a846),x93934),x93935)))
% 155.93/155.63 [9398]~P22(f312(f312(f314(x93984),x93985),x93986))+P22(f312(f312(f227(f861(x93981,a846)),x93982),x93983))+~P22(f312(f312(f227(f861(f860(x93981,x93984),a846)),f312(f312(f247(x93981,x93984),x93982),f312(f16(f861(x93984,a846),x93981),x93986))),f312(f312(f247(x93981,x93984),x93983),f312(f16(f861(x93984,a846),x93981),x93986))))
% 155.93/155.63 [9441]E(x94411,x94412)+~P22(f312(f312(f314(f860(f854(x94413),f854(x94413))),f312(f312(f239(f854(x94413),f854(x94413)),f312(f312(f147(x94413),x94411),x94415)),f312(f312(f147(x94413),x94412),x94416))),f141(x94413,x94414)))+P22(f312(f312(f314(f860(x94413,x94413)),f312(f312(f239(x94413,x94413),x94411),x94412)),x94414))
% 155.93/155.63 [9442]E(x94421,x94422)+~P22(f312(f312(f314(f860(f854(x94423),f854(x94423))),f312(f312(f239(f854(x94423),f854(x94423)),f312(f312(f147(x94423),x94421),x94425)),f312(f312(f147(x94423),x94422),x94426))),f143(x94423,x94424)))+P22(f312(f312(f314(f860(x94423,x94423)),f312(f312(f239(x94423,x94423),x94421),x94422)),x94424))
% 155.93/155.63 [9443]E(x94431,x94432)+~P22(f312(f312(f314(f860(f854(x94433),f854(x94433))),f312(f312(f239(f854(x94433),f854(x94433)),f312(f312(f147(x94433),x94431),x94435)),f312(f312(f147(x94433),x94432),x94436))),f153(x94433,x94434)))+P22(f312(f312(f314(f860(x94433,x94433)),f312(f312(f239(x94433,x94433),x94431),x94432)),x94434))
% 155.93/155.63 [9476]P22(f312(f312(f314(f860(f854(x94761),f854(x94761))),f312(f312(f239(f854(x94761),f854(x94761)),f312(f312(f147(x94761),x94762),x94763)),f312(f312(f147(x94761),x94764),x94765))),f154(x94761,x94766)))+~P22(f312(f312(f314(f860(f854(x94761),f854(x94761))),f312(f312(f239(f854(x94761),f854(x94761)),x94763),x94765)),f154(x94761,x94766)))+~P22(f312(f312(f314(f860(x94761,x94761)),f312(f312(f239(x94761,x94761),x94762),x94764)),x94766))
% 155.93/155.63 [9496]P22(f312(x94961,x94962))+~P22(f312(x94961,f406(x94961,x94963,x94964,x94965,x94966)))+~P22(f312(f312(f314(x94966),x94962),f312(f312(f50(x94965,f861(x94966,a846)),x94964),x94963)))
% 155.93/155.63 [9501]~P22(f312(f312(f314(f860(f854(x95011),f854(x95011))),f312(f312(f239(f854(x95011),f854(x95011)),f312(f312(f147(x95011),x95012),x95015)),f312(f312(f147(x95011),x95013),x95016))),f141(x95011,x95014)))+P22(f312(f312(f314(f860(f854(x95011),f854(x95011))),f312(f312(f239(f854(x95011),f854(x95011)),x95015),x95016)),f141(x95011,x95014)))+P22(f312(f312(f314(f860(x95011,x95011)),f312(f312(f239(x95011,x95011),x95012),x95013)),x95014))
% 155.93/155.63 [9502]~P22(f312(f312(f314(f860(f854(x95021),f854(x95021))),f312(f312(f239(f854(x95021),f854(x95021)),f312(f312(f147(x95021),x95022),x95025)),f312(f312(f147(x95021),x95023),x95026))),f143(x95021,x95024)))+P22(f312(f312(f314(f860(f854(x95021),f854(x95021))),f312(f312(f239(f854(x95021),f854(x95021)),x95025),x95026)),f143(x95021,x95024)))+P22(f312(f312(f314(f860(x95021,x95021)),f312(f312(f239(x95021,x95021),x95022),x95023)),x95024))
% 155.93/155.63 [9503]~P22(f312(f312(f314(f860(f854(x95031),f854(x95031))),f312(f312(f239(f854(x95031),f854(x95031)),f312(f312(f147(x95031),x95032),x95035)),f312(f312(f147(x95031),x95033),x95036))),f153(x95031,x95034)))+P22(f312(f312(f314(f860(f854(x95031),f854(x95031))),f312(f312(f239(f854(x95031),f854(x95031)),x95035),x95036)),f153(x95031,x95034)))+P22(f312(f312(f314(f860(x95031,x95031)),f312(f312(f239(x95031,x95031),x95032),x95033)),x95034))
% 155.93/155.63 [9579]P22(f312(x95791,x95792))+P22(f312(f312(f314(x95793),f407(x95791,x95794,x95795,x95793,x95796)),x95795))+~P22(f312(f312(f314(x95796),x95792),f312(f312(f50(x95793,f861(x95796,a846)),x95795),x95794)))
% 155.93/155.63 [9588]~E(x95882,x95884)+P22(f312(f312(f314(f860(f854(x95881),f854(x95881))),f312(f312(f239(f854(x95881),f854(x95881)),f312(f312(f129(x95881),x95882),f312(f312(f147(x95881),x95883),f127(x95881)))),f312(f312(f129(x95881),x95884),f312(f312(f147(x95881),x95885),f127(x95881))))),f153(x95881,x95886)))+~P22(f312(f312(f314(f860(x95881,x95881)),f312(f312(f239(x95881,x95881),x95883),x95885)),x95886))
% 155.93/155.63 [9677]E(x96771,x96772)+~P22(f312(f312(f314(f860(f854(x96773),f854(x96773))),f312(f312(f239(f854(x96773),f854(x96773)),f312(f312(f129(x96773),x96775),f312(f312(f147(x96773),x96771),f127(x96773)))),f312(f312(f129(x96773),x96776),f312(f312(f147(x96773),x96772),f127(x96773))))),f153(x96773,x96774)))+P22(f312(f312(f314(f860(x96773,x96773)),f312(f312(f239(x96773,x96773),x96771),x96772)),x96774))
% 155.93/155.63 [9702]~P22(f312(f312(f314(f860(f854(x97021),f854(x97021))),f312(f312(f239(f854(x97021),f854(x97021)),f312(f312(f129(x97021),x97025),f312(f312(f147(x97021),x97022),f127(x97021)))),f312(f312(f129(x97021),x97026),f312(f312(f147(x97021),x97023),f127(x97021))))),f153(x97021,x97024)))+P22(f312(f312(f314(f860(f854(x97021),f854(x97021))),f312(f312(f239(f854(x97021),f854(x97021)),x97025),x97026)),f153(x97021,x97024)))+P22(f312(f312(f314(f860(x97021,x97021)),f312(f312(f239(x97021,x97021),x97022),x97023)),x97024))
% 155.93/155.63 [9720]P22(f312(x97201,x97202))+P22(f312(f312(f314(x97203),f406(x97201,x97204,x97205,x97206,x97203)),f312(x97204,f407(x97201,x97204,x97205,x97206,x97203))))+~P22(f312(f312(f314(x97203),x97202),f312(f312(f50(x97206,f861(x97203,a846)),x97205),x97204)))
% 155.93/155.63 [8814]~E(f312(f312(f173(x88141,x88142),x88144),x88145),f312(f219(x88142),x88146))+~P22(f312(f312(x88143,x88145),x88146))+E(f312(f312(f173(x88141,x88142),f312(f132(f860(x88141,x88142),f312(f249(x88141,x88142,a846),x88143)),x88144)),x88145),f312(f219(x88142),x88146))
% 155.93/155.63 [9032]~P22(f312(f312(f314(x90325),x90323),x90326))+P22(f312(f312(f227(f861(x90321,a846)),f312(x90322,x90323)),x90324))+~P22(f312(f312(f227(f861(x90321,a846)),f312(f312(f50(x90325,f861(x90321,a846)),x90326),x90322)),x90324))
% 155.93/155.63 [9652]~P3(x96521,x96525,x96524)+P22(f312(f312(f314(f860(x96521,x96521)),f312(f312(f239(x96521,x96521),x96522),x96523)),x96524))+~P22(f312(f312(f314(x96521),x96526),f312(f312(f115(f861(x96521,a846)),f312(f264(x96521,x96521,x96524),f312(f312(f289(x96521),x96522),f189(f861(x96521,a846))))),f312(f264(x96521,x96521,x96524),f312(f312(f289(x96521),x96523),f189(f861(x96521,a846)))))))
% 155.93/155.63 [8488]~P120(x84882)+~E(f312(f312(f89(x84882),f312(f312(f90(x84882),x84884),x84885)),x84881),f312(f312(f89(x84882),f312(f312(f90(x84882),x84883),x84885)),x84886))+E(x84881,f312(f312(f89(x84882),f312(f312(f90(x84882),f312(f312(f21(x84882),x84883),x84884)),x84885)),x84886))
% 155.93/155.63 [8489]~P120(x84891)+~E(f312(f312(f89(x84891),f312(f312(f90(x84891),x84892),x84894)),x84895),f312(f312(f89(x84891),f312(f312(f90(x84891),x84893),x84894)),x84896))+E(f312(f312(f89(x84891),f312(f312(f90(x84891),f312(f312(f21(x84891),x84892),x84893)),x84894)),x84895),x84896)
% 155.93/155.63 [8647]~P120(x86471)+E(f312(f312(f89(x86471),f312(f312(f90(x86471),x86472),x86473)),x86474),f312(f312(f89(x86471),f312(f312(f90(x86471),x86475),x86473)),x86476))+~E(x86476,f312(f312(f89(x86471),f312(f312(f90(x86471),f312(f312(f21(x86471),x86472),x86475)),x86473)),x86474))
% 155.93/155.63 [8648]~P120(x86481)+E(f312(f312(f89(x86481),f312(f312(f90(x86481),x86482),x86483)),x86484),f312(f312(f89(x86481),f312(f312(f90(x86481),x86485),x86483)),x86486))+~E(f312(f312(f89(x86481),f312(f312(f90(x86481),f312(f312(f21(x86481),x86482),x86485)),x86483)),x86484),x86486)
% 155.93/155.63 [8972]~P22(f312(f312(x89724,x89725),x89726))+~P22(f312(f312(x89723,x89725),x89726))+P22(f312(f312(f312(f312(f115(f861(x89721,f861(x89722,a846))),x89723),x89724),x89725),x89726))
% 155.93/155.63 [9230]P22(f312(f312(x92301,x92302),x92303))+P22(f312(f312(x92304,x92302),x92303))+~P22(f312(f312(f312(f312(f124(f861(x92305,f861(x92306,a846))),x92304),x92301),x92302),x92303))
% 155.93/155.63 [9516]~P128(x95161)+~P22(f312(f312(f228(x95161),f312(f312(f89(x95161),f312(f312(f90(x95161),x95164),x95165)),x95162)),f312(f312(f89(x95161),f312(f312(f90(x95161),x95163),x95165)),x95166)))+P22(f312(f312(f228(x95161),x95162),f312(f312(f89(x95161),f312(f312(f90(x95161),f312(f312(f21(x95161),x95163),x95164)),x95165)),x95166)))
% 155.93/155.63 [9517]~P128(x95171)+~P22(f312(f312(f227(x95171),f312(f312(f89(x95171),f312(f312(f90(x95171),x95174),x95175)),x95172)),f312(f312(f89(x95171),f312(f312(f90(x95171),x95173),x95175)),x95176)))+P22(f312(f312(f227(x95171),x95172),f312(f312(f89(x95171),f312(f312(f90(x95171),f312(f312(f21(x95171),x95173),x95174)),x95175)),x95176)))
% 155.93/155.63 [9534]~P128(x95341)+P22(f312(f312(f228(x95341),f312(f312(f89(x95341),f312(f312(f90(x95341),x95342),x95343)),x95344)),f312(f312(f89(x95341),f312(f312(f90(x95341),x95345),x95343)),x95346)))+~P22(f312(f312(f228(x95341),x95344),f312(f312(f89(x95341),f312(f312(f90(x95341),f312(f312(f21(x95341),x95345),x95342)),x95343)),x95346)))
% 155.93/155.63 [9535]~P128(x95351)+P22(f312(f312(f227(x95351),f312(f312(f89(x95351),f312(f312(f90(x95351),x95352),x95353)),x95354)),f312(f312(f89(x95351),f312(f312(f90(x95351),x95355),x95353)),x95356)))+~P22(f312(f312(f227(x95351),x95354),f312(f312(f89(x95351),f312(f312(f90(x95351),f312(f312(f21(x95351),x95355),x95352)),x95353)),x95356)))
% 155.93/155.63 [9641]~P128(x96411)+~P22(f312(f312(f228(x96411),f312(f312(f89(x96411),f312(f312(f90(x96411),x96412),x96414)),x96415)),f312(f312(f89(x96411),f312(f312(f90(x96411),x96413),x96414)),x96416)))+P22(f312(f312(f228(x96411),f312(f312(f89(x96411),f312(f312(f90(x96411),f312(f312(f21(x96411),x96412),x96413)),x96414)),x96415)),x96416))
% 155.93/155.63 [9642]~P128(x96421)+~P22(f312(f312(f227(x96421),f312(f312(f89(x96421),f312(f312(f90(x96421),x96422),x96424)),x96425)),f312(f312(f89(x96421),f312(f312(f90(x96421),x96423),x96424)),x96426)))+P22(f312(f312(f227(x96421),f312(f312(f89(x96421),f312(f312(f90(x96421),f312(f312(f21(x96421),x96422),x96423)),x96424)),x96425)),x96426))
% 155.93/155.63 [9687]~P128(x96871)+P22(f312(f312(f228(x96871),f312(f312(f89(x96871),f312(f312(f90(x96871),x96872),x96873)),x96874)),f312(f312(f89(x96871),f312(f312(f90(x96871),x96875),x96873)),x96876)))+~P22(f312(f312(f228(x96871),f312(f312(f89(x96871),f312(f312(f90(x96871),f312(f312(f21(x96871),x96872),x96875)),x96873)),x96874)),x96876))
% 155.93/155.63 [9688]~P128(x96881)+P22(f312(f312(f227(x96881),f312(f312(f89(x96881),f312(f312(f90(x96881),x96882),x96883)),x96884)),f312(f312(f89(x96881),f312(f312(f90(x96881),x96885),x96883)),x96886)))+~P22(f312(f312(f227(x96881),f312(f312(f89(x96881),f312(f312(f90(x96881),f312(f312(f21(x96881),x96882),x96885)),x96883)),x96884)),x96886))
% 155.93/155.63 [9863]~P26(x98632)+~P22(f312(f70(x98631),x98636))+E(f312(f312(f6(x98631,x98632),f312(f312(f18(x98631,x98632,x98632),f312(f312(f18(x98631,x98632,f861(x98632,x98632)),f312(f312(f8(a846,f861(x98632,f861(x98632,x98632)),x98631),f108(x98632)),x98633)),x98634)),x98635)),x98636),f312(f312(f89(x98632),f312(f312(f6(x98631,x98632),x98634),f312(f312(f115(f861(x98631,a846)),x98636),f312(f233(x98631),x98633)))),f312(f312(f6(x98631,x98632),x98635),f312(f312(f115(f861(x98631,a846)),x98636),f312(f88(f861(x98631,a846)),f312(f233(x98631),x98633))))))
% 155.93/155.63 [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,f861(x99262,x99262)),f312(f312(f8(a846,f861(x99262,f861(x99262,x99262)),x99261),f108(x99262)),f312(f312(f7(x99261,f861(x99261,a846),a846),f314(x99261)),x99263))),x99264)),x99265)),x99266),f189(f861(x99261,a846)))
% 155.93/155.63 [9927]P22(f312(f312(f314(x99272),x99275),x99276))+~P22(f312(f312(f314(x99272),x99274),x99276))+E(f312(f291(x99271,x99272,f312(f312(f7(x99271,x99272,x99272),f312(f312(f7(x99271,x99272,f861(x99272,x99272)),f312(f312(f8(a846,f861(x99272,f861(x99272,x99272)),x99271),f108(x99272)),f312(f312(f7(x99271,f861(x99271,a846),a846),f314(x99271)),x99273))),x99274)),x99275)),x99276),x99273)
% 155.93/155.63 [9928]P22(f312(f312(f314(x99282),x99284),x99286))+~P22(f312(f312(f314(x99282),x99285),x99286))+E(f312(f291(x99281,x99282,f312(f312(f7(x99281,x99282,x99282),f312(f312(f7(x99281,x99282,f861(x99282,x99282)),f312(f312(f8(a846,f861(x99282,f861(x99282,x99282)),x99281),f108(x99282)),f312(f312(f7(x99281,f861(x99281,a846),a846),f314(x99281)),x99283))),x99284)),x99285)),x99286),f312(f88(f861(x99281,a846)),x99283))
% 155.93/155.63 [9929]~P22(f312(f312(f314(x99292),x99294),x99296))+~P22(f312(f312(f314(x99292),x99295),x99296))+E(f312(f291(x99291,x99292,f312(f312(f7(x99291,x99292,x99292),f312(f312(f7(x99291,x99292,f861(x99292,x99292)),f312(f312(f8(a846,f861(x99292,f861(x99292,x99292)),x99291),f108(x99292)),f312(f312(f7(x99291,f861(x99291,a846),a846),f314(x99291)),x99293))),x99294)),x99295)),x99296),f235(f861(x99291,a846)))
% 155.93/155.63 [10063]P18(x100631,x100632,f312(f312(f289(f852(x100631)),f312(f312(f312(f100(x100631),f312(x100633,x100634)),f312(a27,x100634)),f312(x100635,x100634))),f189(f861(f852(x100631),a846))))+~P22(f312(f312(f314(a849),x100634),x100636))+~P18(x100631,f312(f312(f124(f861(f852(x100631),a846)),x100632),f312(f290(a849,f852(x100631),f312(f312(f18(a849,f861(x100631,f861(a848,a846)),f852(x100631)),f312(f312(f18(a849,a847,f861(f861(x100631,f861(a848,a846)),f852(x100631))),f312(f312(f8(f861(x100631,f861(a848,a846)),f861(a847,f861(f861(x100631,f861(a848,a846)),f852(x100631))),a849),f100(x100631)),x100633)),a27)),x100635)),x100636)),f312(f290(a849,f852(x100631),f312(f312(f18(a849,f861(x100631,f861(a848,a846)),f852(x100631)),f312(f312(f18(a849,a847,f861(f861(x100631,f861(a848,a846)),f852(x100631))),f312(f312(f8(f861(x100631,f861(a848,a846)),f861(a847,f861(f861(x100631,f861(a848,a846)),f852(x100631))),a849),f100(x100631)),x100633)),f312(f312(f8(f857(a847),a847,a849),f223(a847)),a30))),x100635)),x100636))
% 155.93/155.63 [8516]E(x85161,x85162)+~P56(x85164,x85165,x85163,x85166,x85167)+~E(f312(x85163,x85161),f312(x85163,x85162))
% 155.93/155.63 [6903]E(f312(f221(f857(x69031),x69032,f192(x69031),x69033),f312(x69034,x69035)),f312(f219(x69031),x69036))+~E(f312(x69034,x69035),f312(f219(x69032),x69037))+~E(f312(x69033,x69037),f312(f219(x69031),x69036))
% 155.93/155.63 [8541]~P6(x85416,x85415,x85417,x85414,x85411)+E(f312(f312(x85411,x85412),x85413),x85414)+P22(f312(f70(x85415),x85413))
% 155.93/155.63 [9379]P45(x93791,x93792,x93793,x93794,x93795,f312(f312(x93793,x93796),x93797))+~E(f312(f312(x93793,x93796),x93797),x93794)+~E(x93795,f189(f861(x93791,a846)))
% 155.93/155.63 [9556]~P22(f312(x95566,x95563))+~P22(f312(f312(f314(f860(x95562,x95562)),f312(f312(f239(x95562,x95562),x95564),x95565)),f312(x95567,x95563)))+P22(f312(f312(f314(f860(f860(x95561,x95562),f860(x95561,x95562))),f312(f312(f239(f860(x95561,x95562),f860(x95561,x95562)),f312(f312(f239(x95561,x95562),x95563),x95564)),f312(f312(f239(x95561,x95562),x95563),x95565))),f262(x95561,x95562,x95566,x95567)))
% 155.93/155.63 [9982]~P45(x99822,x99827,x99823,x99826,x99821,f312(f312(x99823,x99825),x99824))+E(f312(f312(x99823,f801(x99824,x99825,x99821,x99826,x99823,x99827,x99822)),f802(x99824,x99825,x99821,x99826,x99823,x99827,x99822)),f312(f312(x99823,x99825),x99824))+E(x99821,f189(f861(x99822,a846)))
% 155.93/155.63 [9983]~P45(x99837,x99836,x99831,x99834,x99835,f312(f312(x99831,x99832),x99833))+E(f312(f312(x99831,f801(x99833,x99832,x99835,x99834,x99831,x99836,x99837)),f802(x99833,x99832,x99835,x99834,x99831,x99836,x99837)),f312(f312(x99831,x99832),x99833))+E(f312(f312(x99831,x99832),x99833),x99834)
% 155.93/155.63 [9067]~P39(x90671,x90672,x90673,x90675,x90677)+P39(x90671,x90672,x90673,f312(f312(f147(x90671),x90674),x90675),f312(f312(f147(x90672),x90676),x90677))+~P22(f312(f312(x90673,x90674),x90676))
% 155.93/155.63 [9085]P39(x90851,x90852,x90853,x90854,x90855)+~P39(x90851,x90852,x90853,f312(f312(f129(x90851),x90856),x90854),f312(f312(f129(x90852),x90857),x90855))+~E(f312(f190(f854(x90851)),x90856),f312(f190(f854(x90852)),x90857))
% 155.93/155.63 [9086]P39(x90861,x90862,x90863,x90864,x90865)+~P39(x90861,x90862,x90863,f312(f312(f129(x90861),x90864),x90866),f312(f312(f129(x90862),x90865),x90867))+~E(f312(f190(f854(x90861)),x90864),f312(f190(f854(x90862)),x90865))
% 155.93/155.63 [9290]~P39(x92901,x92902,x92903,x92905,x92907)+~P39(x92901,x92902,x92903,x92904,x92906)+P39(x92901,x92902,x92903,f312(f312(f129(x92901),x92904),x92905),f312(f312(f129(x92902),x92906),x92907))
% 155.93/155.63 [9628]~P22(f312(f75(x96281,x96284,x96285,x96286,x96283),x96287))+P22(f312(f75(x96281,x96284,x96285,x96286,f312(f312(f289(x96281),x96282),x96283)),f312(f312(x96285,x96282),x96287)))+P22(f312(f312(f314(x96281),x96282),x96283))
% 155.93/155.63 [9757]~P19(x97573,x97571,x97574,f235(f861(x97573,a846)))+E(f312(f312(f173(x97571,x97572),f312(f312(f150(f860(x97573,x97572),f860(x97571,x97572)),f312(f249(x97573,x97572,f860(x97571,x97572)),f312(f312(f8(x97571,f861(x97572,f860(x97571,x97572)),x97573),f239(x97571,x97572)),x97574))),x97575)),f312(x97574,x97576)),f312(f219(x97572),x97577))+~E(f312(f312(f173(x97573,x97572),x97575),x97576),f312(f219(x97572),x97577))
% 155.93/155.63 [10006]~P45(x100062,x100067,x100066,x100065,x100061,f312(f312(x100066,x100064),x100063))+E(x100061,f189(f861(x100062,a846)))+P22(f312(f312(f314(x100062),f801(x100063,x100064,x100061,x100065,x100066,x100067,x100062)),x100061))
% 155.93/155.63 [10007]~P45(x100075,x100077,x100071,x100074,x100076,f312(f312(x100071,x100072),x100073))+E(f312(f312(x100071,x100072),x100073),x100074)+P22(f312(f312(f314(x100075),f801(x100073,x100072,x100076,x100074,x100071,x100077,x100075)),x100076))
% 155.93/155.63 [6693]~E(x66935,x66937)+~E(x66936,x66934)+E(f312(f312(f312(f312(f81(x66931,f857(x66932)),x66933),x66934),f312(f219(x66932),x66935)),x66936),f312(f219(x66932),x66937))
% 155.93/155.63 [6813]E(x68131,x68132)+~E(f312(x68135,x68131),f312(f219(x68134),x68137))+E(f312(f312(f312(f312(f81(x68133,f857(x68134)),x68135),x68132),f312(f219(x68134),x68136)),x68131),f312(f219(x68134),x68137))
% 155.93/155.63 [7527]E(x75271,x75272)+~E(x75273,x75274)+~E(f312(f312(f312(f312(f81(x75275,f857(x75276)),x75277),x75274),f312(f219(x75276),x75271)),x75273),f312(f219(x75276),x75272))
% 155.93/155.63 [7592]E(x75921,x75922)+E(f312(x75923,x75924),f312(f219(x75925),x75921))+~E(f312(f312(f312(f312(f81(x75926,f857(x75925)),x75923),x75927),f312(f219(x75925),x75922)),x75924),f312(f219(x75925),x75921))
% 155.93/155.63 [7593]E(x75931,x75932)+E(f312(x75933,x75931),f312(f219(x75934),x75935))+~E(f312(f312(f312(f312(f81(x75936,f857(x75934)),x75933),x75932),f312(f219(x75934),x75937)),x75931),f312(f219(x75934),x75935))
% 155.93/155.63 [8757]~P16(x87574,x87575,x87576,x87577,x87571)+~P22(f312(f70(x87575),x87573))+E(f312(f312(x87571,x87572),x87573),f312(f312(f312(f74(x87574,x87575,x87576),x87572),x87577),x87573))
% 155.93/155.63 [8758]~P6(x87584,x87585,x87586,x87587,x87581)+~P22(f312(f70(x87585),x87583))+E(f312(f312(x87581,x87582),x87583),f312(f312(f312(f74(x87584,x87585,x87586),x87582),x87587),x87583))
% 155.93/155.63 [9348]~P18(x93481,x93482,f312(f312(f289(f852(x93481)),f312(f312(f312(f100(x93481),x93483),x93484),x93487)),f189(f861(f852(x93481),a846))))+P18(x93481,x93482,f312(f312(f289(f852(x93481)),f312(f312(f312(f100(x93481),x93483),f36(x93484,x93485)),x93486)),f189(f861(f852(x93481),a846))))+~P18(x93481,x93482,f312(f312(f289(f852(x93481)),f312(f312(f312(f100(x93481),x93487),x93485),x93486)),f189(f861(f852(x93481),a846))))
% 155.93/155.63 [9530]~P17(x95303,x95304,x95305,x95307,x95306,x95301)+~P22(f312(f70(x95304),x95302))+E(f312(x95301,x95302),f312(f312(f312(f74(x95303,x95304,x95305),x95306),x95307),x95302))
% 155.93/155.63 [9682]P45(x96821,x96822,x96823,x96824,x96825,f312(f312(x96823,x96826),x96827))+~P45(x96821,x96822,x96823,x96824,f312(f312(f21(f861(x96821,a846)),x96825),f312(f312(f289(x96821),x96826),f189(f861(x96821,a846)))),x96827)+~P22(f312(f312(f314(x96821),x96826),x96825))
% 155.93/155.63 [9959]~P18(x99591,x99592,f312(f312(f289(f852(x99591)),f312(f312(f312(f100(x99591),f103(x99591,x99593,x99594)),x99595),x99597)),f189(f861(f852(x99591),a846))))+P18(x99591,x99592,f312(f312(f289(f852(x99591)),f312(f312(f312(f100(x99591),x99593),f33(x99594,x99595,x99596)),x99597)),f189(f861(f852(x99591),a846))))+~P18(x99591,x99592,f312(f312(f289(f852(x99591)),f312(f312(f312(f100(x99591),f103(x99591,x99593,f312(f82(a846,a846,a848,a307),x99594))),x99596),x99597)),f189(f861(f852(x99591),a846))))
% 155.93/155.63 [10031]~P45(x100312,x100313,x100314,x100315,x100311,f312(f312(x100314,x100317),x100316))+P45(x100312,x100313,x100314,x100315,f312(f312(f21(f861(x100312,a846)),x100311),f312(f312(f289(x100312),f801(x100316,x100317,x100311,x100315,x100314,x100313,x100312)),f189(f861(x100312,a846)))),f802(x100316,x100317,x100311,x100315,x100314,x100313,x100312))+E(x100311,f189(f861(x100312,a846)))
% 155.93/155.63 [10032]~P45(x100325,x100326,x100321,x100324,x100327,f312(f312(x100321,x100322),x100323))+P45(x100325,x100326,x100321,x100324,f312(f312(f21(f861(x100325,a846)),x100327),f312(f312(f289(x100325),f801(x100323,x100322,x100327,x100324,x100321,x100326,x100325)),f189(f861(x100325,a846)))),f802(x100323,x100322,x100327,x100324,x100321,x100326,x100325))+E(f312(f312(x100321,x100322),x100323),x100324)
% 155.93/155.63 [9074]E(f182(x90741,x90742,x90743,x90744,f312(f312(f155(x90742,x90745),x90746),x90747)),f182(x90741,x90742,x90743,x90744,x90745))+~P22(f312(f312(f228(a853),x90746),f312(f190(f854(x90742)),x90745)))+~P22(f312(f312(f227(a853),f312(f190(f854(x90741)),x90744)),x90746))
% 155.93/155.63 [9368]P22(f312(f312(f227(f861(f860(x93681,x93682),a846)),f312(f312(f267(x93681,x93683,x93682),x93684),x93685)),f312(f312(f267(x93681,x93683,x93682),x93686),x93687)))+~P22(f312(f312(f227(f861(f860(x93683,x93682),a846)),x93685),x93687))+~P22(f312(f312(f227(f861(f860(x93681,x93683),a846)),x93684),x93686))
% 155.93/155.63 [9417]~E(f312(f312(f312(a201,x94176),f40(x94171)),f312(f312(a202,x94174),x94171)),f312(f312(f312(a201,x94177),f40(x94171)),f312(f312(a202,x94174),x94171)))+P22(f312(f312(f312(f312(a198,f32(x94171,x94172,x94173)),x94174),x94175),f312(f312(f312(a201,x94176),f40(x94171)),f312(f312(a202,x94174),x94171))))+~P22(f312(f312(f312(f312(a198,x94173),f312(f312(f312(a201,x94174),f40(x94171)),f312(x94172,x94174))),x94175),x94177))
% 155.93/155.63 [9697]~E(f312(f312(f312(a201,f312(f312(a203,x96976),f312(a202,x96974))),x96971),f312(f312(a202,x96976),a25)),f312(f312(f312(a201,f312(f312(a203,x96977),f312(a202,x96974))),x96971),f312(f312(a202,x96977),a25)))+P22(f312(f312(f312(f312(a198,f31(x96971,x96972,x96973)),x96974),x96975),f312(f312(f312(a201,f312(f312(a203,x96976),f312(a202,x96974))),x96971),f312(f312(a202,x96976),a25))))+~P22(f312(f312(f312(f312(a198,f312(a27,x96972)),f312(f312(f312(a201,f312(f312(a203,x96974),a204)),f40(a26)),f312(x96973,x96974))),x96975),x96977))
% 155.93/155.63 [9693]~P22(f312(f312(f314(x96931),x96936),x96935))+P22(f312(f75(x96931,x96932,x96933,x96934,x96935),f312(f312(x96933,x96936),x96937)))+~P22(f312(f75(x96931,x96932,x96933,x96934,f312(f312(f21(f861(x96931,a846)),x96935),f312(f312(f289(x96931),x96936),f189(f861(x96931,a846))))),x96937))
% 155.93/155.63 [10093]~P135(x100931)+~P19(f860(x100932,x100933),x100931,f312(f249(x100932,x100933,x100931),f312(f312(f7(x100932,f861(x100933,x100931),f861(x100933,x100931)),f312(f312(f8(f861(x100931,x100931),f861(f861(x100933,x100931),f861(x100933,x100931)),x100932),f8(x100931,x100931,x100933)),f312(f312(f8(x100931,f861(x100931,x100931),x100932),f90(x100931)),x100934))),x100935)),f312(f312(f247(x100932,x100933),x100936),f312(f16(f861(x100933,a846),x100932),x100937)))+E(f312(f312(f6(x100931,x100931),f39(x100931)),f312(f233(x100931),f312(f312(f8(f861(x100932,a846),a846,x100931),f96(x100932)),f312(f312(f8(f861(x100932,f861(x100933,a846)),f861(x100932,a846),x100931),f312(f8(f861(x100933,a846),a846,x100932),f96(x100933))),f312(f312(f7(x100931,f861(x100932,f861(x100933,a846)),f861(x100932,f861(x100933,a846))),f312(f312(f8(f861(x100932,f861(f861(x100933,a846),f861(x100933,a846))),f861(f861(x100932,f861(x100933,a846)),f861(x100932,f861(x100933,a846))),x100931),f18(x100932,f861(x100933,a846),f861(x100933,a846))),f312(f312(f8(f861(x100932,f861(x100933,f861(a846,a846))),f861(x100932,f861(f861(x100933,a846),f861(x100933,a846))),x100931),f312(f8(f861(x100933,f861(a846,a846)),f861(f861(x100933,a846),f861(x100933,a846)),x100932),f18(x100933,a846,a846))),f312(f312(f8(f861(x100932,f861(x100933,a846)),f861(x100932,f861(x100933,f861(a846,a846))),x100931),f312(f8(f861(x100933,a846),f861(x100933,f861(a846,a846)),x100932),f312(f8(a846,f861(a846,a846),x100933),a310))),f312(f312(f7(x100931,f861(x100932,f861(x100933,x100931)),f861(x100932,f861(x100933,a846))),f312(f312(f8(f861(f861(x100933,x100931),f861(x100933,a846)),f861(f861(x100932,f861(x100933,x100931)),f861(x100932,f861(x100933,a846))),x100931),f8(f861(x100933,x100931),f861(x100933,a846),x100932)),f312(f312(f8(f861(x100931,a846),f861(f861(x100933,x100931),f861(x100933,a846)),x100931),f8(x100931,a846,x100933)),a309))),f312(f312(f7(x100932,f861(x100933,x100931),f861(x100933,x100931)),f312(f312(f8(f861(x100931,x100931),f861(f861(x100933,x100931),f861(x100933,x100931)),x100932),f8(x100931,x100931,x100933)),f312(f312(f8(x100931,f861(x100931,x100931),x100932),f90(x100931)),x100934))),x100935)))))),f312(f312(f7(x100932,f861(x100933,a846),f861(x100933,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x100933,a846),f861(x100933,a846)),x100932),f8(a846,a846,x100933)),f312(f312(f8(a846,f861(a846,a846),x100932),a310),f312(f312(f7(x100932,f861(x100932,a846),a846),f314(x100932)),x100936)))),f312(f312(f7(x100933,f861(x100933,a846),a846),f314(x100933)),x100937))))))),f312(f312(f90(x100931),f312(f312(f6(x100932,x100931),x100934),x100936)),f312(f312(f6(x100933,x100931),x100935),x100937)))
% 155.93/155.63 [9788]P53(x97881,x97882,x97883,x97884,x97885,x97886,x97887)+~P22(f312(f312(x97884,x97886),x97888))+~P22(f312(f312(x97885,x97888),x97887))
% 155.93/155.63 [9136]~P14(x91368,x91361,x91363,x91365)+~P22(f312(f70(x91368),x91366))+E(f312(f82(x91361,x91361,x91362,f312(x91363,x91364)),f312(f82(x91361,x91361,x91362,f312(x91365,x91366)),x91367)),f312(f82(x91361,x91361,x91362,f312(x91365,x91366)),f312(f82(x91361,x91361,x91362,f312(x91363,x91364)),x91367)))
% 155.93/155.63 [9637]~P19(x96372,x96374,x96376,x96378)+~P19(x96371,x96373,x96375,x96377)+P19(f860(x96371,x96372),f860(x96373,x96374),f250(x96371,x96373,x96372,x96374,x96375,x96376),f312(f312(f247(x96371,x96372),x96377),f312(f16(f861(x96372,a846),x96371),x96378)))
% 155.93/155.63 [10057]P22(f312(f312(f312(f312(a198,x100571),x100572),f410(x100573,x100574,x100575,x100576,x100577,x100578,x100572,x100571)),x100577))+~P22(f312(f312(f312(f312(a198,x100571),x100572),x100578),x100577))+~P22(f312(f312(f312(f312(a198,x100576),x100575),x100574),x100573))
% 155.93/155.63 [10058]P22(f312(f312(f312(f312(a198,x100581),x100582),f410(x100583,x100584,x100582,x100581,x100585,x100586,x100587,x100588)),x100583))+~P22(f312(f312(f312(f312(a198,x100581),x100582),x100584),x100583))+~P22(f312(f312(f312(f312(a198,x100588),x100587),x100586),x100585))
% 155.93/155.63 [9315]P22(f312(f312(f314(f860(x93151,x93152)),f312(f312(f239(x93151,x93152),x93153),x93154)),f312(f312(f267(x93151,x93155,x93152),x93156),x93157)))+~P22(f312(f312(f314(f860(x93151,x93155)),f312(f312(f239(x93151,x93155),x93153),x93158)),x93156))+~P22(f312(f312(f314(f860(x93155,x93152)),f312(f312(f239(x93155,x93152),x93158),x93154)),x93157))
% 155.93/155.63 [9504]~P22(f312(f312(f227(f861(f860(x95043,x95042),a846)),x95045),f312(f312(f247(x95043,x95042),x95048),f312(f16(f861(x95042,a846),x95043),x95047))))+~P22(f312(f312(f227(f861(f860(x95041,x95043),a846)),x95044),f312(f312(f247(x95041,x95043),x95046),f312(f16(f861(x95043,a846),x95041),x95048))))+P22(f312(f312(f227(f861(f860(x95041,x95042),a846)),f312(f312(f267(x95041,x95043,x95042),x95044),x95045)),f312(f312(f247(x95041,x95042),x95046),f312(f16(f861(x95042,a846),x95041),x95047))))
% 155.93/155.63 [9551]~E(x95513,x95515)+P22(f312(f312(f314(f860(f860(x95511,x95512),f860(x95511,x95512))),f312(f312(f239(f860(x95511,x95512),f860(x95511,x95512)),f312(f312(f239(x95511,x95512),x95513),x95514)),f312(f312(f239(x95511,x95512),x95515),x95516))),f304(x95511,x95512,x95517,x95518)))+~P22(f312(f312(f314(f860(x95512,x95512)),f312(f312(f239(x95512,x95512),x95514),x95516)),x95518))
% 155.93/155.63 [9659]E(x96591,x96592)+~P22(f312(f312(f314(f860(f860(x96593,x96595),f860(x96593,x96595))),f312(f312(f239(f860(x96593,x96595),f860(x96593,x96595)),f312(f312(f239(x96593,x96595),x96591),x96596)),f312(f312(f239(x96593,x96595),x96592),x96597))),f304(x96593,x96595,x96594,x96598)))+P22(f312(f312(f314(f860(x96593,x96593)),f312(f312(f239(x96593,x96593),x96591),x96592)),x96594))
% 155.93/155.63 [9676]~P22(f312(f312(f314(f860(f860(x96761,x96765),f860(x96761,x96765))),f312(f312(f239(f860(x96761,x96765),f860(x96761,x96765)),f312(f312(f239(x96761,x96765),x96762),x96766)),f312(f312(f239(x96761,x96765),x96763),x96767))),f304(x96761,x96765,x96764,x96768)))+P22(f312(f312(f314(f860(x96761,x96761)),f312(f312(f239(x96761,x96761),x96762),x96763)),x96764))+P22(f312(f312(f314(f860(x96765,x96765)),f312(f312(f239(x96765,x96765),x96766),x96767)),x96768))
% 155.93/155.63 [9580]~P17(x95807,x95805,x95801,x95808,x95802,x95804)+~P22(f312(f70(x95805),x95806))+E(f312(f312(x95801,f312(x95802,x95803)),f312(x95804,f312(f312(f21(f861(x95805,a846)),x95806),f312(f312(f289(x95805),x95803),f189(f861(x95805,a846)))))),f312(x95804,f312(f312(f289(x95805),x95803),x95806)))
% 155.93/155.63 [9093]~P22(f312(f312(f312(x90935,x90938),x90936),x90937))+~P22(f312(f312(f314(x90931),x90938),x90934))+P22(f312(f312(f312(f312(f50(x90931,f861(x90932,f861(x90933,a846))),x90934),x90935),x90936),x90937))
% 155.93/155.63 [9301]P22(f312(f312(f312(x93011,x93012),x93013),x93014))+~P22(f312(f312(f314(x93015),x93012),x93016))+~P22(f312(f312(f312(f312(f51(x93015,f861(x93017,f861(x93018,a846))),x93016),x93011),x93013),x93014))
% 155.93/155.63 [9497]~P16(x94973,x94972,x94974,x94978,x94971)+~P22(f312(f70(x94972),x94977))+E(f312(f312(x94971,f312(f312(f18(x94972,x94973,x94973),f312(f312(f8(x94973,f861(x94973,x94973),x94972),x94974),x94975)),x94976)),x94977),f312(f312(x94974,f312(f312(x94971,x94975),x94977)),f312(f312(x94971,x94976),x94977)))
% 155.93/155.63 [9764]~E(f312(f290(x97642,x97644,x97646),x97648),x976410)+~E(f312(f290(x97641,x97643,x97645),x97647),x97649)+E(f312(f290(f860(x97641,x97642),f860(x97643,x97644),f250(x97641,x97643,x97642,x97644,x97645,x97646)),f312(f312(f247(x97641,x97642),x97647),f312(f16(f861(x97642,a846),x97641),x97648))),f312(f312(f247(x97643,x97644),x97649),f312(f16(f861(x97644,a846),x97643),x976410)))
% 155.93/155.63 [4777]~P103(x47772)+~P33(x47772,x47771)+P33(x47772,f128(x47772,x47771))+E(x47771,f127(x47772))
% 155.93/155.63 [4778]~P103(x47782)+~P33(x47782,x47781)+P33(x47782,f650(x47781,x47782))+E(x47781,f127(x47782))
% 155.93/155.63 [5004]~P31(x50042)+E(f10(x50042,x50041),f48(x50042,x50041))+E(x50041,f189(f861(x50042,a846)))+~P22(f312(f70(x50042),x50041))
% 155.93/155.63 [5005]~P31(x50052)+E(f11(x50052,x50051),f49(x50052,x50051))+E(x50051,f189(f861(x50052,a846)))+~P22(f312(f70(x50052),x50051))
% 155.93/155.63 [5169]~P103(x51692)+~P33(x51692,x51691)+E(x51691,f127(x51692))+E(f312(f312(f147(x51692),f689(x51691,x51692)),f650(x51691,x51692)),x51691)
% 155.93/155.63 [5951]~P87(x59512)+E(x59511,f189(f861(x59512,a846)))+P22(f312(f312(f227(x59512),f11(x59512,x59511)),f10(x59512,x59511)))+~P22(f312(f70(x59512),x59511))
% 155.93/155.63 [5960]~P43(x59602)+~P43(x59601)+E(x59601,x59602)+~E(f312(f290(a1,a853,a118),x59601),f312(f290(a1,a853,a118),x59602))
% 155.93/155.63 [8955]~P112(x89551)+~P22(f312(f312(f314(x89551),x89552),f123(x89551)))+P22(f312(f312(f228(x89551),f312(f312(f89(x89551),f312(f312(f89(x89551),f87(x89551)),x89552)),x89552)),f2(x89551)))+~P22(f312(f312(f228(x89551),x89552),f2(x89551)))
% 155.93/155.63 [9193]~P112(x91931)+~P22(f312(f312(f314(x91931),x91932),f123(x91931)))+~P22(f312(f312(f228(x91931),f312(f312(f89(x91931),f312(f312(f89(x91931),f87(x91931)),x91932)),x91932)),f2(x91931)))+P22(f312(f312(f228(x91931),x91932),f2(x91931)))
% 155.93/155.63 [4832]~P109(x48322)+~P135(x48322)+E(x48321,f2(a853))+E(f312(f312(f240(x48322),f2(x48322)),x48321),f2(x48322))
% 155.93/155.63 [4836]~P109(x48361)+~P135(x48361)+~E(x48362,f2(a853))+E(f312(f312(f240(x48361),f2(x48361)),x48362),f87(x48361))
% 155.93/155.63 [4991]~P134(x49912)+E(x49911,f87(x49912))+E(x49911,f312(f88(x49912),f87(x49912)))+~E(f312(f312(f90(x49912),x49911),x49911),f87(x49912))
% 155.93/155.63 [5247]~P85(x52472)+E(x52471,f2(x52472))+E(f91(x52472,x52471),f312(f88(x52472),f87(x52472)))+P22(f312(f312(f228(x52472),f2(x52472)),x52471))
% 155.93/155.63 [5475]~P85(x54752)+E(f91(x54752,x54751),f87(x54752))+E(x54751,f2(x54752))+~P22(f312(f312(f228(x54752),f2(x54752)),x54751))
% 155.93/155.63 [5486]E(x54861,x54862)+~E(f312(f117(a853),x54861),f312(f117(a853),x54862))+P22(f312(a194,f312(f117(a1),x54862)))+P22(f312(a194,f312(f117(a1),x54861)))
% 155.93/155.63 [5521]E(x55211,f2(a1))+~E(f312(f47(a1,x55212),x55211),f2(a1))+P22(f312(f312(f228(a1),x55211),x55212))+P22(f312(f312(f228(a1),x55212),x55211))
% 155.93/155.63 [5539]~P89(x55391)+~E(x55392,f2(x55391))+E(f312(f312(f89(x55391),x55392),x55392),f2(x55391))+~P22(f312(f312(f314(x55391),x55392),f123(x55391)))
% 155.93/155.63 [5550]E(x55501,f2(a1))+~E(f312(f47(a1,x55502),x55501),f2(a1))+P22(f312(f312(f227(a1),x55502),f2(a1)))+P22(f312(f312(f228(a1),x55502),x55501))
% 155.93/155.63 [5579]E(x55791,f2(a1))+~E(f312(f47(a1,x55792),x55791),f2(a1))+P22(f312(f312(f227(a1),f2(a1)),x55792))+P22(f312(f312(f228(a1),x55791),x55792))
% 155.93/155.63 [5673]~P89(x56732)+E(x56731,f2(x56732))+~E(f312(f312(f89(x56732),x56731),x56731),f2(x56732))+~P22(f312(f312(f314(x56732),x56731),f123(x56732)))
% 155.93/155.63 [5729]E(f312(f117(a853),x57291),f312(f117(a853),x57292))+~E(f312(f117(a1),x57292),f2(a1))+P22(f312(a194,f312(f117(a1),x57292)))+~P22(f312(a194,f312(f117(a1),x57291)))
% 155.93/155.63 [5752]~E(f312(f117(a853),x57522),f312(f117(a853),x57521))+E(f312(f117(a1),x57521),f2(a1))+P22(f312(a194,f312(f117(a1),x57521)))+~P22(f312(a194,f312(f117(a1),x57522)))
% 155.93/155.63 [5761]~P103(x57612)+E(x57611,f189(f861(x57612,a846)))+~P22(f312(f70(x57612),x57611))+P22(f312(f312(f314(x57612),f14(x57612,x57611)),x57611))
% 155.93/155.63 [5762]~P103(x57622)+E(x57621,f189(f861(x57622,a846)))+~P22(f312(f70(x57622),x57621))+P22(f312(f312(f314(x57622),f15(x57622,x57621)),x57621))
% 155.93/155.63 [5932]~P112(x59321)+~P90(x59321)+P22(f312(f312(f228(x59321),f2(x59321)),f312(f117(x59321),x59322)))+~P22(f312(f312(f228(a1),a92),x59322))
% 155.93/155.63 [5933]~P112(x59331)+~P90(x59331)+P22(f312(f312(f227(x59331),f2(x59331)),f312(f117(x59331),x59332)))+~P22(f312(f312(f227(a1),a92),x59332))
% 155.93/155.63 [5950]~P112(x59501)+~P90(x59501)+E(f312(f84(x59501),f312(f117(x59501),x59502)),f312(f117(x59501),x59502))+P22(f312(f312(f228(x59501),f312(f117(x59501),x59502)),f2(x59501)))
% 155.93/155.63 [5986]E(x59861,x59862)+~E(f312(a118,x59861),f312(a118,x59862))+~P22(f312(f312(f227(a1),f2(a1)),x59862))+~P22(f312(f312(f227(a1),f2(a1)),x59861))
% 155.93/155.63 [6176]~P90(x61762)+~P112(x61762)+~P22(f312(f312(f228(x61762),f2(x61762)),f312(f117(x61762),x61761)))+P22(f312(f312(f228(a1),a92),x61761))
% 155.93/155.63 [6177]~P90(x61772)+~P112(x61772)+~P22(f312(f312(f227(x61772),f2(x61772)),f312(f117(x61772),x61771)))+P22(f312(f312(f227(a1),a92),x61771))
% 155.93/155.63 [6182]~P112(x61821)+~P90(x61821)+P22(f312(f312(f228(x61821),f312(f117(x61821),x61822)),f2(x61821)))+~P22(f312(f312(f228(a1),x61822),a92))
% 155.93/155.63 [6183]~P112(x61831)+~P90(x61831)+P22(f312(f312(f227(x61831),f312(f117(x61831),x61832)),f2(x61831)))+~P22(f312(f312(f227(a1),x61832),a92))
% 155.93/155.63 [6483]~P90(x64832)+~P112(x64832)+~P22(f312(f312(f228(x64832),f312(f117(x64832),x64831)),f2(x64832)))+P22(f312(f312(f228(a1),x64831),a92))
% 155.93/155.63 [6484]~P90(x64842)+~P112(x64842)+~P22(f312(f312(f227(x64842),f312(f117(x64842),x64841)),f2(x64842)))+P22(f312(f312(f227(a1),x64841),a92))
% 155.93/155.63 [6574]~P112(x65741)+~P90(x65741)+E(f312(f84(x65741),f312(f117(x65741),x65742)),f312(f88(x65741),f312(f117(x65741),x65742)))+~P22(f312(f312(f228(x65741),f312(f117(x65741),x65742)),f2(x65741)))
% 155.93/155.63 [6597]E(f312(f117(a853),x65971),f312(f117(a853),x65972))+~E(f312(f117(a1),x65972),f2(a1))+~P22(f312(f312(f227(a1),f312(f117(a1),x65971)),f2(a1)))+~P22(f312(a194,f312(f117(a1),x65971)))
% 155.93/155.63 [7458]~P103(x74582)+E(x74581,f189(f861(x74582,a846)))+~P22(f312(f70(x74582),x74581))+P22(f312(f312(f227(x74582),f13(x74582,f225(x74582),x74581)),f12(x74582,f226(x74582),x74581)))
% 155.93/155.63 [7774]~P43(x77742)+~P32(x77741)+P22(f312(f312(f314(a1),x77741),x77742))+~P22(f312(f312(f314(a853),f312(a118,x77741)),f312(f290(a1,a853,a118),x77742)))
% 155.93/155.63 [8044]~P63(x80442)+P22(f312(x80441,f192(x80442)))+~P22(f312(f66(f857(x80442)),x80441))+P22(f312(f66(x80442),f312(f312(f8(f857(x80442),a846,x80442),x80441),f219(x80442))))
% 155.93/155.63 [8522]~P63(x85221)+~P22(f312(x85222,f192(x85221)))+P22(f312(f67(f857(x85221)),x85222))+~P22(f312(f67(x85221),f312(f312(f8(f857(x85221),a846,x85221),x85222),f219(x85221))))
% 155.93/155.63 [9335]E(x93351,f2(a1))+E(x93352,f2(a1))+E(f312(f312(f95(a1,f860(a1,a1)),f312(f312(a200,x93352),x93351)),f312(f312(f18(a1,a1,f860(a1,a1)),f312(f312(f8(a1,f861(a1,f860(a1,a1)),a1),f239(a1,a1)),f47(a1,x93352))),f47(a1,x93351))),f210(x93352,x93351))+P22(f312(f312(f228(a1),x93351),f2(a1)))
% 155.93/155.63 [5758]~P111(x57582)+E(x57581,f2(a1))+E(f312(f88(x57582),f312(f116(x57582),f312(f88(a1),x57581))),f312(f116(x57582),x57581))+~P22(f312(f312(f228(a1),x57581),f2(a1)))
% 155.93/155.63 [5831]~P89(x58311)+~P90(x58311)+~P35(x58311,f312(f117(x58311),x58312))+P35(x58311,f312(f117(x58311),f312(f312(f89(a1),x58312),x58312)))
% 155.93/155.63 [6164]~P70(x61642)+E(x61641,f189(f861(x61642,a846)))+E(f15(x61642,f312(f290(x61642,x61642,f88(x61642)),x61641)),f312(f88(x61642),f14(x61642,x61641)))+~P22(f312(f70(x61642),x61641))
% 155.93/155.63 [6165]~P70(x61652)+E(x61651,f189(f861(x61652,a846)))+E(f14(x61652,f312(f290(x61652,x61652,f88(x61652)),x61651)),f312(f88(x61652),f15(x61652,x61651)))+~P22(f312(f70(x61652),x61651))
% 155.93/155.63 [6198]~P89(x61981)+~P90(x61981)+P35(x61981,f312(f117(x61981),x61982))+~P35(x61981,f312(f117(x61981),f312(f312(f89(a1),x61982),x61982)))
% 155.93/155.63 [7136]E(x71361,f2(a1))+E(f312(f312(f239(a1,a1),f312(f47(a1,x71361),x71362)),f54(a1,x71361,x71362)),f312(a59,f58(f312(f88(a1),x71361),f312(f88(a1),x71362))))+P22(f312(f312(f227(a1),f2(a1)),x71362))+~P22(f312(f312(f227(a1),f2(a1)),x71361))
% 155.93/155.63 [8563]~P43(x85632)+~P43(x85631)+P22(f312(f312(f228(f861(a853,a846)),f312(f290(a1,a853,a118),x85631)),f312(f290(a1,a853,a118),x85632)))+~P22(f312(f312(f228(f861(a1,a846)),x85631),x85632))
% 155.93/155.63 [8774]~E(f701(x87742,x87741),f702(x87742,x87741))+~P22(f312(f133(x87741),f703(x87742,x87741)))+~P22(f312(f133(f854(x87741)),x87742))+P22(f312(f133(x87741),f312(f138(f854(x87741),f854(x87741),f129(x87741),f127(x87741)),x87742)))
% 155.93/155.63 [8871]~P43(x88712)+~P43(x88711)+~P22(f312(f312(f228(f861(a853,a846)),f312(f290(a1,a853,a118),x88711)),f312(f290(a1,a853,a118),x88712)))+P22(f312(f312(f228(f861(a1,a846)),x88711),x88712))
% 155.93/155.63 [8872]~P43(x88722)+~P43(x88721)+~P22(f312(f312(f227(f861(a853,a846)),f312(f290(a1,a853,a118),x88721)),f312(f290(a1,a853,a118),x88722)))+P22(f312(f312(f227(f861(a1,a846)),x88721),x88722))
% 155.93/155.63 [8879]~E(f701(x88792,x88791),f702(x88792,x88791))+~P22(f312(f133(f854(x88791)),x88792))+P22(f312(f133(x88791),f312(f138(f854(x88791),f854(x88791),f129(x88791),f127(x88791)),x88792)))+P22(f312(f312(f314(f854(x88791)),f703(x88792,x88791)),f312(f168(f854(x88791)),x88792)))
% 155.93/155.63 [8923]~P22(f312(f133(x89231),f703(x89232,x89231)))+~P22(f312(f133(f854(x89231)),x89232))+P22(f312(f133(x89231),f312(f138(f854(x89231),f854(x89231),f129(x89231),f127(x89231)),x89232)))+P22(f312(f312(f314(f854(x89231)),f702(x89232,x89231)),f312(f168(f854(x89231)),x89232)))
% 155.93/155.63 [8924]~P22(f312(f133(x89241),f703(x89242,x89241)))+~P22(f312(f133(f854(x89241)),x89242))+P22(f312(f133(x89241),f312(f138(f854(x89241),f854(x89241),f129(x89241),f127(x89241)),x89242)))+P22(f312(f312(f314(f854(x89241)),f701(x89242,x89241)),f312(f168(f854(x89241)),x89242)))
% 155.93/155.63 [8996]~P22(f312(f133(f854(x89961)),x89962))+P22(f312(f133(x89961),f312(f138(f854(x89961),f854(x89961),f129(x89961),f127(x89961)),x89962)))+P22(f312(f312(f314(f854(x89961)),f702(x89962,x89961)),f312(f168(f854(x89961)),x89962)))+P22(f312(f312(f314(f854(x89961)),f703(x89962,x89961)),f312(f168(f854(x89961)),x89962)))
% 155.93/155.63 [8997]~P22(f312(f133(f854(x89971)),x89972))+P22(f312(f133(x89971),f312(f138(f854(x89971),f854(x89971),f129(x89971),f127(x89971)),x89972)))+P22(f312(f312(f314(f854(x89971)),f701(x89972,x89971)),f312(f168(f854(x89971)),x89972)))+P22(f312(f312(f314(f854(x89971)),f703(x89972,x89971)),f312(f168(f854(x89971)),x89972)))
% 155.93/155.63 [9009]~E(f312(f312(f115(f861(x90091,a846)),f312(f168(x90091),f702(x90092,x90091))),f312(f168(x90091),f701(x90092,x90091))),f189(f861(x90091,a846)))+~P22(f312(f133(x90091),f703(x90092,x90091)))+~P22(f312(f133(f854(x90091)),x90092))+P22(f312(f133(x90091),f312(f138(f854(x90091),f854(x90091),f129(x90091),f127(x90091)),x90092)))
% 155.93/155.63 [9070]~E(f312(f312(f115(f861(x90701,a846)),f312(f168(x90701),f702(x90702,x90701))),f312(f168(x90701),f701(x90702,x90701))),f189(f861(x90701,a846)))+~P22(f312(f133(f854(x90701)),x90702))+P22(f312(f133(x90701),f312(f138(f854(x90701),f854(x90701),f129(x90701),f127(x90701)),x90702)))+P22(f312(f312(f314(f854(x90701)),f703(x90702,x90701)),f312(f168(f854(x90701)),x90702)))
% 155.93/155.63 [8105]~P90(x81052)+~P112(x81052)+~P22(f312(f312(f228(x81052),f312(f117(x81052),x81051)),f87(x81052)))+P22(f312(f312(f228(a1),x81051),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))
% 155.93/155.63 [8106]~P90(x81062)+~P112(x81062)+~P22(f312(f312(f227(x81062),f312(f117(x81062),x81061)),f87(x81062)))+P22(f312(f312(f227(a1),x81061),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))
% 155.93/155.63 [8393]~P112(x83931)+~P90(x83931)+P22(f312(f312(f228(x83931),f312(f117(x83931),x83932)),f87(x83931)))+~P22(f312(f312(f228(a1),x83932),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))
% 155.93/155.63 [8394]~P112(x83941)+~P90(x83941)+P22(f312(f312(f227(x83941),f312(f117(x83941),x83942)),f87(x83941)))+~P22(f312(f312(f227(a1),x83942),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)))
% 155.93/155.63 [8588]~P90(x85882)+~P112(x85882)+~P22(f312(f312(f228(x85882),f87(x85882)),f312(f117(x85882),x85881)))+P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),x85881))
% 155.93/155.63 [8589]~P90(x85892)+~P112(x85892)+~P22(f312(f312(f227(x85892),f87(x85892)),f312(f117(x85892),x85891)))+P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),x85891))
% 155.93/155.63 [8961]~P112(x89611)+~P90(x89611)+P22(f312(f312(f228(x89611),f87(x89611)),f312(f117(x89611),x89612)))+~P22(f312(f312(f228(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),x89612))
% 155.93/155.63 [8962]~P112(x89621)+~P90(x89621)+P22(f312(f312(f227(x89621),f87(x89621)),f312(f117(x89621),x89622)))+~P22(f312(f312(f227(a1),f312(f312(f21(a1),f312(f312(f89(a1),a92),a92)),a111)),x89622))
% 155.93/155.63 [9467]~P134(x94672)+E(x94671,f87(x94672))+E(x94671,f312(f88(x94672),f87(x94672)))+~E(f312(f312(f240(x94672),x94671),f312(f117(a853),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(x94672))
% 155.93/155.63 [9732]~P90(x97321)+~P66(x97321)+~P22(f312(f312(f228(x97321),f2(x97321)),x97322))+P22(f312(f312(f228(x97321),f2(x97321)),f312(f312(f268(x97321),x97322),f312(f117(x97321),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))))))
% 155.93/155.63 [9798]~P90(x97981)+~P66(x97981)+P22(f312(f312(f228(x97981),f2(x97981)),x97982))+~P22(f312(f312(f228(x97981),f2(x97981)),f312(f312(f268(x97981),x97982),f312(f117(x97981),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))))))
% 155.93/155.63 [10061]~P111(x100612)+E(x100611,f2(a1))+P22(f312(f312(f228(a1),x100611),f2(a1)))+E(f312(f312(f249(a1,a1,x100612),f312(f312(f7(a1,f861(a1,f861(x100612,x100612)),f861(a1,x100612)),f312(f312(f8(f861(f861(x100612,x100612),x100612),f861(f861(a1,f861(x100612,x100612)),f861(a1,x100612)),a1),f8(f861(x100612,x100612),x100612,a1)),f312(f312(f8(x100612,f861(f861(x100612,x100612),x100612),a1),f95(x100612,x100612)),f116(x100612)))),f312(f312(f7(a1,f861(x100612,x100612),f861(x100612,x100612)),f312(f312(f8(f861(x100612,f861(x100612,x100612)),f861(f861(x100612,x100612),f861(x100612,x100612)),a1),f18(x100612,x100612,x100612)),f312(f312(f7(a1,f861(x100612,x100612),f861(x100612,f861(x100612,x100612))),f312(f312(f8(f861(x100612,f861(x100612,x100612)),f861(f861(x100612,x100612),f861(x100612,f861(x100612,x100612))),a1),f8(x100612,f861(x100612,x100612),x100612)),f312(f312(f8(a846,f861(x100612,f861(x100612,x100612)),a1),f108(x100612)),f312(f312(f7(a1,a1,a846),a309),f2(a1))))),f312(f312(f18(x100612,x100612,x100612),f89(x100612)),f5(x100612))))),f312(f312(f7(x100612,x100612,x100612),f312(f312(f8(x100612,f861(x100612,x100612),x100612),f89(x100612)),f312(f312(f18(x100612,x100612,x100612),f89(x100612)),f5(x100612)))),f87(x100612))))),f312(f312(f239(a1,a1),f312(f47(a1,x100611),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,x100611,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(x100612),x100611))
% 155.93/155.63 [5014]~P31(x50143)+~P49(x50143,x50143,x50141)+E(f312(x50141,x50142),x50142)+~E(x50142,f110(x50143,x50141))
% 155.93/155.63 [5015]~P31(x50153)+~P49(x50153,x50153,x50151)+E(f312(x50151,x50152),x50152)+~E(x50152,f109(x50153,x50151))
% 155.93/155.63 [4803]~P89(x48033)+~P90(x48033)+E(x48031,x48032)+~E(f312(f117(x48033),x48031),f312(f117(x48033),x48032))
% 155.93/155.63 [5941]~P22(f312(x59411,x59412))+~P22(f312(x59411,x59413))+~P22(f312(f312(f227(a853),x59413),f839(x59412,x59411)))+P22(f312(x59411,f2(a853)))
% 155.93/155.63 [6346]P139(x63462,x63461,x63463)+E(x63461,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f789(x63463,x63461,x63462)))+P22(f312(f312(f228(a1),x63461),f2(a1)))
% 155.93/155.63 [6347]P140(x63472,x63471,x63473)+E(x63471,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f792(x63473,x63471,x63472)))+P22(f312(f312(f228(a1),x63471),f2(a1)))
% 155.93/155.63 [6463]P139(x64631,x64632,x64633)+~P22(f312(x64631,x64633))+P22(f312(f312(f227(a1),f2(a1)),f789(x64633,x64632,x64631)))+P22(f312(f312(f228(a1),x64632),f2(a1)))
% 155.93/155.63 [6489]P140(x64891,x64892,x64893)+P22(f312(f312(f227(a1),f2(a1)),f792(x64893,x64892,x64891)))+~P22(f312(x64891,f2(a1)))+P22(f312(f312(f228(a1),x64892),f2(a1)))
% 155.93/155.63 [6517]P139(x65172,x65171,x65173)+E(x65171,f2(a1))+~P22(f312(x65172,f789(x65173,x65171,x65172)))+P22(f312(f312(f228(a1),x65171),f2(a1)))
% 155.93/155.63 [6518]P140(x65182,x65181,x65183)+E(x65181,f2(a1))+~P22(f312(x65182,f793(x65183,x65181,x65182)))+P22(f312(f312(f228(a1),x65181),f2(a1)))
% 155.93/155.63 [6617]~P103(x66171)+~P31(x66171)+~P22(f312(f312(f228(x66171),x66172),f48(x66171,x66173)))+P22(f312(f312(f228(x66171),x66172),f676(x66173,x66172,x66171)))
% 155.93/155.63 [6628]P139(x66281,x66282,x66283)+~P22(f312(x66281,x66283))+~P22(f312(x66281,f789(x66283,x66282,x66281)))+P22(f312(f312(f228(a1),x66282),f2(a1)))
% 155.93/155.63 [6660]P140(x66601,x66602,x66603)+~P22(f312(x66601,f793(x66603,x66602,x66601)))+~P22(f312(x66601,f2(a1)))+P22(f312(f312(f228(a1),x66602),f2(a1)))
% 155.93/155.63 [6908]P139(x69082,x69081,x69083)+E(x69081,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f789(x69083,x69081,x69082)))+P22(f312(f312(f228(a1),x69081),f788(x69083,x69081,x69082)))
% 155.93/155.63 [6909]P140(x69092,x69091,x69093)+E(x69091,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f792(x69093,x69091,x69092)))+P22(f312(f312(f228(a1),x69091),f796(x69093,x69091,x69092)))
% 155.93/155.63 [7026]P139(x70261,x70262,x70263)+~P22(f312(x70261,x70263))+P22(f312(f312(f227(a1),f2(a1)),f789(x70263,x70262,x70261)))+P22(f312(f312(f228(a1),x70262),f788(x70263,x70262,x70261)))
% 155.93/155.63 [7044]P140(x70441,x70442,x70443)+P22(f312(f312(f227(a1),f2(a1)),f792(x70443,x70442,x70441)))+P22(f312(f312(f228(a1),x70442),f796(x70443,x70442,x70441)))+~P22(f312(x70441,f2(a1)))
% 155.93/155.63 [7080]P139(x70802,x70801,x70803)+E(x70801,f2(a1))+~P22(f312(x70802,f789(x70803,x70801,x70802)))+P22(f312(f312(f228(a1),x70801),f788(x70803,x70801,x70802)))
% 155.93/155.63 [7081]P140(x70812,x70811,x70813)+E(x70811,f2(a1))+~P22(f312(x70812,f793(x70813,x70811,x70812)))+P22(f312(f312(f228(a1),x70811),f796(x70813,x70811,x70812)))
% 155.93/155.63 [7122]P139(x71222,x71221,x71223)+E(x71221,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f789(x71223,x71221,x71222)))+~P22(f312(x71222,f788(x71223,x71221,x71222)))
% 155.93/155.63 [7123]P140(x71232,x71231,x71233)+E(x71231,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f792(x71233,x71231,x71232)))+~P22(f312(x71232,f797(x71233,x71231,x71232)))
% 155.93/155.63 [7199]P139(x71991,x71992,x71993)+~P22(f312(x71991,x71993))+~P22(f312(x71991,f789(x71993,x71992,x71991)))+P22(f312(f312(f228(a1),x71992),f788(x71993,x71992,x71991)))
% 155.93/155.63 [7217]P140(x72171,x72172,x72173)+~P22(f312(x72171,f793(x72173,x72172,x72171)))+P22(f312(f312(f228(a1),x72172),f796(x72173,x72172,x72171)))+~P22(f312(x72171,f2(a1)))
% 155.93/155.63 [7221]P139(x72211,x72212,x72213)+~P22(f312(x72211,x72213))+P22(f312(f312(f227(a1),f2(a1)),f789(x72213,x72212,x72211)))+~P22(f312(x72211,f788(x72213,x72212,x72211)))
% 155.93/155.63 [7241]P140(x72411,x72412,x72413)+P22(f312(f312(f227(a1),f2(a1)),f792(x72413,x72412,x72411)))+~P22(f312(x72411,f797(x72413,x72412,x72411)))+~P22(f312(x72411,f2(a1)))
% 155.93/155.63 [7263]P139(x72632,x72631,x72633)+E(x72631,f2(a1))+~P22(f312(x72632,f789(x72633,x72631,x72632)))+~P22(f312(x72632,f788(x72633,x72631,x72632)))
% 155.93/155.63 [7264]P140(x72642,x72641,x72643)+E(x72641,f2(a1))+~P22(f312(x72642,f793(x72643,x72641,x72642)))+~P22(f312(x72642,f797(x72643,x72641,x72642)))
% 155.93/155.63 [7354]P139(x73541,x73542,x73543)+~P22(f312(x73541,x73543))+~P22(f312(x73541,f789(x73543,x73542,x73541)))+~P22(f312(x73541,f788(x73543,x73542,x73541)))
% 155.93/155.63 [7372]P140(x73721,x73722,x73723)+~P22(f312(x73721,f793(x73723,x73722,x73721)))+~P22(f312(x73721,f797(x73723,x73722,x73721)))+~P22(f312(x73721,f2(a1)))
% 155.93/155.63 [7417]P139(x74172,x74171,x74173)+E(x74171,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f789(x74173,x74171,x74172)))+P22(f312(f312(f227(a1),f788(x74173,x74171,x74172)),f2(a1)))
% 155.93/155.63 [7418]P140(x74182,x74181,x74183)+E(x74181,f2(a1))+P22(f312(f312(f227(a1),f2(a1)),f792(x74183,x74181,x74182)))+P22(f312(f312(f227(a1),f796(x74183,x74181,x74182)),f2(a1)))
% 155.93/155.63 [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(f89(x74191),x74192),x74193)),f123(x74191)))
% 155.93/155.63 [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(f89(x74201),x74202),x74203)),f187(x74201)))
% 155.93/155.63 [7421]~P111(x74211)+~P22(f312(f312(f314(x74211),x74213),f123(x74211)))+~P22(f312(f312(f314(x74211),x74212),f123(x74211)))+P22(f312(f312(f314(x74211),f312(f312(f21(x74211),x74212),x74213)),f123(x74211)))
% 155.93/155.63 [7422]~P111(x74221)+~P22(f312(f312(f314(x74221),x74223),f123(x74221)))+~P22(f312(f312(f314(x74221),x74222),f123(x74221)))+P22(f312(f312(f314(x74221),f312(f312(f90(x74221),x74222),x74223)),f123(x74221)))
% 155.93/155.63 [7423]~P23(x74231)+~P22(f312(f312(f314(x74231),x74233),f187(x74231)))+~P22(f312(f312(f314(x74231),x74232),f187(x74231)))+P22(f312(f312(f314(x74231),f312(f312(f90(x74231),x74232),x74233)),f187(x74231)))
% 155.93/155.63 [7424]~P84(x74241)+~P22(f312(f312(f228(x74241),x74243),f2(x74241)))+~P22(f312(f312(f228(x74241),x74242),f2(x74241)))+P22(f312(f312(f228(x74241),f312(f312(f89(x74241),x74242),x74243)),f2(x74241)))
% 155.93/155.63 [7425]~P84(x74251)+~P22(f312(f312(f227(x74251),x74252),f2(x74251)))+~P22(f312(f312(f228(x74251),x74253),f2(x74251)))+P22(f312(f312(f228(x74251),f312(f312(f89(x74251),x74252),x74253)),f2(x74251)))
% 155.93/155.63 [7426]~P84(x74261)+~P22(f312(f312(f227(x74261),x74263),f2(x74261)))+~P22(f312(f312(f228(x74261),x74262),f2(x74261)))+P22(f312(f312(f228(x74261),f312(f312(f89(x74261),x74262),x74263)),f2(x74261)))
% 155.93/155.63 [7427]~P84(x74271)+~P22(f312(f312(f227(x74271),x74273),f2(x74271)))+~P22(f312(f312(f227(x74271),x74272),f2(x74271)))+P22(f312(f312(f227(x74271),f312(f312(f89(x74271),x74272),x74273)),f2(x74271)))
% 155.93/155.63 [7453]P139(x74533,x74531,x74532)+E(x74531,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x74531),f790(x74532,x74531,x74533))),f789(x74532,x74531,x74533)),x74532)+P22(f312(f312(f228(a1),x74531),f2(a1)))
% 155.93/155.63 [7454]P140(x74543,x74541,x74542)+E(x74541,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x74541),f793(x74542,x74541,x74543))),f792(x74542,x74541,x74543)),x74542)+P22(f312(f312(f228(a1),x74541),f2(a1)))
% 155.93/155.63 [7538]P139(x75381,x75382,x75383)+~P22(f312(x75381,x75383))+P22(f312(f312(f227(a1),f2(a1)),f789(x75383,x75382,x75381)))+P22(f312(f312(f227(a1),f788(x75383,x75382,x75381)),f2(a1)))
% 155.93/155.63 [7565]P140(x75651,x75652,x75653)+P22(f312(f312(f227(a1),f2(a1)),f792(x75653,x75652,x75651)))+~P22(f312(x75651,f2(a1)))+P22(f312(f312(f227(a1),f796(x75653,x75652,x75651)),f2(a1)))
% 155.93/155.63 [7575]P139(x75753,x75751,x75752)+~P22(f312(x75753,x75752))+E(f312(f312(f89(a1),f312(f312(f90(a1),x75751),f790(x75752,x75751,x75753))),f789(x75752,x75751,x75753)),x75752)+P22(f312(f312(f228(a1),x75751),f2(a1)))
% 155.93/155.63 [7581]P139(x75812,x75811,x75813)+E(x75811,f2(a1))+~P22(f312(x75812,f789(x75813,x75811,x75812)))+P22(f312(f312(f227(a1),f788(x75813,x75811,x75812)),f2(a1)))
% 155.93/155.63 [7582]P140(x75822,x75821,x75823)+E(x75821,f2(a1))+~P22(f312(x75822,f793(x75823,x75821,x75822)))+P22(f312(f312(f227(a1),f796(x75823,x75821,x75822)),f2(a1)))
% 155.93/155.63 [7587]P140(x75873,x75871,x75872)+E(f312(f312(f89(a1),f312(f312(f90(a1),x75871),f793(x75872,x75871,x75873))),f792(x75872,x75871,x75873)),x75872)+~P22(f312(x75873,f2(a1)))+P22(f312(f312(f228(a1),x75871),f2(a1)))
% 155.93/155.63 [7643]P139(x76431,x76432,x76433)+~P22(f312(x76431,x76433))+~P22(f312(x76431,f789(x76433,x76432,x76431)))+P22(f312(f312(f227(a1),f788(x76433,x76432,x76431)),f2(a1)))
% 155.93/155.63 [7648]P140(x76481,x76482,x76483)+~P22(f312(x76481,f793(x76483,x76482,x76481)))+~P22(f312(x76481,f2(a1)))+P22(f312(f312(f227(a1),f796(x76483,x76482,x76481)),f2(a1)))
% 155.93/155.63 [7718]~P66(x77181)+~P22(f312(f312(f228(x77181),f312(f312(f268(x77181),x77183),x77182)),f2(x77181)))+P22(f312(f312(f228(x77181),x77182),f2(x77181)))+P22(f312(f312(f228(x77181),x77183),f2(x77181)))
% 155.93/155.63 [7719]~P118(x77191)+~P22(f312(f312(f227(x77191),f312(f312(f90(x77191),x77193),x77192)),f2(x77191)))+P22(f312(f312(f227(x77191),x77192),f2(x77191)))+P22(f312(f312(f227(x77191),x77193),f2(x77191)))
% 155.93/155.63 [7720]~P66(x77201)+~P22(f312(f312(f227(x77201),f312(f312(f268(x77201),x77203),x77202)),f2(x77201)))+P22(f312(f312(f227(x77201),x77202),f2(x77201)))+P22(f312(f312(f227(x77201),x77203),f2(x77201)))
% 155.93/155.63 [7827]P139(x78273,x78271,x78272)+E(x78271,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x78271),f790(x78272,x78271,x78273))),f789(x78272,x78271,x78273)),x78272)+P22(f312(f312(f228(a1),x78271),f788(x78272,x78271,x78273)))
% 155.93/155.63 [7828]P140(x78283,x78281,x78282)+E(x78281,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x78281),f793(x78282,x78281,x78283))),f792(x78282,x78281,x78283)),x78282)+P22(f312(f312(f228(a1),x78281),f796(x78282,x78281,x78283)))
% 155.93/155.63 [7839]P139(x78393,x78391,x78392)+E(x78391,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x78391),f791(x78392,x78391,x78393))),f788(x78392,x78391,x78393)),x78392)+P22(f312(f312(f227(a1),f2(a1)),f789(x78392,x78391,x78393)))
% 155.93/155.63 [7840]P140(x78403,x78401,x78402)+E(x78401,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x78401),f797(x78402,x78401,x78403))),f796(x78402,x78401,x78403)),x78402)+P22(f312(f312(f227(a1),f2(a1)),f792(x78402,x78401,x78403)))
% 155.93/155.63 [7883]P139(x78833,x78831,x78832)+~P22(f312(x78833,x78832))+E(f312(f312(f89(a1),f312(f312(f90(a1),x78831),f790(x78832,x78831,x78833))),f789(x78832,x78831,x78833)),x78832)+P22(f312(f312(f228(a1),x78831),f788(x78832,x78831,x78833)))
% 155.93/155.63 [7895]P140(x78953,x78951,x78952)+E(f312(f312(f89(a1),f312(f312(f90(a1),x78951),f793(x78952,x78951,x78953))),f792(x78952,x78951,x78953)),x78952)+P22(f312(f312(f228(a1),x78951),f796(x78952,x78951,x78953)))+~P22(f312(x78953,f2(a1)))
% 155.93/155.63 [7901]P139(x79013,x79011,x79012)+~P22(f312(x79013,x79012))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79011),f791(x79012,x79011,x79013))),f788(x79012,x79011,x79013)),x79012)+P22(f312(f312(f227(a1),f2(a1)),f789(x79012,x79011,x79013)))
% 155.93/155.63 [7907]P140(x79073,x79071,x79072)+E(f312(f312(f89(a1),f312(f312(f90(a1),x79071),f797(x79072,x79071,x79073))),f796(x79072,x79071,x79073)),x79072)+P22(f312(f312(f227(a1),f2(a1)),f792(x79072,x79071,x79073)))+~P22(f312(x79073,f2(a1)))
% 155.93/155.63 [7918]P139(x79183,x79181,x79182)+E(x79181,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79181),f790(x79182,x79181,x79183))),f789(x79182,x79181,x79183)),x79182)+~P22(f312(x79183,f788(x79182,x79181,x79183)))
% 155.93/155.63 [7919]P140(x79193,x79191,x79192)+E(x79191,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79191),f793(x79192,x79191,x79193))),f792(x79192,x79191,x79193)),x79192)+~P22(f312(x79193,f797(x79192,x79191,x79193)))
% 155.93/155.63 [7920]P139(x79203,x79201,x79202)+E(x79201,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79201),f791(x79202,x79201,x79203))),f788(x79202,x79201,x79203)),x79202)+~P22(f312(x79203,f789(x79202,x79201,x79203)))
% 155.93/155.63 [7921]P140(x79213,x79211,x79212)+E(x79211,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79211),f797(x79212,x79211,x79213))),f796(x79212,x79211,x79213)),x79212)+~P22(f312(x79213,f793(x79212,x79211,x79213)))
% 155.93/155.63 [7979]P139(x79793,x79791,x79792)+~P22(f312(x79793,x79792))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79791),f790(x79792,x79791,x79793))),f789(x79792,x79791,x79793)),x79792)+~P22(f312(x79793,f788(x79792,x79791,x79793)))
% 155.93/155.63 [7980]P139(x79803,x79801,x79802)+~P22(f312(x79803,x79802))+E(f312(f312(f89(a1),f312(f312(f90(a1),x79801),f791(x79802,x79801,x79803))),f788(x79802,x79801,x79803)),x79802)+~P22(f312(x79803,f789(x79802,x79801,x79803)))
% 155.93/155.63 [7989]P140(x79893,x79891,x79892)+E(f312(f312(f89(a1),f312(f312(f90(a1),x79891),f793(x79892,x79891,x79893))),f792(x79892,x79891,x79893)),x79892)+~P22(f312(x79893,f797(x79892,x79891,x79893)))+~P22(f312(x79893,f2(a1)))
% 155.93/155.63 [7990]P140(x79903,x79901,x79902)+E(f312(f312(f89(a1),f312(f312(f90(a1),x79901),f797(x79902,x79901,x79903))),f796(x79902,x79901,x79903)),x79902)+~P22(f312(x79903,f793(x79902,x79901,x79903)))+~P22(f312(x79903,f2(a1)))
% 155.93/155.63 [8098]P139(x80983,x80981,x80982)+E(x80981,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x80981),f790(x80982,x80981,x80983))),f789(x80982,x80981,x80983)),x80982)+P22(f312(f312(f227(a1),f788(x80982,x80981,x80983)),f2(a1)))
% 155.93/155.63 [8099]P140(x80993,x80991,x80992)+E(x80991,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x80991),f793(x80992,x80991,x80993))),f792(x80992,x80991,x80993)),x80992)+P22(f312(f312(f227(a1),f796(x80992,x80991,x80993)),f2(a1)))
% 155.93/155.63 [8140]P139(x81403,x81401,x81402)+~P22(f312(x81403,x81402))+E(f312(f312(f89(a1),f312(f312(f90(a1),x81401),f790(x81402,x81401,x81403))),f789(x81402,x81401,x81403)),x81402)+P22(f312(f312(f227(a1),f788(x81402,x81401,x81403)),f2(a1)))
% 155.93/155.63 [8145]P140(x81453,x81451,x81452)+E(f312(f312(f89(a1),f312(f312(f90(a1),x81451),f793(x81452,x81451,x81453))),f792(x81452,x81451,x81453)),x81452)+~P22(f312(x81453,f2(a1)))+P22(f312(f312(f227(a1),f796(x81452,x81451,x81453)),f2(a1)))
% 155.93/155.63 [8275]P139(x82753,x82751,x82752)+E(x82751,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x82751),f791(x82752,x82751,x82753))),f788(x82752,x82751,x82753)),x82752)+E(f312(f312(f89(a1),f312(f312(f90(a1),x82751),f790(x82752,x82751,x82753))),f789(x82752,x82751,x82753)),x82752)
% 155.93/155.63 [8276]P140(x82763,x82761,x82762)+E(x82761,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x82761),f797(x82762,x82761,x82763))),f796(x82762,x82761,x82763)),x82762)+E(f312(f312(f89(a1),f312(f312(f90(a1),x82761),f793(x82762,x82761,x82763))),f792(x82762,x82761,x82763)),x82762)
% 155.93/155.63 [8301]P139(x83013,x83011,x83012)+~P22(f312(x83013,x83012))+E(f312(f312(f89(a1),f312(f312(f90(a1),x83011),f791(x83012,x83011,x83013))),f788(x83012,x83011,x83013)),x83012)+E(f312(f312(f89(a1),f312(f312(f90(a1),x83011),f790(x83012,x83011,x83013))),f789(x83012,x83011,x83013)),x83012)
% 155.93/155.63 [8314]P140(x83143,x83141,x83142)+E(f312(f312(f89(a1),f312(f312(f90(a1),x83141),f797(x83142,x83141,x83143))),f796(x83142,x83141,x83143)),x83142)+E(f312(f312(f89(a1),f312(f312(f90(a1),x83141),f793(x83142,x83141,x83143))),f792(x83142,x83141,x83143)),x83142)+~P22(f312(x83143,f2(a1)))
% 155.93/155.63 [8966]~P118(x89661)+~E(x89663,f2(x89661))+~E(x89662,f2(x89661))+P22(f312(f312(f227(x89661),f312(f312(f89(x89661),f312(f312(f90(x89661),x89662),x89662)),f312(f312(f90(x89661),x89663),x89663))),f2(x89661)))
% 155.93/155.63 [10009]~P112(x100091)+~E(x100093,f2(x100091))+~E(x100092,f2(x100091))+P22(f312(f312(f227(x100091),f312(f312(f89(x100091),f312(f312(f240(x100091),x100092),f312(f117(a853),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(x100091),x100093),f312(f117(a853),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(x100091)))
% 155.93/155.63 [4752]~E(x47523,x47521)+~P114(x47522)+E(x47521,f2(x47522))+E(f312(f312(f268(x47522),x47523),x47521),f87(x47522))
% 155.93/155.63 [4804]~P94(x48041)+~E(x48043,f189(x48041))+~E(x48042,f189(x48041))+E(f312(f312(f124(x48041),x48042),x48043),f189(x48041))
% 155.93/155.63 [4805]~P97(x48051)+~E(x48053,f235(x48051))+~E(x48052,f235(x48051))+E(f312(f312(f115(x48051),x48052),x48053),f235(x48051))
% 155.93/155.63 [4894]~P114(x48943)+E(x48941,x48942)+E(x48942,f2(x48943))+~E(f312(f312(f268(x48943),x48941),x48942),f87(x48943))
% 155.93/155.63 [4912]~P133(x49122)+E(x49121,f2(x49122))+E(x49123,f2(x49122))+~E(f312(f312(f90(x49122),x49123),x49121),f2(x49122))
% 155.93/155.63 [4914]~P127(x49142)+E(x49141,f2(x49142))+E(x49143,f2(x49142))+~E(f312(f312(f90(x49142),x49143),x49141),f2(x49142))
% 155.93/155.63 [5283]~P113(x52833)+E(x52831,x52832)+E(x52831,f312(f88(x52833),x52832))+~E(f312(f312(f90(x52833),x52831),x52831),f312(f312(f90(x52833),x52832),x52832))
% 155.93/155.63 [5319]~P88(x53191)+E(f312(f88(x53191),x53192),x53193)+~E(f312(f312(f124(x53191),x53192),x53193),f235(x53191))+~E(f312(f312(f115(x53191),x53192),x53193),f189(x53191))
% 155.93/155.63 [5394]~P112(x53943)+E(x53941,x53942)+P22(f312(f312(f228(x53943),x53942),x53941))+P22(f312(f312(f228(x53943),x53941),x53942))
% 155.93/155.63 [5400]~P103(x54003)+E(x54001,x54002)+P22(f312(f312(f228(x54003),x54002),x54001))+P22(f312(f312(f228(x54003),x54001),x54002))
% 155.93/155.63 [5401]~E(x54012,x54013)+~P103(x54011)+P22(f312(f312(f227(x54011),x54012),x54013))+P22(f312(f312(f228(x54011),x54012),x54013))
% 155.93/155.63 [5655]~P105(x56553)+E(x56551,x56552)+~P22(f312(f312(f227(x56553),x56552),x56551))+P22(f312(f312(f228(x56553),x56552),x56551))
% 155.93/155.63 [5657]~P103(x56573)+E(x56571,x56572)+~P22(f312(f312(f227(x56573),x56571),x56572))+P22(f312(f312(f228(x56573),x56571),x56572))
% 155.93/155.63 [5663]~P105(x56633)+E(x56631,x56632)+~P22(f312(f312(f227(x56633),x56631),x56632))+P22(f312(f312(f228(x56633),x56631),x56632))
% 155.93/155.63 [5755]P139(x57551,x57552,x57553)+~P22(f312(x57551,x57553))+P22(f312(f312(f228(a1),x57552),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x57552))
% 155.93/155.63 [5804]P140(x58041,x58042,x58043)+~P22(f312(x58041,f2(a1)))+P22(f312(f312(f228(a1),x58042),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x58042))
% 155.93/155.63 [5808]~P87(x58081)+E(f312(f312(f124(x58081),x58082),f11(x58081,x58083)),x58082)+~P22(f312(f70(x58081),x58083))+~P22(f312(f312(f314(x58081),x58082),x58083))
% 155.93/155.63 [5809]~P87(x58091)+E(f312(f312(f115(x58091),x58092),f10(x58091,x58093)),x58092)+~P22(f312(f70(x58091),x58093))+~P22(f312(f312(f314(x58091),x58092),x58093))
% 155.93/155.63 [5841]~P87(x58411)+E(f312(f312(f124(x58411),x58412),f10(x58411,x58413)),f10(x58411,x58413))+~P22(f312(f70(x58411),x58413))+~P22(f312(f312(f314(x58411),x58412),x58413))
% 155.93/155.63 [5842]~P87(x58421)+E(f312(f312(f115(x58421),x58422),f11(x58421,x58423)),f11(x58421,x58423))+~P22(f312(f70(x58421),x58423))+~P22(f312(f312(f314(x58421),x58422),x58423))
% 155.93/155.63 [5843]~P103(x58431)+E(f312(f312(f225(x58431),x58432),f15(x58431,x58433)),f15(x58431,x58433))+~P22(f312(f70(x58431),x58433))+~P22(f312(f312(f314(x58431),x58432),x58433))
% 155.93/155.63 [5844]~P103(x58441)+E(f312(f312(f226(x58441),x58442),f14(x58441,x58443)),f14(x58441,x58443))+~P22(f312(f70(x58441),x58443))+~P22(f312(f312(f314(x58441),x58442),x58443))
% 155.93/155.63 [5889]E(x58891,x58892)+~P105(x58893)+~P22(f312(f312(f227(x58893),x58892),x58891))+~P22(f312(f312(f227(x58893),x58891),x58892))
% 155.93/155.63 [6027]~P102(x60271)+P22(f312(f312(f227(x60271),x60273),x60272))+~P22(f312(f312(f227(x60271),x60272),x60273))+P22(f312(f312(f228(x60271),x60272),x60273))
% 155.93/155.63 [6048]~P103(x60481)+~P22(f312(f70(x60481),x60483))+P22(f312(f312(f227(x60481),x60482),f14(x60481,x60483)))+~P22(f312(f312(f314(x60481),x60482),x60483))
% 155.93/155.63 [6097]~P103(x60971)+E(f312(f312(f225(x60971),x60972),f12(x60971,f226(x60971),x60973)),x60972)+~P22(f312(f70(x60971),x60973))+~P22(f312(f312(f314(x60971),x60972),x60973))
% 155.93/155.63 [6098]~P103(x60981)+E(f312(f312(f226(x60981),x60982),f13(x60981,f225(x60981),x60983)),x60982)+~P22(f312(f70(x60981),x60983))+~P22(f312(f312(f314(x60981),x60982),x60983))
% 155.93/155.63 [6234]E(x62341,x62342)+~E(f312(f312(f21(a853),x62341),x62343),f312(f312(f21(a853),x62342),x62343))+~P22(f312(f312(f227(a853),x62343),x62341))+~P22(f312(f312(f227(a853),x62343),x62342))
% 155.93/155.63 [6264]~P103(x62641)+~P22(f312(f70(x62641),x62642))+~P22(f312(f312(f314(x62641),x62643),x62642))+P22(f312(f312(f227(x62641),f15(x62641,x62642)),x62643))
% 155.93/155.63 [6324]P139(x63242,x63241,x63243)+E(x63241,f2(a1))+P22(f312(f312(f228(a1),x63241),f788(x63243,x63241,x63242)))+P22(f312(f312(f228(a1),f2(a1)),x63241))
% 155.93/155.63 [6325]P140(x63252,x63251,x63253)+E(x63251,f2(a1))+P22(f312(f312(f228(a1),x63251),f796(x63253,x63251,x63252)))+P22(f312(f312(f228(a1),f2(a1)),x63251))
% 155.93/155.63 [6327]~P103(x63271)+E(f312(f312(f225(x63271),x63272),f13(x63271,f225(x63271),x63273)),f13(x63271,f225(x63271),x63273))+~P22(f312(f70(x63271),x63273))+~P22(f312(f312(f314(x63271),x63272),x63273))
% 155.93/155.63 [6328]~P103(x63281)+E(f312(f312(f226(x63281),x63282),f12(x63281,f226(x63281),x63283)),f12(x63281,f226(x63281),x63283))+~P22(f312(f70(x63281),x63283))+~P22(f312(f312(f314(x63281),x63282),x63283))
% 155.93/155.63 [6335]~P22(f312(x63351,x63352))+P22(f312(x63351,f738(x63352,x63351,x63353)))+P22(f312(x63351,f2(a853)))+~P22(f312(f312(f228(a853),x63352),x63353))
% 155.93/155.63 [6388]~P22(f312(x63881,x63882))+~P22(f312(f70(x63883),x63882))+P22(f312(x63881,f431(x63881,x63882,x63883)))+P22(f312(x63881,f189(f861(x63883,a846))))
% 155.93/155.63 [6401]~P112(x64011)+~P90(x64011)+P22(f312(f312(f228(x64011),f312(f117(x64011),x64012)),f312(f117(x64011),x64013)))+~P22(f312(f312(f228(a1),x64012),x64013))
% 155.93/155.63 [6402]~P112(x64021)+~P90(x64021)+P22(f312(f312(f227(x64021),f312(f117(x64021),x64022)),f312(f117(x64021),x64023)))+~P22(f312(f312(f227(a1),x64022),x64023))
% 155.93/155.63 [6406]~P22(f312(x64061,x64063))+~P22(f312(f70(x64062),x64063))+P22(f312(f70(x64062),f431(x64061,x64063,x64062)))+P22(f312(x64061,f189(f861(x64062,a846))))
% 155.93/155.63 [6434]P139(x64341,x64342,x64343)+~P22(f312(x64341,x64343))+P22(f312(f312(f228(a1),x64342),f788(x64343,x64342,x64341)))+P22(f312(f312(f228(a1),f2(a1)),x64342))
% 155.93/155.63 [6472]P140(x64721,x64722,x64723)+P22(f312(f312(f228(a1),x64722),f796(x64723,x64722,x64721)))+~P22(f312(x64721,f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x64722))
% 155.93/155.63 [6500]~P104(x65001)+~P91(x65001)+E(f312(f312(f225(x65001),f312(f117(x65001),x65002)),f312(f117(x65001),x65003)),f312(f117(x65001),x65003))+P22(f312(f312(f227(x65001),f312(f117(x65001),x65002)),f312(f117(x65001),x65003)))
% 155.93/155.63 [6501]~P104(x65011)+~P91(x65011)+E(f312(f312(f226(x65011),f312(f117(x65011),x65012)),f312(f117(x65011),x65013)),f312(f117(x65011),x65012))+P22(f312(f312(f227(x65011),f312(f117(x65011),x65012)),f312(f117(x65011),x65013)))
% 155.93/155.63 [6559]P139(x65592,x65591,x65593)+E(x65591,f2(a1))+~P22(f312(x65592,f788(x65593,x65591,x65592)))+P22(f312(f312(f228(a1),f2(a1)),x65591))
% 155.93/155.63 [6560]P140(x65602,x65601,x65603)+E(x65601,f2(a1))+~P22(f312(x65602,f797(x65603,x65601,x65602)))+P22(f312(f312(f228(a1),f2(a1)),x65601))
% 155.93/155.63 [6649]P139(x66491,x66492,x66493)+~P22(f312(x66491,x66493))+~P22(f312(x66491,f788(x66493,x66492,x66491)))+P22(f312(f312(f228(a1),f2(a1)),x66492))
% 155.93/155.63 [6678]P140(x66781,x66782,x66783)+~P22(f312(x66781,f797(x66783,x66782,x66781)))+~P22(f312(x66781,f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x66782))
% 155.93/155.63 [6778]~P90(x67783)+~P112(x67783)+~P22(f312(f312(f228(x67783),f312(f117(x67783),x67781)),f312(f117(x67783),x67782)))+P22(f312(f312(f228(a1),x67781),x67782))
% 155.93/155.63 [6779]~P90(x67793)+~P112(x67793)+~P22(f312(f312(f227(x67793),f312(f117(x67793),x67791)),f312(f117(x67793),x67792)))+P22(f312(f312(f227(a1),x67791),x67792))
% 155.93/155.63 [6805]~P103(x68051)+~P33(x68051,x68053)+P33(x68051,f312(f312(f147(x68051),x68052),x68053))+~P22(f312(f312(f227(x68051),x68052),f646(x68053,x68052,x68051)))
% 155.93/155.63 [6806]~P103(x68061)+~P33(x68061,x68063)+P33(x68061,f312(f312(f147(x68061),x68062),x68063))+~P22(f312(f312(f227(x68061),x68062),f655(x68063,x68062,x68061)))
% 155.93/155.63 [6807]~P103(x68071)+~P33(x68071,x68073)+P33(x68071,f312(f312(f147(x68071),x68072),x68073))+~P22(f312(f312(f227(x68071),x68072),f743(x68072,x68073,x68071)))
% 155.93/155.63 [6895]P139(x68952,x68951,x68953)+E(x68951,f2(a1))+P22(f312(f312(f228(a1),x68951),f2(a1)))+P22(f312(f312(f228(a1),f789(x68953,x68951,x68952)),x68951))
% 155.93/155.63 [6896]P140(x68962,x68961,x68963)+E(x68961,f2(a1))+P22(f312(f312(f228(a1),x68961),f2(a1)))+P22(f312(f312(f228(a1),f792(x68963,x68961,x68962)),x68961))
% 155.93/155.63 [6940]P139(x69402,x69401,x69403)+E(x69401,f2(a1))+P22(f312(f312(f227(a1),f788(x69403,x69401,x69402)),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x69401))
% 155.93/155.63 [6941]P140(x69412,x69411,x69413)+E(x69411,f2(a1))+P22(f312(f312(f227(a1),f796(x69413,x69411,x69412)),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x69411))
% 155.93/155.63 [6961]~P103(x69611)+~P33(x69611,x69613)+E(f312(f312(f145(x69611,x69611,f5(x69611)),x69612),f166(x69611,x69612,x69613)),x69613)+~P22(f312(f312(f314(x69611),x69612),f312(f168(x69611),x69613)))
% 155.93/155.63 [7011]P139(x70111,x70112,x70113)+~P22(f312(x70111,x70113))+P22(f312(f312(f228(a1),x70112),f2(a1)))+P22(f312(f312(f228(a1),f789(x70113,x70112,x70111)),x70112))
% 155.93/155.63 [7015]~P104(x70151)+~P91(x70151)+E(f312(f312(f225(x70151),f312(f117(x70151),x70152)),f312(f117(x70151),x70153)),f312(f117(x70151),x70152))+~P22(f312(f312(f227(x70151),f312(f117(x70151),x70152)),f312(f117(x70151),x70153)))
% 155.93/155.63 [7016]~P104(x70161)+~P91(x70161)+E(f312(f312(f226(x70161),f312(f117(x70161),x70162)),f312(f117(x70161),x70163)),f312(f117(x70161),x70163))+~P22(f312(f312(f227(x70161),f312(f117(x70161),x70162)),f312(f117(x70161),x70163)))
% 155.93/155.63 [7031]P140(x70311,x70312,x70313)+~P22(f312(x70311,f2(a1)))+P22(f312(f312(f228(a1),x70312),f2(a1)))+P22(f312(f312(f228(a1),f792(x70313,x70312,x70311)),x70312))
% 155.93/155.63 [7037]P139(x70371,x70372,x70373)+~P22(f312(x70371,x70373))+P22(f312(f312(f227(a1),f788(x70373,x70372,x70371)),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x70372))
% 155.93/155.63 [7064]P140(x70641,x70642,x70643)+~P22(f312(x70641,f2(a1)))+P22(f312(f312(f227(a1),f796(x70643,x70642,x70641)),f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x70642))
% 155.93/155.63 [7093]~P22(f312(x70931,x70932))+P22(f312(x70931,f2(a853)))+~P22(f312(f312(f228(a853),x70932),x70933))+P22(f312(f312(f228(a853),f738(x70932,x70931,x70933)),x70933))
% 155.93/155.63 [7109]~P103(x71091)+~P33(x71091,x71093)+P33(x71091,f312(f312(f147(x71091),x71092),x71093))+P22(f312(f312(f314(x71091),f646(x71093,x71092,x71091)),f312(f168(x71091),x71093)))
% 155.93/155.63 [7110]~P103(x71101)+~P33(x71101,x71103)+P33(x71101,f312(f312(f147(x71101),x71102),x71103))+P22(f312(f312(f314(x71101),f655(x71103,x71102,x71101)),f312(f168(x71101),x71103)))
% 155.93/155.63 [7111]~P103(x71111)+~P33(x71111,x71113)+P33(x71111,f312(f312(f147(x71111),x71112),x71113))+P22(f312(f312(f314(x71111),f743(x71112,x71113,x71111)),f312(f168(x71111),x71113)))
% 155.93/155.63 [7205]~P103(x72051)+~P31(x72051)+~P22(f312(f312(f228(x72051),x72053),f48(x72051,x72052)))+P22(f312(f312(f314(x72051),f676(x72052,x72053,x72051)),x72052))
% 155.93/155.63 [7370]~P103(x73701)+~P31(x73701)+~P22(f312(f312(f228(x73701),f49(x73701,x73703)),x73702))+P22(f312(f312(f314(x73701),f682(x73702,x73703,x73701)),x73703))
% 155.93/155.63 [7371]~P103(x73711)+~P31(x73711)+~P22(f312(f312(f228(x73711),f49(x73711,x73713)),x73712))+P22(f312(f312(f228(x73711),f682(x73712,x73713,x73711)),x73712))
% 155.93/155.63 [7384]P139(x73842,x73841,x73843)+E(x73841,f2(a1))+P22(f312(f312(f228(a1),x73841),f788(x73843,x73841,x73842)))+P22(f312(f312(f228(a1),f789(x73843,x73841,x73842)),x73841))
% 155.93/155.63 [7385]P140(x73852,x73851,x73853)+E(x73851,f2(a1))+P22(f312(f312(f228(a1),x73851),f796(x73853,x73851,x73852)))+P22(f312(f312(f228(a1),f792(x73853,x73851,x73852)),x73851))
% 155.93/155.63 [7475]P139(x74753,x74751,x74752)+E(x74751,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x74751),f791(x74752,x74751,x74753))),f788(x74752,x74751,x74753)),x74752)+P22(f312(f312(f228(a1),f2(a1)),x74751))
% 155.93/155.63 [7476]P140(x74763,x74761,x74762)+E(x74761,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x74761),f797(x74762,x74761,x74763))),f796(x74762,x74761,x74763)),x74762)+P22(f312(f312(f228(a1),f2(a1)),x74761))
% 155.93/155.63 [7478]~P122(x74781)+~P22(f312(f312(f228(x74781),x74783),f2(x74781)))+P22(f312(f312(f228(x74781),f312(f312(f90(x74781),x74782),x74783)),f2(x74781)))+~P22(f312(f312(f228(x74781),f2(x74781)),x74782))
% 155.93/155.63 [7479]~P122(x74791)+~P22(f312(f312(f228(x74791),x74792),f2(x74791)))+P22(f312(f312(f228(x74791),f312(f312(f90(x74791),x74792),x74793)),f2(x74791)))+~P22(f312(f312(f228(x74791),f2(x74791)),x74793))
% 155.93/155.63 [7480]~P67(x74801)+~P22(f312(f312(f228(x74801),x74803),f2(x74801)))+P22(f312(f312(f228(x74801),f312(f312(f268(x74801),x74802),x74803)),f2(x74801)))+~P22(f312(f312(f228(x74801),f2(x74801)),x74802))
% 155.93/155.63 [7481]~P67(x74811)+~P22(f312(f312(f228(x74811),x74812),f2(x74811)))+P22(f312(f312(f228(x74811),f312(f312(f268(x74811),x74812),x74813)),f2(x74811)))+~P22(f312(f312(f228(x74811),f2(x74811)),x74813))
% 155.93/155.63 [7482]~P66(x74821)+~P22(f312(f312(f228(x74821),x74823),f2(x74821)))+P22(f312(f312(f228(x74821),f312(f312(f268(x74821),x74822),x74823)),f2(x74821)))+~P22(f312(f312(f228(x74821),f2(x74821)),x74822))
% 155.93/155.63 [7483]~P66(x74831)+~P22(f312(f312(f228(x74831),x74832),f2(x74831)))+P22(f312(f312(f228(x74831),f312(f312(f268(x74831),x74832),x74833)),f2(x74831)))+~P22(f312(f312(f228(x74831),f2(x74831)),x74833))
% 155.93/155.63 [7486]~P121(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))
% 155.93/155.63 [7488]~P121(x74881)+~P22(f312(f312(f227(x74881),x74882),f2(x74881)))+P22(f312(f312(f227(x74881),f312(f312(f90(x74881),x74882),x74883)),f2(x74881)))+~P22(f312(f312(f227(x74881),f2(x74881)),x74883))
% 155.93/155.63 [7489]~P118(x74891)+~P22(f312(f312(f227(x74891),x74893),f2(x74891)))+P22(f312(f312(f227(x74891),f312(f312(f90(x74891),x74892),x74893)),f2(x74891)))+~P22(f312(f312(f227(x74891),f2(x74891)),x74892))
% 155.93/155.63 [7490]~P118(x74901)+~P22(f312(f312(f227(x74901),x74902),f2(x74901)))+P22(f312(f312(f227(x74901),f312(f312(f90(x74901),x74902),x74903)),f2(x74901)))+~P22(f312(f312(f227(x74901),f2(x74901)),x74903))
% 155.93/155.63 [7491]~P67(x74911)+~P22(f312(f312(f228(x74911),x74913),f2(x74911)))+P22(f312(f312(f227(x74911),f312(f312(f268(x74911),x74912),x74913)),f2(x74911)))+~P22(f312(f312(f227(x74911),f2(x74911)),x74912))
% 155.93/155.63 [7492]~P67(x74921)+~P22(f312(f312(f227(x74921),x74922),f2(x74921)))+P22(f312(f312(f227(x74921),f312(f312(f268(x74921),x74922),x74923)),f2(x74921)))+~P22(f312(f312(f228(x74921),f2(x74921)),x74923))
% 155.93/155.63 [7493]~P66(x74931)+~P22(f312(f312(f227(x74931),x74933),f2(x74931)))+P22(f312(f312(f227(x74931),f312(f312(f268(x74931),x74932),x74933)),f2(x74931)))+~P22(f312(f312(f227(x74931),f2(x74931)),x74932))
% 155.93/155.63 [7494]~P66(x74941)+~P22(f312(f312(f227(x74941),x74942),f2(x74941)))+P22(f312(f312(f227(x74941),f312(f312(f268(x74941),x74942),x74943)),f2(x74941)))+~P22(f312(f312(f227(x74941),f2(x74941)),x74943))
% 155.93/155.63 [7509]P139(x75091,x75092,x75093)+~P22(f312(x75091,x75093))+P22(f312(f312(f228(a1),x75092),f788(x75093,x75092,x75091)))+P22(f312(f312(f228(a1),f789(x75093,x75092,x75091)),x75092))
% 155.93/155.63 [7522]P140(x75221,x75222,x75223)+P22(f312(f312(f228(a1),x75222),f796(x75223,x75222,x75221)))+~P22(f312(x75221,f2(a1)))+P22(f312(f312(f228(a1),f792(x75223,x75222,x75221)),x75222))
% 155.93/155.63 [7571]P139(x75712,x75711,x75713)+E(x75711,f2(a1))+~P22(f312(x75712,f788(x75713,x75711,x75712)))+P22(f312(f312(f228(a1),f789(x75713,x75711,x75712)),x75711))
% 155.93/155.63 [7572]P140(x75722,x75721,x75723)+E(x75721,f2(a1))+~P22(f312(x75722,f797(x75723,x75721,x75722)))+P22(f312(f312(f228(a1),f792(x75723,x75721,x75722)),x75721))
% 155.93/155.63 [7584]P139(x75843,x75841,x75842)+~P22(f312(x75843,x75842))+E(f312(f312(f89(a1),f312(f312(f90(a1),x75841),f791(x75842,x75841,x75843))),f788(x75842,x75841,x75843)),x75842)+P22(f312(f312(f228(a1),f2(a1)),x75841))
% 155.93/155.63 [7601]P140(x76013,x76011,x76012)+E(f312(f312(f89(a1),f312(f312(f90(a1),x76011),f797(x76012,x76011,x76013))),f796(x76012,x76011,x76013)),x76012)+~P22(f312(x76013,f2(a1)))+P22(f312(f312(f228(a1),f2(a1)),x76011))
% 155.93/155.63 [7626]~P22(f312(x76261,x76263))+~P22(f312(f70(x76262),x76263))+P22(f312(f312(f314(x76262),f432(x76261,x76263,x76262)),f431(x76261,x76263,x76262)))+P22(f312(x76261,f189(f861(x76262,a846))))
% 155.93/155.63 [7629]~P22(f312(f312(f228(a1),x76291),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x76292))+~P22(f312(f312(f227(a1),x76292),x76293))+P22(f312(f312(f227(a1),f312(f47(a1,x76291),x76292)),f312(f47(a1,x76291),x76293)))
% 155.93/155.63 [7638]P139(x76381,x76382,x76383)+~P22(f312(x76381,x76383))+~P22(f312(x76381,f788(x76383,x76382,x76381)))+P22(f312(f312(f228(a1),f789(x76383,x76382,x76381)),x76382))
% 155.93/155.63 [7640]~P22(f312(f312(f228(a1),f2(a1)),x76403))+~P22(f312(f312(f227(a1),f2(a1)),x76401))+~P22(f312(f312(f227(a1),x76403),x76402))+P22(f312(f312(f227(a1),f312(f47(a1,x76401),x76402)),f312(f47(a1,x76401),x76403)))
% 155.93/155.63 [7644]P140(x76441,x76442,x76443)+~P22(f312(x76441,f797(x76443,x76442,x76441)))+~P22(f312(x76441,f2(a1)))+P22(f312(f312(f228(a1),f792(x76443,x76442,x76441)),x76442))
% 155.93/155.63 [7750]~P66(x77501)+~P22(f312(f312(f228(x77501),f312(f312(f268(x77501),x77503),x77502)),f2(x77501)))+P22(f312(f312(f228(x77501),x77502),f2(x77501)))+P22(f312(f312(f228(x77501),f2(x77501)),x77502))
% 155.93/155.63 [7751]~P66(x77511)+~P22(f312(f312(f228(x77511),f312(f312(f268(x77511),x77512),x77513)),f2(x77511)))+P22(f312(f312(f228(x77511),x77512),f2(x77511)))+P22(f312(f312(f228(x77511),f2(x77511)),x77512))
% 155.93/155.63 [7752]~P118(x77521)+~P22(f312(f312(f227(x77521),f312(f312(f90(x77521),x77523),x77522)),f2(x77521)))+P22(f312(f312(f227(x77521),x77522),f2(x77521)))+P22(f312(f312(f227(x77521),f2(x77521)),x77522))
% 155.93/155.63 [7753]~P118(x77531)+~P22(f312(f312(f227(x77531),f312(f312(f90(x77531),x77532),x77533)),f2(x77531)))+P22(f312(f312(f227(x77531),x77532),f2(x77531)))+P22(f312(f312(f227(x77531),f2(x77531)),x77532))
% 155.93/155.63 [7754]~P66(x77541)+~P22(f312(f312(f227(x77541),f312(f312(f268(x77541),x77543),x77542)),f2(x77541)))+P22(f312(f312(f227(x77541),x77542),f2(x77541)))+P22(f312(f312(f227(x77541),f2(x77541)),x77542))
% 155.93/155.63 [7755]~P66(x77551)+~P22(f312(f312(f227(x77551),f312(f312(f268(x77551),x77552),x77553)),f2(x77551)))+P22(f312(f312(f227(x77551),x77552),f2(x77551)))+P22(f312(f312(f227(x77551),f2(x77551)),x77552))
% 155.93/155.63 [7776]~P66(x77761)+~P22(f312(f312(f228(x77761),f312(f312(f268(x77761),x77762),x77763)),f2(x77761)))+P22(f312(f312(f228(x77761),f2(x77761)),x77762))+P22(f312(f312(f228(x77761),f2(x77761)),x77763))
% 155.93/155.63 [7777]~P118(x77771)+~P22(f312(f312(f227(x77771),f312(f312(f90(x77771),x77772),x77773)),f2(x77771)))+P22(f312(f312(f227(x77771),f2(x77771)),x77772))+P22(f312(f312(f227(x77771),f2(x77771)),x77773))
% 155.93/155.63 [7778]~P66(x77781)+~P22(f312(f312(f227(x77781),f312(f312(f268(x77781),x77782),x77783)),f2(x77781)))+P22(f312(f312(f227(x77781),f2(x77781)),x77782))+P22(f312(f312(f227(x77781),f2(x77781)),x77783))
% 155.93/155.63 [7798]P139(x77982,x77981,x77983)+E(x77981,f2(a1))+P22(f312(f312(f227(a1),f788(x77983,x77981,x77982)),f2(a1)))+P22(f312(f312(f228(a1),f789(x77983,x77981,x77982)),x77981))
% 155.93/155.63 [7799]P140(x77992,x77991,x77993)+E(x77991,f2(a1))+P22(f312(f312(f227(a1),f796(x77993,x77991,x77992)),f2(a1)))+P22(f312(f312(f228(a1),f792(x77993,x77991,x77992)),x77991))
% 155.93/155.63 [7804]~P117(x78041)+~P22(f312(f312(f228(x78041),x78042),f87(x78041)))+P22(f312(f312(f228(x78041),f312(f312(f240(x78041),x78042),f312(a126,x78043))),f87(x78041)))+~P22(f312(f312(f228(x78041),f2(x78041)),x78042))
% 155.93/155.63 [7856]~P103(x78561)+~E(x78563,f127(x78561))+~P33(x78561,f312(f165(x78561),x78563))+E(f312(f138(x78561,x78561,f312(f7(x78561,x78561,x78561),f226(x78561)),x78562),f312(f165(x78561),x78563)),x78562)
% 155.93/155.63 [7858]P139(x78581,x78582,x78583)+~P22(f312(x78581,x78583))+P22(f312(f312(f227(a1),f788(x78583,x78582,x78581)),f2(a1)))+P22(f312(f312(f228(a1),f789(x78583,x78582,x78581)),x78582))
% 155.93/155.63 [7867]P140(x78671,x78672,x78673)+~P22(f312(x78671,f2(a1)))+P22(f312(f312(f227(a1),f796(x78673,x78672,x78671)),f2(a1)))+P22(f312(f312(f228(a1),f792(x78673,x78672,x78671)),x78672))
% 155.93/155.63 [8092]P139(x80923,x80921,x80922)+E(x80921,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x80921),f791(x80922,x80921,x80923))),f788(x80922,x80921,x80923)),x80922)+P22(f312(f312(f228(a1),f789(x80922,x80921,x80923)),x80921))
% 155.93/155.63 [8093]P140(x80933,x80931,x80932)+E(x80931,f2(a1))+E(f312(f312(f89(a1),f312(f312(f90(a1),x80931),f797(x80932,x80931,x80933))),f796(x80932,x80931,x80933)),x80932)+P22(f312(f312(f228(a1),f792(x80932,x80931,x80933)),x80931))
% 155.93/155.63 [8130]P139(x81303,x81301,x81302)+~P22(f312(x81303,x81302))+E(f312(f312(f89(a1),f312(f312(f90(a1),x81301),f791(x81302,x81301,x81303))),f788(x81302,x81301,x81303)),x81302)+P22(f312(f312(f228(a1),f789(x81302,x81301,x81303)),x81301))
% 155.93/155.63 [8131]~P26(x81311)+~P72(x81311)+~P43(x81313)+E(f312(f312(f9(a853,x81311),f312(f312(f8(a1,x81311,a853),x81312),f114(a1))),f312(f290(a1,a853,a118),x81313)),f312(f312(f9(a1,x81311),x81312),x81313))
% 155.93/155.63 [8132]~P26(x81321)+~P72(x81321)+~P43(x81323)+E(f312(f312(f6(a853,x81321),f312(f312(f8(a1,x81321,a853),x81322),f114(a1))),f312(f290(a1,a853,a118),x81323)),f312(f312(f6(a1,x81321),x81322),x81323))
% 155.93/155.63 [8142]P140(x81423,x81421,x81422)+E(f312(f312(f89(a1),f312(f312(f90(a1),x81421),f797(x81422,x81421,x81423))),f796(x81422,x81421,x81423)),x81422)+~P22(f312(x81423,f2(a1)))+P22(f312(f312(f228(a1),f792(x81422,x81421,x81423)),x81421))
% 155.93/155.63 [8161]~E(x81612,f2(a853))+~E(f312(f246(a853,a853),x81613),f2(a853))+~E(x81611,f312(f312(f89(a853),f312(f312(f90(a853),f312(f246(a853,a853),x81613)),x81612)),f312(f248(a853,a853),x81613)))+P22(f312(f56(x81611,x81612),x81613))
% 155.93/155.63 [9066]P22(f312(f312(f227(a1),x90661),f2(a1)))+~P22(f312(f312(f228(a1),f312(f312(f89(a1),f312(f312(f90(a1),x90662),x90661)),x90663)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x90662))+~P22(f312(f312(f227(a1),f2(a1)),x90663))
% 155.93/155.63 [5720]~P87(x57202)+E(x57201,f189(f861(x57202,a846)))+~P22(f312(f70(x57202),x57201))+E(f11(x57202,f312(f312(f289(x57202),x57203),x57201)),f312(f312(f115(x57202),x57203),f11(x57202,x57201)))
% 155.93/155.63 [5721]~P87(x57212)+E(x57211,f189(f861(x57212,a846)))+~P22(f312(f70(x57212),x57211))+E(f10(x57212,f312(f312(f289(x57212),x57213),x57211)),f312(f312(f124(x57212),x57213),f10(x57212,x57211)))
% 155.93/155.63 [5722]~P103(x57222)+E(x57221,f189(f861(x57222,a846)))+~P22(f312(f70(x57222),x57221))+E(f14(x57222,f312(f312(f289(x57222),x57223),x57221)),f312(f312(f226(x57222),x57223),f14(x57222,x57221)))
% 155.93/155.63 [5723]~P103(x57232)+E(x57231,f189(f861(x57232,a846)))+~P22(f312(f70(x57232),x57231))+E(f15(x57232,f312(f312(f289(x57232),x57233),x57231)),f312(f312(f225(x57232),x57233),f15(x57232,x57231)))
% 155.93/155.63 [6025]~P118(x60251)+~E(x60253,f2(x60251))+~E(x60252,f2(x60251))+E(f312(f312(f89(x60251),f312(f312(f90(x60251),x60252),x60252)),f312(f312(f90(x60251),x60253),x60253)),f2(x60251))
% 155.93/155.63 [6091]~P93(x60912)+E(x60911,f189(f861(x60912,a846)))+~P22(f312(f70(x60912),x60911))+E(f312(f72(x60912,f90(x60912)),f312(f312(f289(x60912),x60913),x60911)),f312(f312(f90(x60912),x60913),f312(f72(x60912,f90(x60912)),x60911)))
% 155.93/155.63 [6217]~P103(x62172)+E(x62171,f189(f861(x62172,a846)))+~P22(f312(f70(x62172),x62171))+E(f12(x62172,f226(x62172),f312(f312(f289(x62172),x62173),x62171)),f312(f312(f226(x62172),x62173),f12(x62172,f226(x62172),x62171)))
% 155.93/155.63 [6218]~P103(x62182)+E(x62181,f189(f861(x62182,a846)))+~P22(f312(f70(x62182),x62181))+E(f13(x62182,f225(x62182),f312(f312(f289(x62182),x62183),x62181)),f312(f312(f225(x62182),x62183),f13(x62182,f225(x62182),x62181)))
% 155.93/155.63 [6726]~P103(x67261)+~P22(f312(f70(x67261),x67263))+E(f12(x67261,f226(x67261),f312(f312(f289(x67261),x67262),x67263)),f312(f312(f73(x67261,x67261,f226(x67261)),x67262),x67263))+P22(f312(f312(f314(x67261),x67262),x67263))
% 155.93/155.63 [6783]~E(f312(f312(f89(a1),x67832),f312(f312(f90(a1),x67833),x67831)),x67833)+~P22(f312(f312(f228(a1),f2(a1)),x67833))+P22(f312(f312(f227(a1),f87(a1)),x67831))+~P22(f312(f312(f228(a1),x67832),x67833))
% 155.93/155.63 [6812]~E(f312(f312(f89(a1),x68122),f312(f312(f90(a1),x68123),x68121)),x68123)+P22(f312(f312(f227(a1),x68121),f87(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x68123))+~P22(f312(f312(f227(a1),f2(a1)),x68122))
% 155.93/155.63 [6830]E(x68301,f2(a853))+~P22(f312(f56(x68303,x68301),x68302))+~P22(f312(f312(f228(a853),f2(a853)),x68301))+P22(f312(f312(f228(a853),f312(f248(a853,a853),x68302)),x68301))
% 155.93/155.63 [6861]~P131(x68611)+~P22(f312(f312(f227(x68611),x68612),f2(x68611)))+~P22(f312(f312(f227(x68611),x68613),f2(x68611)))+E(f312(f312(f90(x68611),f312(f84(x68611),x68612)),f312(f84(x68611),x68613)),f312(f84(x68611),f312(f312(f90(x68611),x68612),x68613)))
% 155.93/155.63 [6917]~P131(x69171)+~P22(f312(f312(f227(x69171),x69172),f2(x69171)))+E(f312(f312(f90(x69171),f312(f84(x69171),x69172)),f312(f84(x69171),x69173)),f312(f84(x69171),f312(f312(f90(x69171),x69172),x69173)))+~P22(f312(f312(f227(x69171),f2(x69171)),x69173))
% 155.93/155.63 [6918]~P131(x69181)+~P22(f312(f312(f227(x69181),x69183),f2(x69181)))+E(f312(f312(f90(x69181),f312(f84(x69181),x69182)),f312(f84(x69181),x69183)),f312(f84(x69181),f312(f312(f90(x69181),x69182),x69183)))+~P22(f312(f312(f227(x69181),f2(x69181)),x69182))
% 155.93/155.63 [6971]~P131(x69711)+E(f312(f312(f90(x69711),f312(f84(x69711),x69712)),f312(f84(x69711),x69713)),f312(f84(x69711),f312(f312(f90(x69711),x69712),x69713)))+~P22(f312(f312(f227(x69711),f2(x69711)),x69712))+~P22(f312(f312(f227(x69711),f2(x69711)),x69713))
% 155.93/155.63 [6987]~P118(x69871)+~P22(f312(f312(f228(x69871),x69873),f2(x69871)))+~P22(f312(f312(f228(x69871),x69872),f2(x69871)))+P22(f312(f312(f228(x69871),f2(x69871)),f312(f312(f90(x69871),x69872),x69873)))
% 155.93/155.63 [6988]~P67(x69881)+~P22(f312(f312(f228(x69881),x69883),f2(x69881)))+~P22(f312(f312(f228(x69881),x69882),f2(x69881)))+P22(f312(f312(f228(x69881),f2(x69881)),f312(f312(f268(x69881),x69882),x69883)))
% 155.93/155.63 [6989]~P66(x69891)+~P22(f312(f312(f228(x69891),x69893),f2(x69891)))+~P22(f312(f312(f228(x69891),x69892),f2(x69891)))+P22(f312(f312(f228(x69891),f2(x69891)),f312(f312(f268(x69891),x69892),x69893)))
% 155.93/155.63 [6991]~P128(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(f90(x69911),x69912),x69913)))
% 155.93/155.63 [6992]~P118(x69921)+~P22(f312(f312(f227(x69921),x69923),f2(x69921)))+~P22(f312(f312(f227(x69921),x69922),f2(x69921)))+P22(f312(f312(f227(x69921),f2(x69921)),f312(f312(f90(x69921),x69922),x69923)))
% 155.93/155.63 [6993]~P67(x69931)+~P22(f312(f312(f228(x69931),x69933),f2(x69931)))+~P22(f312(f312(f227(x69931),x69932),f2(x69931)))+P22(f312(f312(f227(x69931),f2(x69931)),f312(f312(f268(x69931),x69932),x69933)))
% 155.93/155.63 [6994]~P66(x69941)+~P22(f312(f312(f227(x69941),x69943),f2(x69941)))+~P22(f312(f312(f227(x69941),x69942),f2(x69941)))+P22(f312(f312(f227(x69941),f2(x69941)),f312(f312(f268(x69941),x69942),x69943)))
% 155.93/155.63 [6995]~P117(x69951)+~P22(f312(f312(f228(a853),f2(a853)),x69953))+~P22(f312(f312(f228(x69951),f87(x69951)),x69952))+P22(f312(f312(f228(x69951),f87(x69951)),f312(f312(f240(x69951),x69952),x69953)))
% 155.93/155.63 [7094]~P84(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(f89(x70941),x70942),x70943)))
% 155.93/155.63 [7097]~P122(x70971)+~P22(f312(f312(f228(x70971),f2(x70971)),x70973))+~P22(f312(f312(f228(x70971),f2(x70971)),x70972))+P22(f312(f312(f228(x70971),f2(x70971)),f312(f312(f90(x70971),x70972),x70973)))
% 155.93/155.63 [7098]~P67(x70981)+~P22(f312(f312(f228(x70981),f2(x70981)),x70983))+~P22(f312(f312(f228(x70981),f2(x70981)),x70982))+P22(f312(f312(f228(x70981),f2(x70981)),f312(f312(f268(x70981),x70982),x70983)))
% 155.93/155.63 [7099]~P66(x70991)+~P22(f312(f312(f228(x70991),f2(x70991)),x70993))+~P22(f312(f312(f228(x70991),f2(x70991)),x70992))+P22(f312(f312(f228(x70991),f2(x70991)),f312(f312(f268(x70991),x70992),x70993)))
% 155.93/155.63 [7100]~P117(x71001)+~P22(f312(f312(f228(x71001),f87(x71001)),x71003))+~P22(f312(f312(f228(x71001),f87(x71001)),x71002))+P22(f312(f312(f228(x71001),f87(x71001)),f312(f312(f90(x71001),x71002),x71003)))
% 155.93/155.63 [7102]~P121(x71021)+~P22(f312(f312(f227(x71021),f2(x71021)),x71023))+~P22(f312(f312(f227(x71021),f2(x71021)),x71022))+P22(f312(f312(f227(x71021),f2(x71021)),f312(f312(f90(x71021),x71022),x71023)))
% 155.93/155.63 [7103]~P128(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(f90(x71031),x71032),x71033)))
% 155.93/155.63 [7104]~P118(x71041)+~P22(f312(f312(f227(x71041),f2(x71041)),x71043))+~P22(f312(f312(f227(x71041),f2(x71041)),x71042))+P22(f312(f312(f227(x71041),f2(x71041)),f312(f312(f90(x71041),x71042),x71043)))
% 155.93/155.63 [7105]~P67(x71051)+~P22(f312(f312(f228(x71051),f2(x71051)),x71053))+~P22(f312(f312(f227(x71051),f2(x71051)),x71052))+P22(f312(f312(f227(x71051),f2(x71051)),f312(f312(f268(x71051),x71052),x71053)))
% 155.93/155.63 [7106]~P66(x71061)+~P22(f312(f312(f227(x71061),f2(x71061)),x71063))+~P22(f312(f312(f227(x71061),f2(x71061)),x71062))+P22(f312(f312(f227(x71061),f2(x71061)),f312(f312(f268(x71061),x71062),x71063)))
% 155.93/155.63 [7173]~P87(x71731)+~P22(f312(f70(x71731),x71733))+E(f11(x71731,f312(f312(f289(x71731),x71732),x71733)),x71732)+~E(f312(f312(f21(f861(x71731,a846)),x71733),f312(f312(f289(x71731),x71732),f189(f861(x71731,a846)))),f189(f861(x71731,a846)))
% 155.93/155.63 [7174]~P87(x71741)+~P22(f312(f70(x71741),x71743))+E(f10(x71741,f312(f312(f289(x71741),x71742),x71743)),x71742)+~E(f312(f312(f21(f861(x71741,a846)),x71743),f312(f312(f289(x71741),x71742),f189(f861(x71741,a846)))),f189(f861(x71741,a846)))
% 155.93/155.63 [7175]~P103(x71751)+~P22(f312(f70(x71751),x71753))+E(f14(x71751,f312(f312(f289(x71751),x71752),x71753)),x71752)+~E(f312(f312(f21(f861(x71751,a846)),x71753),f312(f312(f289(x71751),x71752),f189(f861(x71751,a846)))),f189(f861(x71751,a846)))
% 155.93/155.63 [7176]~P103(x71761)+~P22(f312(f70(x71761),x71763))+E(f15(x71761,f312(f312(f289(x71761),x71762),x71763)),x71762)+~E(f312(f312(f21(f861(x71761,a846)),x71763),f312(f312(f289(x71761),x71762),f189(f861(x71761,a846)))),f189(f861(x71761,a846)))
% 155.93/155.63 [7177]~P66(x71771)+P22(f312(f312(f228(x71771),x71772),f2(x71771)))+P22(f312(f312(f228(x71771),f2(x71771)),x71773))+~P22(f312(f312(f228(x71771),f2(x71771)),f312(f312(f268(x71771),x71773),x71772)))
% 155.93/155.63 [7178]~P66(x71781)+P22(f312(f312(f228(x71781),x71782),f2(x71781)))+P22(f312(f312(f228(x71781),f2(x71781)),x71783))+~P22(f312(f312(f228(x71781),f2(x71781)),f312(f312(f268(x71781),x71782),x71783)))
% 155.93/155.63 [7179]~P66(x71791)+P22(f312(f312(f228(x71791),x71792),f2(x71791)))+P22(f312(f312(f228(x71791),f2(x71791)),x71792))+~P22(f312(f312(f228(x71791),f2(x71791)),f312(f312(f268(x71791),x71793),x71792)))
% 155.93/155.63 [7180]~P66(x71801)+P22(f312(f312(f228(x71801),x71802),f2(x71801)))+P22(f312(f312(f228(x71801),f2(x71801)),x71802))+~P22(f312(f312(f228(x71801),f2(x71801)),f312(f312(f268(x71801),x71802),x71803)))
% 155.93/155.63 [7181]~P118(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(f90(x71811),x71813),x71812)))
% 155.93/155.63 [7182]~P118(x71821)+P22(f312(f312(f227(x71821),x71822),f2(x71821)))+P22(f312(f312(f227(x71821),f2(x71821)),x71823))+~P22(f312(f312(f227(x71821),f2(x71821)),f312(f312(f90(x71821),x71822),x71823)))
% 155.93/155.63 [7183]~P66(x71831)+P22(f312(f312(f227(x71831),x71832),f2(x71831)))+P22(f312(f312(f227(x71831),f2(x71831)),x71833))+~P22(f312(f312(f227(x71831),f2(x71831)),f312(f312(f268(x71831),x71833),x71832)))
% 155.93/155.63 [7184]~P66(x71841)+P22(f312(f312(f227(x71841),x71842),f2(x71841)))+P22(f312(f312(f227(x71841),f2(x71841)),x71843))+~P22(f312(f312(f227(x71841),f2(x71841)),f312(f312(f268(x71841),x71842),x71843)))
% 155.93/155.63 [7185]~P118(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(f90(x71851),x71853),x71852)))
% 155.93/155.63 [7186]~P118(x71861)+P22(f312(f312(f227(x71861),x71862),f2(x71861)))+P22(f312(f312(f227(x71861),f2(x71861)),x71862))+~P22(f312(f312(f227(x71861),f2(x71861)),f312(f312(f90(x71861),x71862),x71863)))
% 155.93/155.63 [7187]~P66(x71871)+P22(f312(f312(f227(x71871),x71872),f2(x71871)))+P22(f312(f312(f227(x71871),f2(x71871)),x71872))+~P22(f312(f312(f227(x71871),f2(x71871)),f312(f312(f268(x71871),x71873),x71872)))
% 155.93/155.63 [7188]~P66(x71881)+P22(f312(f312(f227(x71881),x71882),f2(x71881)))+P22(f312(f312(f227(x71881),f2(x71881)),x71882))+~P22(f312(f312(f227(x71881),f2(x71881)),f312(f312(f268(x71881),x71882),x71883)))
% 155.93/155.63 [7271]~E(f312(f312(f115(f861(x72711,a846)),f312(f168(x72711),x72712)),f312(f168(x72711),x72713)),f189(f861(x72711,a846)))+~P22(f312(f133(x72711),x72713))+~P22(f312(f133(x72711),x72712))+P22(f312(f133(x72711),f312(f312(f129(x72711),x72712),x72713)))
% 155.93/155.63 [7272]~P103(x72721)+~P22(f312(f70(x72721),x72723))+E(f12(x72721,f226(x72721),f312(f312(f289(x72721),x72722),x72723)),x72722)+~E(f312(f312(f21(f861(x72721,a846)),x72723),f312(f312(f289(x72721),x72722),f189(f861(x72721,a846)))),f189(f861(x72721,a846)))
% 155.93/155.63 [7273]~P103(x72731)+~P22(f312(f70(x72731),x72733))+E(f13(x72731,f225(x72731),f312(f312(f289(x72731),x72732),x72733)),x72732)+~E(f312(f312(f21(f861(x72731,a846)),x72733),f312(f312(f289(x72731),x72732),f189(f861(x72731,a846)))),f189(f861(x72731,a846)))
% 155.93/155.63 [7289]~P112(x72891)+~P22(f312(f312(f228(x72891),x72892),x72893))+~P22(f312(f312(f228(x72891),f312(f88(x72891),x72892)),x72893))+P22(f312(f312(f228(x72891),f312(f84(x72891),x72892)),x72893))
% 155.93/155.63 [7291]~P83(x72911)+~P22(f312(f312(f227(x72911),x72912),x72913))+~P22(f312(f312(f227(x72911),f312(f88(x72911),x72912)),x72913))+P22(f312(f312(f227(x72911),f312(f84(x72911),x72912)),x72913))
% 155.93/155.63 [7358]~P122(x73581)+P22(f312(f312(f228(x73581),f2(x73581)),x73582))+~P22(f312(f312(f228(x73581),f2(x73581)),x73583))+~P22(f312(f312(f228(x73581),f2(x73581)),f312(f312(f90(x73581),x73583),x73582)))
% 155.93/155.63 [7359]~P122(x73591)+P22(f312(f312(f228(x73591),f2(x73591)),x73592))+~P22(f312(f312(f228(x73591),f2(x73591)),x73593))+~P22(f312(f312(f228(x73591),f2(x73591)),f312(f312(f90(x73591),x73592),x73593)))
% 155.93/155.63 [7661]E(x76611,x76612)+~P22(f312(f70(x76613),x76611))+~P22(f312(f312(f227(a853),f312(f53(x76613),x76611)),f312(f53(x76613),x76612)))+~P22(f312(f312(f227(f861(x76613,a846)),x76612),x76611))
% 155.93/155.63 [7946]E(f312(x79461,f842(x79462,x79461,x79463)),x79462)+~P22(f312(f312(f227(a1),x79462),f312(x79461,x79463)))+P22(f312(f312(f228(a853),f843(x79462,x79461,x79463)),x79463))+~P22(f312(f312(f227(a1),f312(x79461,f2(a853))),x79462))
% 155.93/155.63 [7947]E(f312(x79471,f322(x79472,x79471,x79473)),x79472)+~P22(f312(f312(f227(a1),x79472),f312(x79471,x79473)))+P22(f312(f312(f228(a853),f844(x79472,x79471,x79473)),x79473))+~P22(f312(f312(f227(a1),f312(x79471,f2(a853))),x79472))
% 155.93/155.63 [8054]~P22(f312(f70(x80541),x80543))+~P22(f312(f312(f228(a853),f312(f53(x80541),x80542)),f312(f53(x80541),x80543)))+~P22(f312(f312(f227(f861(x80541,a846)),x80542),x80543))+P22(f312(f312(f228(f861(x80541,a846)),x80542),x80543))
% 155.93/155.63 [8083]E(f312(f312(f21(a1),f465(x80833,x80831,x80832)),f466(x80833,x80831,x80832)),x80831)+E(f312(f312(f89(a1),x80831),x80832),x80831)+~P22(f312(f312(f228(a1),f2(a1)),x80832))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x80831),f87(a1))),x80833))
% 155.93/155.63 [8084]E(f312(f312(f89(a1),f457(x80843,x80841,x80842)),f458(x80843,x80841,x80842)),x80841)+E(f312(f312(f21(a1),x80841),x80842),x80841)+~P22(f312(f312(f228(a1),f2(a1)),x80842))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x80841),f87(a1))),x80843))
% 155.93/155.63 [8138]~P22(f312(f312(f227(a853),x81383),x81381))+P22(f312(f312(f228(a853),x81381),x81382))+~P22(f312(f312(f227(a853),x81383),x81382))+~P22(f312(f312(f228(a853),f312(f312(f21(a853),x81381),x81383)),f312(f312(f21(a853),x81382),x81383)))
% 155.93/155.63 [8139]~P22(f312(f312(f227(a853),x81393),x81391))+P22(f312(f312(f227(a853),x81391),x81392))+~P22(f312(f312(f227(a853),x81393),x81392))+~P22(f312(f312(f227(a853),f312(f312(f21(a853),x81391),x81393)),f312(f312(f21(a853),x81392),x81393)))
% 155.93/155.63 [8154]~P103(x81542)+E(x81541,f127(x81542))+~P33(x81542,f312(f165(x81542),x81541))+E(f312(f138(x81542,x81542,f312(f7(x81542,x81542,x81542),f226(x81542)),x81543),f312(f165(x81542),x81541)),f312(f312(f226(x81542),f312(f312(f161(x81542),x81541),f2(a853))),x81543))
% 155.93/155.63 [8200]~P31(x82001)+~P49(x82001,x82001,x82003)+P22(f312(f312(f227(x82001),x82002),f110(x82001,x82003)))+~P22(f312(f312(f227(x82001),x82002),f312(x82003,f312(f312(f124(x82001),x82002),f110(x82001,x82003)))))
% 155.93/155.63 [8220]E(f312(f312(f89(a1),x82201),x82202),x82201)+~P22(f312(f312(f228(a1),f2(a1)),x82202))+P22(f312(f312(f314(a1),f465(x82203,x82201,x82202)),x82203))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x82201),f87(a1))),x82203))
% 155.93/155.63 [8221]E(f312(f312(f21(a1),x82211),x82212),x82211)+~P22(f312(f312(f228(a1),f2(a1)),x82212))+P22(f312(f312(f314(a1),f457(x82213,x82211,x82212)),x82213))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x82211),f87(a1))),x82213))
% 155.93/155.63 [8299]~P22(f312(f312(f227(a1),x82991),f312(x82992,x82993)))+P22(f312(f312(f227(a853),f842(x82991,x82992,x82993)),x82993))+P22(f312(f312(f228(a853),f843(x82991,x82992,x82993)),x82993))+~P22(f312(f312(f227(a1),f312(x82992,f2(a853))),x82991))
% 155.93/155.63 [8300]~P22(f312(f312(f227(a1),x83001),f312(x83002,x83003)))+P22(f312(f312(f227(a853),f322(x83001,x83002,x83003)),x83003))+P22(f312(f312(f228(a853),f844(x83001,x83002,x83003)),x83003))+~P22(f312(f312(f227(a1),f312(x83002,f2(a853))),x83001))
% 155.93/155.63 [8384]E(f312(f312(f89(a1),x83841),x83842),x83841)+~P22(f312(f312(f228(a1),f2(a1)),x83842))+P22(f312(f312(f314(a1),f466(x83843,x83841,x83842)),f283(a1,f87(a1),x83842)))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x83841),f87(a1))),x83843))
% 155.93/155.63 [8385]E(f312(f312(f21(a1),x83851),x83852),x83851)+~P22(f312(f312(f228(a1),f2(a1)),x83852))+P22(f312(f312(f314(a1),f458(x83853,x83851,x83852)),f283(a1,f87(a1),x83852)))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x83851),f87(a1))),x83853))
% 155.93/155.63 [8517]~P117(x85171)+~P22(f312(f312(f228(x85171),x85172),f87(x85171)))+~P22(f312(f312(f228(x85171),f2(x85171)),x85172))+P22(f312(f312(f228(x85171),f312(f312(f90(x85171),x85172),f312(f312(f240(x85171),x85172),x85173))),f312(f312(f240(x85171),x85172),x85173)))
% 155.93/155.63 [8595]~P22(f312(x85951,x85952))+P22(f312(x85951,f2(a853)))+~P22(f312(f312(f228(a853),x85952),x85953))+~P22(f312(x85951,f54(a853,f312(a126,f738(x85952,x85951,x85953)),x85953)))
% 155.93/155.63 [8733]E(f358(x87331,x87332,x87333),f2(a853))+P22(f312(f312(x87331,x87333),x87332))+P22(f312(f312(x87331,f358(x87331,x87332,x87333)),f54(a853,f357(x87331,x87332,x87333),f358(x87331,x87332,x87333))))+~P22(f312(f300(f860(a853,a853),a211),f312(f312(f239(a853,a853),x87333),x87332)))
% 155.93/155.63 [8771]~P19(x87711,x87711,x87712,x87713)+E(f312(f290(x87711,x87711,x87712),x87713),x87713)+~P22(f312(f70(x87711),x87713))+~P22(f312(f312(f227(f861(x87711,a846)),f312(f290(x87711,x87711,x87712),x87713)),x87713))
% 155.93/155.63 [8844]~P31(x88441)+~P49(x88441,x88441,x88443)+P22(f312(f312(f227(x88441),f312(f312(f124(x88441),x88442),f110(x88441,x88443))),f312(x88443,f312(f312(f124(x88441),x88442),f110(x88441,x88443)))))+~P22(f312(f312(f227(x88441),x88442),f312(x88443,f312(f312(f124(x88441),x88442),f110(x88441,x88443)))))
% 155.93/155.63 [9008]P22(f312(f312(x90081,x90082),x90083))+~P22(f312(f312(f228(a1),f356(x90081,x90083,x90082)),f2(a1)))+P22(f312(f312(x90081,f312(f88(a1),f355(x90081,x90083,x90082))),f312(f88(a1),f356(x90081,x90083,x90082))))+~P22(f312(f300(f860(a1,a1),a212),f312(f312(f239(a1,a1),x90082),x90083)))
% 155.93/155.63 [9197]P22(f312(f312(x91971,x91972),x91973))+P22(f312(f312(x91971,f312(f312(f89(a1),f617(x91971,x91973,x91972)),f87(a1))),f619(x91971,x91973,x91972)))+~P22(f312(f312(f227(a1),f617(x91971,x91973,x91972)),f619(x91971,x91973,x91972)))+~P22(f312(f300(f860(a1,a1),a178),f312(f312(f239(a1,a1),x91972),x91973)))
% 155.93/155.63 [9613]~P63(x96132)+~P63(x96131)+~P22(f312(f67(f860(x96131,x96132)),x96133))+P22(f312(f67(x96131),f312(f312(f8(f861(x96132,a846),a846,x96131),f67(x96132)),f312(f312(f8(f861(x96132,f860(x96131,x96132)),f861(x96132,a846),x96131),f312(f8(f860(x96131,x96132),a846,x96132),x96133)),f239(x96131,x96132)))))
% 155.93/155.63 [9614]~P63(x96142)+~P63(x96141)+~P22(f312(f66(f860(x96141,x96142)),x96143))+P22(f312(f66(x96141),f312(f312(f8(f861(x96142,a846),a846,x96141),f66(x96142)),f312(f312(f8(f861(x96142,f860(x96141,x96142)),f861(x96142,a846),x96141),f312(f8(f860(x96141,x96142),a846,x96142),x96143)),f239(x96141,x96142)))))
% 155.93/155.63 [9712]~P63(x97122)+~P63(x97121)+P22(f312(f67(f860(x97121,x97122)),x97123))+~P22(f312(f67(x97121),f312(f312(f8(f861(x97122,a846),a846,x97121),f67(x97122)),f312(f312(f8(f861(x97122,f860(x97121,x97122)),f861(x97122,a846),x97121),f312(f8(f860(x97121,x97122),a846,x97122),x97123)),f239(x97121,x97122)))))
% 155.93/155.63 [9713]~P63(x97132)+~P63(x97131)+P22(f312(f66(f860(x97131,x97132)),x97133))+~P22(f312(f66(x97131),f312(f312(f8(f861(x97132,a846),a846,x97131),f66(x97132)),f312(f312(f8(f861(x97132,f860(x97131,x97132)),f861(x97132,a846),x97131),f312(f8(f860(x97131,x97132),a846,x97132),x97133)),f239(x97131,x97132)))))
% 155.93/155.63 [9894]E(f312(x98941,f842(x98942,x98941,x98943)),x98942)+~P22(f312(f312(f227(a1),x98942),f312(x98941,x98943)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x98941,f312(f312(f89(a853),f843(x98942,x98941,x98943)),f87(a853)))),f312(x98941,f843(x98942,x98941,x98943))))),f87(a1)))+~P22(f312(f312(f227(a1),f312(x98941,f2(a853))),x98942))
% 155.93/155.63 [9895]E(f312(x98951,f322(x98952,x98951,x98953)),x98952)+~P22(f312(f312(f227(a1),x98952),f312(x98951,x98953)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x98951,f312(f312(f89(a853),f844(x98952,x98951,x98953)),f87(a853)))),f312(x98951,f844(x98952,x98951,x98953))))),f87(a1)))+~P22(f312(f312(f227(a1),f312(x98951,f2(a853))),x98952))
% 155.93/155.63 [9899]~P22(f312(f312(f227(a1),x98991),f312(x98992,x98993)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x98992,f312(f312(f89(a853),f843(x98991,x98992,x98993)),f87(a853)))),f312(x98992,f843(x98991,x98992,x98993))))),f87(a1)))+P22(f312(f312(f227(a853),f842(x98991,x98992,x98993)),x98993))+~P22(f312(f312(f227(a1),f312(x98992,f2(a853))),x98991))
% 155.93/155.63 [9900]~P22(f312(f312(f227(a1),x99001),f312(x99002,x99003)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x99002,f312(f312(f89(a853),f844(x99001,x99002,x99003)),f87(a853)))),f312(x99002,f844(x99001,x99002,x99003))))),f87(a1)))+P22(f312(f312(f227(a853),f322(x99001,x99002,x99003)),x99003))+~P22(f312(f312(f227(a1),f312(x99002,f2(a853))),x99001))
% 155.93/155.63 [9954]E(x99541,x99542)+~E(f312(f138(f854(x99543),f854(x99543),f129(x99543),f127(x99543)),x99541),f312(f138(f854(x99543),f854(x99543),f129(x99543),f127(x99543)),x99542))+~E(f312(f190(f854(f854(x99543))),x99541),f312(f190(f854(f854(x99543))),x99542))+~P22(f312(f312(f249(f854(x99543),f854(x99543),a846),f312(f312(f7(f854(x99543),f861(f854(x99543),a853),f861(f854(x99543),a846)),f312(f312(f8(f861(a853,a846),f861(f861(f854(x99543),a853),f861(f854(x99543),a846)),f854(x99543)),f8(a853,a846,f854(x99543))),f312(f312(f8(a853,f861(a853,a846),f854(x99543)),a309),f190(f854(x99543))))),f190(f854(x99543)))),f661(x99541,x99542,x99543)))
% 155.93/155.63 [9955]E(x99551,x99552)+~E(f312(f138(f854(x99553),f854(x99553),f129(x99553),f127(x99553)),x99551),f312(f138(f854(x99553),f854(x99553),f129(x99553),f127(x99553)),x99552))+~E(f312(f190(f854(f854(x99553))),x99551),f312(f190(f854(f854(x99553))),x99552))+~P22(f312(f312(f249(f854(x99553),f854(x99553),a846),f312(f312(f7(f854(x99553),f861(f854(x99553),a853),f861(f854(x99553),a846)),f312(f312(f8(f861(a853,a846),f861(f861(f854(x99553),a853),f861(f854(x99553),a846)),f854(x99553)),f8(a853,a846,f854(x99553))),f312(f312(f8(a853,f861(a853,a846),f854(x99553)),a309),f190(f854(x99553))))),f190(f854(x99553)))),f662(x99552,x99551,x99553)))
% 155.93/155.63 [6698]~E(f87(a853),f2(a853))+~P22(f312(f70(x66981),x66983))+~P22(f312(f70(x66981),x66982))+E(f312(f312(f89(a853),f312(f53(x66981),x66982)),f312(f53(x66981),x66983)),f312(f53(x66981),f312(f312(f124(f861(x66981,a846)),x66982),x66983)))
% 155.93/155.63 [7112]~P99(x71121)+~P22(f312(f70(x71121),x71122))+~P22(f312(f312(f314(x71121),x71123),x71122))+P22(f312(f312(f227(x71121),f312(f72(x71121,f115(x71121)),x71122)),x71123))
% 155.93/155.63 [7113]~P103(x71131)+~P22(f312(f70(x71131),x71132))+~P22(f312(f312(f314(x71131),x71133),x71132))+P22(f312(f312(f227(x71131),f312(f72(x71131,f225(x71131)),x71132)),x71133))
% 155.93/155.63 [7353]~P22(f312(f70(x73531),x73533))+~P22(f312(f70(x73531),x73532))+~E(f312(f312(f115(f861(x73531,a846)),x73532),x73533),f189(f861(x73531,a846)))+E(f312(f312(f89(a853),f312(f53(x73531),x73532)),f312(f53(x73531),x73533)),f312(f53(x73531),f312(f312(f124(f861(x73531,a846)),x73532),x73533)))
% 155.93/155.63 [8143]~P41(x81431,x81433)+~P41(x81431,x81432)+~E(f312(f312(f115(f861(x81431,a846)),f312(f238(x81431,x81431),x81432)),f312(f236(x81431,x81431),x81433)),f189(f861(x81431,a846)))+P41(x81431,f312(f312(f124(f861(f860(x81431,x81431),a846)),x81432),x81433))
% 155.93/155.63 [8225]E(x82251,f312(f47(a853,x82252),x82253))+~P22(f312(f312(f228(a853),f2(a853)),x82253))+~P22(f312(f312(f228(a853),x82252),f312(f312(f90(a853),x82253),f312(a126,x82251))))+~P22(f312(f312(f227(a853),f312(f312(f90(a853),x82253),x82251)),x82252))
% 155.93/155.63 [8382]~P22(f312(f70(x83821),x83822))+~P22(f312(f70(x83821),x83823))+E(f312(f312(f89(a853),f312(f53(x83821),x83822)),f312(f53(x83821),x83823)),f312(f53(x83821),f312(f312(f124(f861(x83821,a846)),x83822),x83823)))+P22(f312(f312(f314(x83821),f393(x83823,x83822,x83821)),f312(f312(f115(f861(x83821,a846)),x83822),x83823)))
% 155.93/155.63 [8745]~P118(x87452)+~E(x87451,f2(x87452))+~E(x87453,f2(x87452))+~P22(f312(f312(f228(x87452),f2(x87452)),f312(f312(f89(x87452),f312(f312(f90(x87452),x87453),x87453)),f312(f312(f90(x87452),x87451),x87451))))
% 155.93/155.63 [9273]~P41(x92731,x92733)+~P41(x92731,x92732)+P41(x92731,f312(f312(f124(f861(f860(x92731,x92731),a846)),x92732),x92733))+~P22(f312(f312(f227(f861(f860(x92731,x92731),a846)),f312(f312(f267(x92731,x92731,x92731),x92732),x92733)),x92732))
% 155.93/155.63 [9401]~P22(f312(x94011,x94013))+~P22(f312(f70(x94012),x94013))+P22(f312(x94011,f189(f861(x94012,a846))))+~P22(f312(x94011,f312(f312(f21(f861(x94012,a846)),f431(x94011,x94013,x94012)),f312(f312(f289(x94012),f432(x94011,x94013,x94012)),f189(f861(x94012,a846))))))
% 155.93/155.63 [9646]~P63(x96461)+~P63(x96462)+P8(x96461,f312(f312(f8(f861(x96462,x96461),a846,f854(x96461)),x96463),f312(f312(f8(f861(x96462,f857(x96461)),f861(x96462,x96461),f854(x96461)),f82(f857(x96461),x96461,x96462,f223(x96461))),f312(f312(f8(f854(f860(x96462,x96461)),f861(x96462,f857(x96461)),f854(x96461)),f173(x96462,x96461)),f312(f177(x96462,x96461),f64(x96462))))),f312(f190(f854(x96462)),f64(x96462)))+~P22(f312(f67(f861(x96462,x96461)),x96463))
% 155.93/155.63 [9647]~P63(x96471)+~P63(x96472)+P7(x96471,f312(f312(f8(f861(x96472,x96471),a846,f854(x96471)),x96473),f312(f312(f8(f861(x96472,f857(x96471)),f861(x96472,x96471),f854(x96471)),f82(f857(x96471),x96471,x96472,f223(x96471))),f312(f312(f8(f854(f860(x96472,x96471)),f861(x96472,f857(x96471)),f854(x96471)),f173(x96472,x96471)),f312(f177(x96472,x96471),f64(x96472))))),f312(f190(f854(x96472)),f64(x96472)))+~P22(f312(f66(f861(x96472,x96471)),x96473))
% 155.93/155.63 [9739]~P63(x97391)+~P63(x97392)+~P8(x97392,f312(f312(f8(f861(x97391,x97392),a846,f854(x97392)),x97393),f312(f312(f8(f861(x97391,f857(x97392)),f861(x97391,x97392),f854(x97392)),f82(f857(x97392),x97392,x97391,f223(x97392))),f312(f312(f8(f854(f860(x97391,x97392)),f861(x97391,f857(x97392)),f854(x97392)),f173(x97391,x97392)),f312(f177(x97391,x97392),f64(x97391))))),f312(f190(f854(x97391)),f64(x97391)))+P22(f312(f67(f861(x97391,x97392)),x97393))
% 155.93/155.63 [9740]~P63(x97401)+~P63(x97402)+~P7(x97402,f312(f312(f8(f861(x97401,x97402),a846,f854(x97402)),x97403),f312(f312(f8(f861(x97401,f857(x97402)),f861(x97401,x97402),f854(x97402)),f82(f857(x97402),x97402,x97401,f223(x97402))),f312(f312(f8(f854(f860(x97401,x97402)),f861(x97401,f857(x97402)),f854(x97402)),f173(x97401,x97402)),f312(f177(x97401,x97402),f64(x97401))))),f312(f190(f854(x97401)),f64(x97401)))+P22(f312(f66(f861(x97401,x97402)),x97403))
% 155.93/155.63 [8549]~P22(f312(f312(f228(a1),f2(a1)),x85493))+P22(f312(f312(f227(a1),f2(a1)),x85491))+~P22(f312(f312(f228(a1),x85492),x85493))+~P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),f312(f312(f90(a1),x85493),x85491)),x85492)))
% 155.93/155.63 [8569]~P87(x85691)+~P22(f312(f70(x85691),x85692))+E(f312(f312(f21(f861(x85691,a846)),x85692),f312(f312(f289(x85691),x85693),f189(f861(x85691,a846)))),f189(f861(x85691,a846)))+E(f312(f312(f115(x85691),x85693),f11(x85691,f312(f312(f21(f861(x85691,a846)),x85692),f312(f312(f289(x85691),x85693),f189(f861(x85691,a846)))))),f11(x85691,f312(f312(f289(x85691),x85693),x85692)))
% 155.93/155.63 [8570]~P87(x85701)+~P22(f312(f70(x85701),x85702))+E(f312(f312(f21(f861(x85701,a846)),x85702),f312(f312(f289(x85701),x85703),f189(f861(x85701,a846)))),f189(f861(x85701,a846)))+E(f312(f312(f124(x85701),x85703),f10(x85701,f312(f312(f21(f861(x85701,a846)),x85702),f312(f312(f289(x85701),x85703),f189(f861(x85701,a846)))))),f10(x85701,f312(f312(f289(x85701),x85703),x85702)))
% 155.93/155.63 [8571]~P103(x85711)+~P22(f312(f70(x85711),x85712))+E(f312(f312(f21(f861(x85711,a846)),x85712),f312(f312(f289(x85711),x85713),f189(f861(x85711,a846)))),f189(f861(x85711,a846)))+E(f312(f312(f226(x85711),x85713),f14(x85711,f312(f312(f21(f861(x85711,a846)),x85712),f312(f312(f289(x85711),x85713),f189(f861(x85711,a846)))))),f14(x85711,f312(f312(f289(x85711),x85713),x85712)))
% 155.93/155.63 [8572]~P103(x85721)+~P22(f312(f70(x85721),x85722))+E(f312(f312(f21(f861(x85721,a846)),x85722),f312(f312(f289(x85721),x85723),f189(f861(x85721,a846)))),f189(f861(x85721,a846)))+E(f312(f312(f225(x85721),x85723),f15(x85721,f312(f312(f21(f861(x85721,a846)),x85722),f312(f312(f289(x85721),x85723),f189(f861(x85721,a846)))))),f15(x85721,f312(f312(f289(x85721),x85723),x85722)))
% 155.93/155.63 [8637]~P103(x86371)+~P22(f312(f70(x86371),x86372))+E(f312(f312(f21(f861(x86371,a846)),x86372),f312(f312(f289(x86371),x86373),f189(f861(x86371,a846)))),f189(f861(x86371,a846)))+E(f312(f312(f226(x86371),x86373),f12(x86371,f226(x86371),f312(f312(f21(f861(x86371,a846)),x86372),f312(f312(f289(x86371),x86373),f189(f861(x86371,a846)))))),f12(x86371,f226(x86371),f312(f312(f289(x86371),x86373),x86372)))
% 155.93/155.63 [8638]~P103(x86381)+~P22(f312(f70(x86381),x86382))+E(f312(f312(f21(f861(x86381,a846)),x86382),f312(f312(f289(x86381),x86383),f189(f861(x86381,a846)))),f189(f861(x86381,a846)))+E(f312(f312(f225(x86381),x86383),f13(x86381,f225(x86381),f312(f312(f21(f861(x86381,a846)),x86382),f312(f312(f289(x86381),x86383),f189(f861(x86381,a846)))))),f13(x86381,f225(x86381),f312(f312(f289(x86381),x86383),x86382)))
% 155.93/155.63 [9012]~P31(x90121)+~P49(x90121,x90121,x90122)+P22(f312(f312(f227(x90121),f109(x90121,x90122)),x90123))+~P22(f312(f312(f227(x90121),f312(x90122,f312(f312(f115(x90121),f109(x90121,x90122)),x90123))),x90123))
% 155.93/155.63 [9216]E(x92161,x92162)+~E(f312(f138(f854(x92163),f854(x92163),f129(x92163),f127(x92163)),x92161),f312(f138(f854(x92163),f854(x92163),f129(x92163),f127(x92163)),x92162))+~E(f312(f190(f854(f854(x92163))),x92161),f312(f190(f854(f854(x92163))),x92162))+P22(f312(f312(f314(f860(f854(x92163),f854(x92163))),f661(x92161,x92162,x92163)),f312(f168(f860(f854(x92163),f854(x92163))),f312(f312(f177(f854(x92163),f854(x92163)),x92162),x92161))))
% 155.93/155.63 [9217]E(x92171,x92172)+~E(f312(f138(f854(x92173),f854(x92173),f129(x92173),f127(x92173)),x92171),f312(f138(f854(x92173),f854(x92173),f129(x92173),f127(x92173)),x92172))+~E(f312(f190(f854(f854(x92173))),x92171),f312(f190(f854(f854(x92173))),x92172))+P22(f312(f312(f314(f860(f854(x92173),f854(x92173))),f662(x92172,x92171,x92173)),f312(f168(f860(f854(x92173),f854(x92173))),f312(f312(f177(f854(x92173),f854(x92173)),x92171),x92172))))
% 155.93/155.63 [10041]~P74(x100412)+E(x100411,f189(f861(x100412,a846)))+~P22(f312(f70(x100412),x100411))+E(f14(x100412,f312(f233(x100412),f312(f312(f8(f861(x100412,a846),a846,x100412),f96(x100412)),f312(f312(f7(x100412,f861(x100412,a846),f861(x100412,a846)),f312(f312(f8(f861(x100412,f861(a846,a846)),f861(f861(x100412,a846),f861(x100412,a846)),x100412),f18(x100412,a846,a846)),f312(f312(f8(f861(x100412,a846),f861(x100412,f861(a846,a846)),x100412),f312(f8(a846,f861(a846,a846),x100412),a310)),f312(f312(f7(x100412,f861(x100412,x100412),f861(x100412,a846)),f312(f312(f8(f861(x100412,a846),f861(f861(x100412,x100412),f861(x100412,a846)),x100412),f8(x100412,a846,x100412)),a309)),f312(f89(x100412),x100413))))),f312(f312(f7(x100412,f861(x100412,a846),a846),f314(x100412)),x100411))))),f312(f312(f89(x100412),x100413),f14(x100412,x100411)))
% 155.93/155.63 [10042]~P74(x100422)+E(x100421,f189(f861(x100422,a846)))+~P22(f312(f70(x100422),x100421))+E(f15(x100422,f312(f233(x100422),f312(f312(f8(f861(x100422,a846),a846,x100422),f96(x100422)),f312(f312(f7(x100422,f861(x100422,a846),f861(x100422,a846)),f312(f312(f8(f861(x100422,f861(a846,a846)),f861(f861(x100422,a846),f861(x100422,a846)),x100422),f18(x100422,a846,a846)),f312(f312(f8(f861(x100422,a846),f861(x100422,f861(a846,a846)),x100422),f312(f8(a846,f861(a846,a846),x100422),a310)),f312(f312(f7(x100422,f861(x100422,x100422),f861(x100422,a846)),f312(f312(f8(f861(x100422,a846),f861(f861(x100422,x100422),f861(x100422,a846)),x100422),f8(x100422,a846,x100422)),a309)),f312(f89(x100422),x100423))))),f312(f312(f7(x100422,f861(x100422,a846),a846),f314(x100422)),x100421))))),f312(f312(f89(x100422),x100423),f15(x100422,x100421)))
% 155.93/155.63 [10043]~P96(x100432)+E(x100431,f189(f861(x100432,a846)))+~P22(f312(f70(x100432),x100431))+E(f11(x100432,f312(f233(x100432),f312(f312(f8(f861(x100432,a846),a846,x100432),f96(x100432)),f312(f312(f7(x100432,f861(x100432,a846),f861(x100432,a846)),f312(f312(f8(f861(x100432,f861(a846,a846)),f861(f861(x100432,a846),f861(x100432,a846)),x100432),f18(x100432,a846,a846)),f312(f312(f8(f861(x100432,a846),f861(x100432,f861(a846,a846)),x100432),f312(f8(a846,f861(a846,a846),x100432),a310)),f312(f312(f7(x100432,f861(x100432,x100432),f861(x100432,a846)),f312(f312(f8(f861(x100432,a846),f861(f861(x100432,x100432),f861(x100432,a846)),x100432),f8(x100432,a846,x100432)),a309)),f312(f124(x100432),x100433))))),f312(f312(f7(x100432,f861(x100432,a846),a846),f314(x100432)),x100431))))),f312(f312(f124(x100432),x100433),f11(x100432,x100431)))
% 155.93/155.63 [10044]~P96(x100442)+E(x100441,f189(f861(x100442,a846)))+~P22(f312(f70(x100442),x100441))+E(f10(x100442,f312(f233(x100442),f312(f312(f8(f861(x100442,a846),a846,x100442),f96(x100442)),f312(f312(f7(x100442,f861(x100442,a846),f861(x100442,a846)),f312(f312(f8(f861(x100442,f861(a846,a846)),f861(f861(x100442,a846),f861(x100442,a846)),x100442),f18(x100442,a846,a846)),f312(f312(f8(f861(x100442,a846),f861(x100442,f861(a846,a846)),x100442),f312(f8(a846,f861(a846,a846),x100442),a310)),f312(f312(f7(x100442,f861(x100442,x100442),f861(x100442,a846)),f312(f312(f8(f861(x100442,a846),f861(f861(x100442,x100442),f861(x100442,a846)),x100442),f8(x100442,a846,x100442)),a309)),f312(f115(x100442),x100443))))),f312(f312(f7(x100442,f861(x100442,a846),a846),f314(x100442)),x100441))))),f312(f312(f115(x100442),x100443),f10(x100442,x100441)))
% 155.93/155.63 [10045]~P103(x100452)+E(x100451,f189(f861(x100452,a846)))+~P22(f312(f70(x100452),x100451))+E(f12(x100452,f226(x100452),f312(f233(x100452),f312(f312(f8(f861(x100452,a846),a846,x100452),f96(x100452)),f312(f312(f7(x100452,f861(x100452,a846),f861(x100452,a846)),f312(f312(f8(f861(x100452,f861(a846,a846)),f861(f861(x100452,a846),f861(x100452,a846)),x100452),f18(x100452,a846,a846)),f312(f312(f8(f861(x100452,a846),f861(x100452,f861(a846,a846)),x100452),f312(f8(a846,f861(a846,a846),x100452),a310)),f312(f312(f7(x100452,f861(x100452,x100452),f861(x100452,a846)),f312(f312(f8(f861(x100452,a846),f861(f861(x100452,x100452),f861(x100452,a846)),x100452),f8(x100452,a846,x100452)),a309)),f312(f225(x100452),x100453))))),f312(f312(f7(x100452,f861(x100452,a846),a846),f314(x100452)),x100451))))),f312(f312(f225(x100452),x100453),f12(x100452,f226(x100452),x100451)))
% 155.93/155.63 [10046]~P103(x100462)+E(x100461,f189(f861(x100462,a846)))+~P22(f312(f70(x100462),x100461))+E(f13(x100462,f225(x100462),f312(f233(x100462),f312(f312(f8(f861(x100462,a846),a846,x100462),f96(x100462)),f312(f312(f7(x100462,f861(x100462,a846),f861(x100462,a846)),f312(f312(f8(f861(x100462,f861(a846,a846)),f861(f861(x100462,a846),f861(x100462,a846)),x100462),f18(x100462,a846,a846)),f312(f312(f8(f861(x100462,a846),f861(x100462,f861(a846,a846)),x100462),f312(f8(a846,f861(a846,a846),x100462),a310)),f312(f312(f7(x100462,f861(x100462,x100462),f861(x100462,a846)),f312(f312(f8(f861(x100462,a846),f861(f861(x100462,x100462),f861(x100462,a846)),x100462),f8(x100462,a846,x100462)),a309)),f312(f226(x100462),x100463))))),f312(f312(f7(x100462,f861(x100462,a846),a846),f314(x100462)),x100461))))),f312(f312(f226(x100462),x100463),f13(x100462,f225(x100462),x100461)))
% 155.93/155.63 [9791]~P112(x97911)+~E(x97913,f2(x97911))+~E(x97912,f2(x97911))+E(f312(f312(f89(x97911),f312(f312(f240(x97911),x97912),f312(f117(a853),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(x97911),x97913),f312(f117(a853),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(x97911))
% 155.93/155.63 [9939]~P117(x99391)+~P22(f312(f312(f227(x99391),f2(x99391)),x99393))+P22(f312(f312(f227(x99391),x99392),x99393))+~P22(f312(f312(f227(x99391),f312(f312(f240(x99391),x99392),f312(f117(a853),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(x99391),x99393),f312(f117(a853),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))))))
% 155.93/155.63 [9984]~P112(x99842)+~E(x99841,f2(x99842))+~E(x99843,f2(x99842))+~P22(f312(f312(f228(x99842),f2(x99842)),f312(f312(f89(x99842),f312(f312(f240(x99842),x99843),f312(f117(a853),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(x99842),x99841),f312(f117(a853),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)))))))
% 155.93/155.63 [9179]E(x91791,x91792)+~E(f605(x91791,x91792,x91794,x91793),f610(x91791,x91792,x91794,x91793))+P22(f312(f312(f314(f860(f854(x91793),f854(x91793))),f312(f312(f239(f854(x91793),f854(x91793)),x91792),x91791)),f143(x91793,x91794)))+P22(f312(f312(f314(f860(f854(x91793),f854(x91793))),f312(f312(f239(f854(x91793),f854(x91793)),x91791),x91792)),f143(x91793,x91794)))
% 155.93/155.63 [4790]~P64(x47902)+~E(x47904,f2(x47902))+~E(x47901,f2(x47902))+E(x47901,f312(f312(f268(x47902),x47903),x47904))
% 155.93/155.63 [4791]~P64(x47911)+~E(x47913,f2(x47911))+~E(x47914,f2(x47911))+E(f312(f312(f268(x47911),x47912),x47913),x47914)
% 155.93/155.63 [4903]~P64(x49032)+E(x49031,f2(x49032))+~E(x49033,f2(x49032))+~E(x49031,f312(f312(f268(x49032),x49034),x49033))
% 155.94/155.63 [4904]~P64(x49042)+E(x49041,f2(x49042))+~E(x49043,f2(x49042))+~E(f312(f312(f268(x49042),x49044),x49043),x49041)
% 155.94/155.63 [5077]~P114(x50772)+E(x50771,f2(x50772))+~E(f312(f312(f268(x50772),x50773),x50771),x50774)+E(x50773,f312(f312(f90(x50772),x50774),x50771))
% 155.94/155.63 [5079]~P114(x50792)+E(x50791,f2(x50792))+~E(f312(f312(f90(x50792),x50793),x50791),x50794)+E(x50793,f312(f312(f268(x50792),x50794),x50791))
% 155.94/155.63 [5080]~P64(x50802)+E(x50801,f2(x50802))+~E(f312(f312(f268(x50802),x50803),x50801),x50804)+E(x50803,f312(f312(f90(x50802),x50804),x50801))
% 155.94/155.63 [5081]~P64(x50812)+E(x50811,f2(x50812))+~E(f312(f312(f90(x50812),x50813),x50811),x50814)+E(x50813,f312(f312(f268(x50812),x50814),x50811))
% 155.94/155.63 [5082]~P114(x50822)+E(x50821,f2(x50822))+~E(x50823,f312(f312(f268(x50822),x50824),x50821))+E(f312(f312(f90(x50822),x50823),x50821),x50824)
% 155.94/155.63 [5084]~P114(x50842)+E(x50841,f2(x50842))+~E(x50843,f312(f312(f90(x50842),x50844),x50841))+E(f312(f312(f268(x50842),x50843),x50841),x50844)
% 155.94/155.63 [5085]~P64(x50852)+E(x50851,f2(x50852))+~E(x50853,f312(f312(f268(x50852),x50854),x50851))+E(f312(f312(f90(x50852),x50853),x50851),x50854)
% 155.94/155.63 [5086]~P64(x50862)+E(x50861,f2(x50862))+~E(x50863,f312(f312(f90(x50862),x50864),x50861))+E(f312(f312(f268(x50862),x50863),x50861),x50864)
% 155.94/155.63 [5119]~P64(x51192)+~E(x51191,f2(x51192))+~E(f312(f312(f90(x51192),x51191),x51194),x51193)+E(x51191,f312(f312(f268(x51192),x51193),x51194))
% 155.94/155.63 [5120]~P64(x51201)+~E(x51204,f2(x51201))+~E(x51202,f312(f312(f90(x51201),x51204),x51203))+E(f312(f312(f268(x51201),x51202),x51203),x51204)
% 155.94/155.63 [5191]~E(x51913,x51914)+~E(x51912,x51913)+~P105(x51911)+E(f283(x51911,x51912,x51913),f312(f312(f289(x51911),x51914),f189(f861(x51911,a846))))
% 155.94/155.63 [5389]~E(f128(x53892,x53891),x53893)+~E(f140(x53892,x53891),x53894)+E(x53891,f127(x53892))+E(f312(f312(f129(x53892),x53893),f312(f312(f147(x53892),x53894),f127(x53892))),x53891)
% 155.94/155.63 [5994]~P117(x59943)+E(x59941,x59942)+~E(f312(f312(f240(x59943),x59944),x59941),f312(f312(f240(x59943),x59944),x59942))+~P22(f312(f312(f228(x59943),f87(x59943)),x59944))
% 155.94/155.63 [5995]E(x59951,x59952)+~E(f312(f312(f289(x59953),x59954),x59951),f312(f312(f289(x59953),x59954),x59952))+P22(f312(f312(f314(x59953),x59954),x59952))+P22(f312(f312(f314(x59953),x59954),x59951))
% 155.94/155.63 [6031]E(f312(x60311,x60312),f2(a853))+~E(f312(f312(f6(x60313,a853),x60311),x60314),f2(a853))+~P22(f312(f70(x60313),x60314))+~P22(f312(f312(f314(x60313),x60312),x60314))
% 155.94/155.63 [6032]E(f312(x60321,x60322),f87(a853))+~E(f312(f312(f9(x60323,a853),x60321),x60324),f87(a853))+~P22(f312(f70(x60323),x60324))+~P22(f312(f312(f314(x60323),x60322),x60324))
% 155.94/155.63 [6247]~P105(x62471)+~P22(f312(f312(f228(x62471),x62474),x62473))+P22(f312(f312(f228(x62471),x62472),x62473))+~P22(f312(f312(f228(x62471),x62472),x62474))
% 155.94/155.63 [6248]~P105(x62481)+~P22(f312(f312(f227(x62481),x62484),x62483))+P22(f312(f312(f228(x62481),x62482),x62483))+~P22(f312(f312(f228(x62481),x62482),x62484))
% 155.94/155.63 [6249]~P105(x62491)+~P22(f312(f312(f227(x62491),x62492),x62494))+P22(f312(f312(f228(x62491),x62492),x62493))+~P22(f312(f312(f228(x62491),x62494),x62493))
% 155.94/155.63 [6250]~P102(x62501)+~P22(f312(f312(f228(x62501),x62502),x62504))+P22(f312(f312(f228(x62501),x62502),x62503))+~P22(f312(f312(f228(x62501),x62504),x62503))
% 155.94/155.63 [6251]~P102(x62511)+~P22(f312(f312(f227(x62511),x62512),x62514))+P22(f312(f312(f228(x62511),x62512),x62513))+~P22(f312(f312(f228(x62511),x62514),x62513))
% 155.94/155.63 [6252]~P102(x62521)+~P22(f312(f312(f227(x62521),x62524),x62523))+P22(f312(f312(f228(x62521),x62522),x62523))+~P22(f312(f312(f228(x62521),x62522),x62524))
% 155.94/155.63 [6253]~P105(x62531)+~P22(f312(f312(f227(x62531),x62534),x62533))+P22(f312(f312(f227(x62531),x62532),x62533))+~P22(f312(f312(f227(x62531),x62532),x62534))
% 155.94/155.63 [6254]~P102(x62541)+~P22(f312(f312(f227(x62541),x62542),x62544))+P22(f312(f312(f227(x62541),x62542),x62543))+~P22(f312(f312(f227(x62541),x62544),x62543))
% 155.94/155.63 [6477]~P31(x64771)+~P22(f312(f312(f227(x64771),x64772),f49(x64771,x64774)))+P22(f312(f312(f227(x64771),x64772),x64773))+~P22(f312(f312(f314(x64771),x64773),x64774))
% 155.94/155.63 [6620]~P103(x66201)+~P33(x66201,f312(f312(f147(x66201),x66202),x66204))+~P22(f312(f312(f314(x66201),x66203),f312(f168(x66201),x66204)))+P22(f312(f312(f227(x66201),x66202),x66203))
% 155.94/155.63 [6707]~P31(x67071)+~P22(f312(f312(f227(x67071),f48(x67071,x67074)),x67073))+P22(f312(f312(f227(x67071),x67072),x67073))+~P22(f312(f312(f314(x67071),x67072),x67074))
% 155.94/155.63 [7115]~P103(x71151)+E(f312(f312(f124(f861(x71151,a846)),f312(f282(x71151,x71152),x71153)),f312(f282(x71151,x71153),x71154)),f312(f282(x71151,x71152),x71154))+~P22(f312(f312(f227(x71151),x71153),x71154))+~P22(f312(f312(f227(x71151),x71152),x71153))
% 155.94/155.63 [7216]~P103(x72161)+E(f312(f312(f124(f861(x72161,a846)),f312(f282(x72161,x72162),x72163)),f283(x72161,x72163,x72164)),f283(x72161,x72162,x72164))+~P22(f312(f312(f227(x72161),x72163),x72164))+~P22(f312(f312(f227(x72161),x72162),x72163))
% 155.94/155.63 [7281]~P103(x72811)+E(f312(f312(f124(f861(x72811,a846)),f285(x72811,x72812,x72813)),f312(f282(x72811,x72813),x72814)),f285(x72811,x72812,x72814))+~P22(f312(f312(f228(x72811),x72812),x72813))+~P22(f312(f312(f227(x72811),x72813),x72814))
% 155.94/155.63 [7303]~P103(x73031)+E(f312(f312(f124(f861(x73031,a846)),f283(x73031,x73032,x73033)),f285(x73031,x73033,x73034)),f312(f282(x73031,x73032),x73034))+~P22(f312(f312(f228(x73031),x73033),x73034))+~P22(f312(f312(f227(x73031),x73032),x73033))
% 155.94/155.63 [7333]~P103(x73331)+E(f312(f312(f124(f861(x73331,a846)),f285(x73331,x73332,x73333)),f283(x73331,x73333,x73334)),f284(x73331,x73332,x73334))+~P22(f312(f312(f228(x73331),x73332),x73333))+~P22(f312(f312(f227(x73331),x73333),x73334))
% 155.94/155.63 [7334]~P103(x73341)+E(f312(f312(f124(f861(x73341,a846)),f284(x73341,x73342,x73343)),f285(x73341,x73343,x73344)),f285(x73341,x73342,x73344))+~P22(f312(f312(f228(x73341),x73343),x73344))+~P22(f312(f312(f227(x73341),x73342),x73343))
% 155.94/155.63 [7335]~P103(x73351)+E(f312(f312(f124(f861(x73351,a846)),f284(x73351,x73352,x73353)),f284(x73351,x73353,x73354)),f284(x73351,x73352,x73354))+~P22(f312(f312(f227(x73351),x73353),x73354))+~P22(f312(f312(f227(x73351),x73352),x73353))
% 155.94/155.63 [7336]~P103(x73361)+E(f312(f312(f124(f861(x73361,a846)),f283(x73361,x73362,x73363)),f284(x73361,x73363,x73364)),f283(x73361,x73362,x73364))+~P22(f312(f312(f227(x73361),x73363),x73364))+~P22(f312(f312(f227(x73361),x73362),x73363))
% 155.94/155.63 [8126]P19(x81261,x81262,f388(x81263,x81262,x81264,x81261),x81264)+~P22(f312(f70(x81262),x81263))+~P22(f312(f70(x81261),x81264))+~P22(f312(f312(f227(a853),f312(f53(x81261),x81264)),f312(f53(x81262),x81263)))
% 155.94/155.63 [8199]~P72(x81991)+~E(f312(x81993,f736(x81993,x81994,x81992,x81991)),f87(x81991))+E(f312(f312(f312(f74(x81991,x81992,f90(x81991)),x81993),f87(x81991)),x81994),f87(x81991))+~P22(f312(f70(x81992),x81994))
% 155.94/155.63 [8486]~P117(x84861)+~P22(f312(f312(f227(x84861),f2(x84861)),x84863))+P22(f312(f312(f227(x84861),x84862),x84863))+~P22(f312(f312(f227(x84861),f312(f312(f240(x84861),x84862),f312(a126,x84864))),f312(f312(f240(x84861),x84863),f312(a126,x84864))))
% 155.94/155.63 [8636]~P49(f861(x86364,a846),f861(x86364,a846),x86363)+P22(f312(x86361,x86362))+~P22(f312(x86361,f558(x86361,x86363,x86362,x86364)))+~P22(f312(f312(f314(x86364),x86362),f109(f861(x86364,a846),x86363)))
% 155.94/155.63 [8855]~P72(x88551)+E(f312(f312(f312(f74(x88551,x88552,f90(x88551)),x88553),f87(x88551)),x88554),f87(x88551))+~P22(f312(f70(x88552),x88554))+P22(f312(f312(f314(x88552),f736(x88553,x88554,x88552,x88551)),x88554))
% 155.94/155.63 [9341]~P22(f312(f312(f227(a1),x93414),f2(a1)))+P22(f312(f312(f227(a1),f312(f312(f89(a1),f312(f312(f90(a1),x93411),f54(a1,x93412,x93413))),x93414)),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x93413))+~P22(f312(f312(f228(a1),x93411),x93414))
% 155.94/155.63 [9780]~P22(f312(f70(x97801),x97802))+~P22(f312(f312(f314(x97801),x97804),x97802))+~P22(f312(f312(f314(x97801),x97803),x97802))+P22(f312(f312(f228(a853),f312(f53(x97801),f312(f312(f21(f861(x97801,a846)),f312(f312(f21(f861(x97801,a846)),x97802),f312(f312(f289(x97801),x97803),f189(f861(x97801,a846))))),f312(f312(f289(x97801),x97804),f189(f861(x97801,a846)))))),f312(f53(x97801),x97802)))
% 155.94/155.63 [6815]~P103(x68151)+~P22(f312(f312(f228(x68151),x68152),x68154))+~P22(f312(f312(f228(x68151),x68152),x68153))+P22(f312(f312(f228(x68151),x68152),f312(f312(f225(x68151),x68153),x68154)))
% 155.94/155.63 [6818]~P99(x68181)+~P22(f312(f312(f227(x68181),x68182),x68184))+~P22(f312(f312(f227(x68181),x68182),x68183))+P22(f312(f312(f227(x68181),x68182),f312(f312(f115(x68181),x68183),x68184)))
% 155.94/155.63 [6821]~P103(x68211)+~P22(f312(f312(f227(x68211),x68212),x68214))+~P22(f312(f312(f227(x68211),x68212),x68213))+P22(f312(f312(f227(x68211),x68212),f312(f312(f225(x68211),x68213),x68214)))
% 155.94/155.63 [6843]~P65(x68432)+E(x68431,f2(x68432))+E(f312(f312(f268(x68432),f312(f312(f240(x68432),x68431),x68433)),f312(f312(f240(x68432),x68431),x68434)),f312(f312(f240(x68432),x68431),f312(f312(f21(a853),x68433),x68434)))+~P22(f312(f312(f227(a853),x68434),x68433))
% 155.94/155.63 [6889]~P103(x68891)+~P33(x68891,f312(f312(f147(x68891),x68893),x68894))+P33(x68891,f312(f312(f147(x68891),x68892),f312(f312(f147(x68891),x68893),x68894)))+~P22(f312(f312(f227(x68891),x68892),x68893))
% 155.94/155.63 [6933]~P117(x69331)+~P22(f312(f312(f228(x69331),f2(x69331)),x69333))+~P22(f312(f312(f228(x69331),x69332),x69334))+P22(f312(f312(f228(x69331),x69332),f312(f312(f89(x69331),x69333),x69334)))
% 155.94/155.63 [6934]~P84(x69341)+~P22(f312(f312(f227(x69341),f2(x69341)),x69343))+~P22(f312(f312(f228(x69341),x69342),x69344))+P22(f312(f312(f228(x69341),x69342),f312(f312(f89(x69341),x69343),x69344)))
% 155.94/155.63 [6935]~P84(x69351)+~P22(f312(f312(f227(x69351),x69352),x69354))+~P22(f312(f312(f228(x69351),f2(x69351)),x69353))+P22(f312(f312(f228(x69351),x69352),f312(f312(f89(x69351),x69353),x69354)))
% 155.94/155.63 [6936]~P84(x69361)+~P22(f312(f312(f227(x69361),f2(x69361)),x69364))+~P22(f312(f312(f227(x69361),x69362),x69363))+P22(f312(f312(f227(x69361),x69362),f312(f312(f89(x69361),x69363),x69364)))
% 155.94/155.63 [6937]~P84(x69371)+~P22(f312(f312(f227(x69371),f2(x69371)),x69373))+~P22(f312(f312(f227(x69371),x69372),x69374))+P22(f312(f312(f227(x69371),x69372),f312(f312(f89(x69371),x69373),x69374)))
% 155.94/155.63 [6974]~P103(x69741)+P22(f312(f312(f228(x69741),x69742),x69743))+P22(f312(f312(f228(x69741),x69742),x69744))+~P22(f312(f312(f228(x69741),x69742),f312(f312(f226(x69741),x69744),x69743)))
% 155.94/155.63 [6975]~P103(x69751)+P22(f312(f312(f227(x69751),x69752),x69753))+P22(f312(f312(f227(x69751),x69752),x69754))+~P22(f312(f312(f227(x69751),x69752),f312(f312(f226(x69751),x69754),x69753)))
% 155.94/155.63 [7256]~P105(x72562)+~P63(x72561)+~P22(f312(f312(f228(f861(x72561,x72562)),x72563),x72564))+P22(f312(f312(f227(f861(x72561,x72562)),x72563),x72564))
% 155.94/155.63 [7620]~P67(x76201)+~P22(f312(f312(f228(x76201),x76204),f2(x76201)))+~P22(f312(f312(f228(x76201),x76203),f312(f312(f268(x76201),x76202),x76204)))+P22(f312(f312(f228(x76201),x76202),f312(f312(f90(x76201),x76203),x76204)))
% 155.94/155.63 [7621]~P67(x76211)+~P22(f312(f312(f228(x76211),x76214),f2(x76211)))+~P22(f312(f312(f228(x76211),x76213),f312(f312(f90(x76211),x76212),x76214)))+P22(f312(f312(f228(x76211),x76212),f312(f312(f268(x76211),x76213),x76214)))
% 155.94/155.63 [7622]~P67(x76221)+~P22(f312(f312(f228(x76221),x76224),f2(x76221)))+~P22(f312(f312(f227(x76221),x76223),f312(f312(f268(x76221),x76222),x76224)))+P22(f312(f312(f227(x76221),x76222),f312(f312(f90(x76221),x76223),x76224)))
% 155.94/155.63 [7623]~P67(x76231)+~P22(f312(f312(f228(x76231),x76234),f2(x76231)))+~P22(f312(f312(f227(x76231),x76233),f312(f312(f90(x76231),x76232),x76234)))+P22(f312(f312(f227(x76231),x76232),f312(f312(f268(x76231),x76233),x76234)))
% 155.94/155.63 [7736]~P118(x77361)+~P22(f312(f312(f228(x77361),x77363),f2(x77361)))+~P22(f312(f312(f228(x77361),x77364),x77362))+P22(f312(f312(f228(x77361),f312(f312(f90(x77361),x77362),x77363)),f312(f312(f90(x77361),x77364),x77363)))
% 155.94/155.63 [7737]~P118(x77371)+~P22(f312(f312(f228(x77371),x77372),f2(x77371)))+~P22(f312(f312(f228(x77371),x77374),x77373))+P22(f312(f312(f228(x77371),f312(f312(f90(x77371),x77372),x77373)),f312(f312(f90(x77371),x77372),x77374)))
% 155.94/155.63 [7738]~P67(x77381)+~P22(f312(f312(f228(x77381),x77383),f2(x77381)))+~P22(f312(f312(f228(x77381),x77384),x77382))+P22(f312(f312(f228(x77381),f312(f312(f268(x77381),x77382),x77383)),f312(f312(f268(x77381),x77384),x77383)))
% 155.94/155.63 [7739]~P128(x77391)+~P22(f312(f312(f227(x77391),x77392),f2(x77391)))+~P22(f312(f312(f227(x77391),x77394),x77393))+P22(f312(f312(f227(x77391),f312(f312(f90(x77391),x77392),x77393)),f312(f312(f90(x77391),x77392),x77394)))
% 155.94/155.63 [7740]~P118(x77401)+~P22(f312(f312(f228(x77401),x77402),f2(x77401)))+~P22(f312(f312(f227(x77401),x77404),x77403))+P22(f312(f312(f227(x77401),f312(f312(f90(x77401),x77402),x77403)),f312(f312(f90(x77401),x77402),x77404)))
% 155.94/155.63 [7741]~P128(x77411)+~P22(f312(f312(f227(x77411),x77413),f2(x77411)))+~P22(f312(f312(f227(x77411),x77414),x77412))+P22(f312(f312(f227(x77411),f312(f312(f90(x77411),x77412),x77413)),f312(f312(f90(x77411),x77414),x77413)))
% 155.94/155.63 [7742]~P66(x77421)+~P22(f312(f312(f227(x77421),x77423),f2(x77421)))+~P22(f312(f312(f227(x77421),x77424),x77422))+P22(f312(f312(f227(x77421),f312(f312(f268(x77421),x77422),x77423)),f312(f312(f268(x77421),x77424),x77423)))
% 155.94/155.63 [7744]~P117(x77441)+~P22(f312(f312(f228(x77441),f87(x77441)),x77442))+~P22(f312(f312(f228(a853),x77443),x77444))+P22(f312(f312(f228(x77441),f312(f312(f240(x77441),x77442),x77443)),f312(f312(f240(x77441),x77442),x77444)))
% 155.94/155.63 [7745]~P117(x77451)+~P22(f312(f312(f228(x77451),f87(x77451)),x77452))+~P22(f312(f312(f227(a853),x77453),x77454))+P22(f312(f312(f227(x77451),f312(f312(f240(x77451),x77452),x77453)),f312(f312(f240(x77451),x77452),x77454)))
% 155.94/155.63 [7746]~P117(x77461)+~P22(f312(f312(f227(x77461),f87(x77461)),x77462))+~P22(f312(f312(f227(a853),x77463),x77464))+P22(f312(f312(f227(x77461),f312(f312(f240(x77461),x77462),x77463)),f312(f312(f240(x77461),x77462),x77464)))
% 155.94/155.63 [7771]P22(f312(f312(f228(a853),f2(a853)),f312(x77711,x77712)))+~P22(f312(f70(x77713),x77714))+~P22(f312(f312(f314(x77713),x77712),x77714))+~P22(f312(f312(f228(a853),f2(a853)),f312(f312(f9(x77713,a853),x77711),x77714)))
% 155.94/155.63 [7779]~P122(x77791)+~P22(f312(f312(f228(x77791),x77793),x77794))+~P22(f312(f312(f228(x77791),f2(x77791)),x77792))+P22(f312(f312(f228(x77791),f312(f312(f90(x77791),x77792),x77793)),f312(f312(f90(x77791),x77792),x77794)))
% 155.94/155.63 [7781]~P116(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)))
% 155.94/155.63 [7782]~P118(x77821)+~P22(f312(f312(f228(x77821),x77822),x77824))+~P22(f312(f312(f228(x77821),f2(x77821)),x77823))+P22(f312(f312(f228(x77821),f312(f312(f90(x77821),x77822),x77823)),f312(f312(f90(x77821),x77824),x77823)))
% 155.94/155.63 [7783]~P122(x77831)+~P22(f312(f312(f228(x77831),x77832),x77834))+~P22(f312(f312(f228(x77831),f2(x77831)),x77833))+P22(f312(f312(f228(x77831),f312(f312(f90(x77831),x77832),x77833)),f312(f312(f90(x77831),x77834),x77833)))
% 155.94/155.63 [7784]~P118(x77841)+~P22(f312(f312(f228(x77841),x77843),x77844))+~P22(f312(f312(f228(x77841),f2(x77841)),x77842))+P22(f312(f312(f228(x77841),f312(f312(f90(x77841),x77842),x77843)),f312(f312(f90(x77841),x77842),x77844)))
% 155.94/155.63 [7785]~P67(x77851)+~P22(f312(f312(f228(x77851),x77852),x77854))+~P22(f312(f312(f228(x77851),f2(x77851)),x77853))+P22(f312(f312(f228(x77851),f312(f312(f268(x77851),x77852),x77853)),f312(f312(f268(x77851),x77854),x77853)))
% 155.94/155.63 [7786]~P130(x77861)+~P22(f312(f312(f227(x77861),x77863),x77864))+~P22(f312(f312(f227(x77861),f2(x77861)),x77862))+P22(f312(f312(f227(x77861),f312(f312(f90(x77861),x77862),x77863)),f312(f312(f90(x77861),x77862),x77864)))
% 155.94/155.63 [7787]~P118(x77871)+~P22(f312(f312(f228(x77871),f2(x77871)),x77872))+~P22(f312(f312(f227(x77871),x77873),x77874))+P22(f312(f312(f227(x77871),f312(f312(f90(x77871),x77872),x77873)),f312(f312(f90(x77871),x77872),x77874)))
% 155.94/155.63 [7788]~P129(x77881)+~P22(f312(f312(f227(x77881),x77883),x77884))+~P22(f312(f312(f227(x77881),f2(x77881)),x77882))+P22(f312(f312(f227(x77881),f312(f312(f90(x77881),x77882),x77883)),f312(f312(f90(x77881),x77882),x77884)))
% 155.94/155.63 [7789]~P130(x77891)+~P22(f312(f312(f227(x77891),x77892),x77894))+~P22(f312(f312(f227(x77891),f2(x77891)),x77893))+P22(f312(f312(f227(x77891),f312(f312(f90(x77891),x77892),x77893)),f312(f312(f90(x77891),x77894),x77893)))
% 155.94/155.63 [7790]~P117(x77901)+~P22(f312(f312(f227(x77901),x77902),x77904))+~P22(f312(f312(f227(x77901),f2(x77901)),x77902))+P22(f312(f312(f227(x77901),f312(f312(f240(x77901),x77902),x77903)),f312(f312(f240(x77901),x77904),x77903)))
% 155.94/155.63 [7791]~P66(x77911)+~P22(f312(f312(f227(x77911),x77912),x77914))+~P22(f312(f312(f227(x77911),f2(x77911)),x77913))+P22(f312(f312(f227(x77911),f312(f312(f268(x77911),x77912),x77913)),f312(f312(f268(x77911),x77914),x77913)))
% 155.94/155.63 [7829]~P104(x78292)+P22(f312(f312(f227(f861(x78291,x78292)),x78294),x78293))+~P22(f312(f312(f227(f861(x78291,x78292)),x78293),x78294))+P22(f312(f312(f228(f861(x78291,x78292)),x78293),x78294))
% 155.94/155.63 [7869]P22(f312(f312(f314(x78691),x78692),x78693))+P22(f312(f312(f314(x78691),x78692),x78694))+~P22(f312(f312(f227(f861(x78691,a846)),x78694),x78693))+P22(f312(f312(f228(f861(x78691,a846)),x78694),f312(f312(f289(x78691),x78692),x78693)))
% 155.94/155.63 [8031]P22(f312(f312(f314(x80311),x80312),x80313))+P22(f312(f312(f314(x80311),x80312),x80314))+~P22(f312(f312(f228(f861(x80311,a846)),x80314),f312(f312(f289(x80311),x80312),x80313)))+P22(f312(f312(f227(f861(x80311,a846)),x80314),x80313))
% 155.94/155.63 [8040]~P63(x80401)+P7(x80401,x80402,x80403)+~P22(f312(x80402,x80404))+~P22(f312(f312(f314(f854(x80401)),x80404),f312(f168(f854(x80401)),f63(x80401,x80403,f64(x80401)))))
% 155.94/155.63 [8050]~P8(x80503,x80501,x80504)+~P63(x80503)+P22(f312(x80501,x80502))+~P22(f312(f312(f314(f854(x80503)),x80502),f312(f168(f854(x80503)),f63(x80503,x80504,f64(x80503)))))
% 155.94/155.63 [8103]~P118(x81031)+P22(f312(f312(f228(x81031),x81033),x81032))+P22(f312(f312(f228(x81031),x81032),x81033))+~P22(f312(f312(f228(x81031),f312(f312(f90(x81031),x81034),x81032)),f312(f312(f90(x81031),x81034),x81033)))
% 155.94/155.63 [8104]~P118(x81041)+P22(f312(f312(f228(x81041),x81043),x81042))+P22(f312(f312(f228(x81041),x81042),x81043))+~P22(f312(f312(f228(x81041),f312(f312(f90(x81041),x81042),x81044)),f312(f312(f90(x81041),x81043),x81044)))
% 155.94/155.63 [8115]~P118(x81151)+P22(f312(f312(f228(x81151),x81154),f2(x81151)))+P22(f312(f312(f228(x81151),x81152),x81153))+~P22(f312(f312(f228(x81151),f312(f312(f90(x81151),x81152),x81154)),f312(f312(f90(x81151),x81153),x81154)))
% 155.94/155.63 [8116]~P118(x81161)+P22(f312(f312(f228(x81161),x81164),f2(x81161)))+P22(f312(f312(f228(x81161),x81162),x81163))+~P22(f312(f312(f228(x81161),f312(f312(f90(x81161),x81164),x81162)),f312(f312(f90(x81161),x81164),x81163)))
% 155.94/155.63 [8120]~P118(x81201)+P22(f312(f312(f228(x81201),x81202),x81203))+P22(f312(f312(f228(x81201),f2(x81201)),x81204))+~P22(f312(f312(f228(x81201),f312(f312(f90(x81201),x81204),x81203)),f312(f312(f90(x81201),x81204),x81202)))
% 155.94/155.63 [8121]~P118(x81211)+P22(f312(f312(f228(x81211),x81212),x81213))+P22(f312(f312(f228(x81211),f2(x81211)),x81214))+~P22(f312(f312(f228(x81211),f312(f312(f90(x81211),x81213),x81214)),f312(f312(f90(x81211),x81212),x81214)))
% 155.94/155.63 [8134]~P118(x81341)+P22(f312(f312(f228(x81341),x81342),f2(x81341)))+P22(f312(f312(f228(x81341),f2(x81341)),x81342))+~P22(f312(f312(f228(x81341),f312(f312(f90(x81341),x81343),x81342)),f312(f312(f90(x81341),x81344),x81342)))
% 155.94/155.63 [8135]~P118(x81351)+P22(f312(f312(f228(x81351),x81352),f2(x81351)))+P22(f312(f312(f228(x81351),f2(x81351)),x81352))+~P22(f312(f312(f228(x81351),f312(f312(f90(x81351),x81352),x81353)),f312(f312(f90(x81351),x81352),x81354)))
% 155.94/155.63 [8162]~P118(x81621)+~P22(f312(f312(f228(x81621),x81624),f2(x81621)))+P22(f312(f312(f228(x81621),x81622),x81623))+~P22(f312(f312(f228(x81621),f312(f312(f90(x81621),x81624),x81623)),f312(f312(f90(x81621),x81624),x81622)))
% 155.94/155.63 [8163]~P118(x81631)+~P22(f312(f312(f228(x81631),x81634),f2(x81631)))+P22(f312(f312(f227(x81631),x81632),x81633))+~P22(f312(f312(f227(x81631),f312(f312(f90(x81631),x81634),x81633)),f312(f312(f90(x81631),x81634),x81632)))
% 155.94/155.63 [8175]~P117(x81753)+~P22(f312(f312(f228(x81753),f87(x81753)),x81754))+P22(f312(f312(f228(a853),x81751),x81752))+~P22(f312(f312(f228(x81753),f312(f312(f240(x81753),x81754),x81751)),f312(f312(f240(x81753),x81754),x81752)))
% 155.94/155.63 [8177]~P117(x81773)+~P22(f312(f312(f228(x81773),f87(x81773)),x81774))+P22(f312(f312(f227(a853),x81771),x81772))+~P22(f312(f312(f227(x81773),f312(f312(f240(x81773),x81774),x81771)),f312(f312(f240(x81773),x81774),x81772)))
% 155.94/155.63 [8187]~P122(x81871)+P22(f312(f312(f228(x81871),x81872),x81873))+~P22(f312(f312(f227(x81871),f2(x81871)),x81874))+~P22(f312(f312(f228(x81871),f312(f312(f90(x81871),x81874),x81872)),f312(f312(f90(x81871),x81874),x81873)))
% 155.94/155.63 [8188]~P123(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),x81884),x81882)),f312(f312(f90(x81881),x81884),x81883)))
% 155.94/155.63 [8189]~P118(x81891)+P22(f312(f312(f228(x81891),x81892),x81893))+~P22(f312(f312(f228(x81891),f2(x81891)),x81894))+~P22(f312(f312(f228(x81891),f312(f312(f90(x81891),x81894),x81892)),f312(f312(f90(x81891),x81894),x81893)))
% 155.94/155.63 [8190]~P117(x81901)+~P22(f312(f312(f227(x81901),f2(x81901)),x81903))+P22(f312(f312(f228(x81901),x81902),x81903))+~P22(f312(f312(f228(x81901),f312(f312(f240(x81901),x81902),x81904)),f312(f312(f240(x81901),x81903),x81904)))
% 155.94/155.63 [8191]~P122(x81911)+P22(f312(f312(f228(x81911),x81912),x81913))+~P22(f312(f312(f227(x81911),f2(x81911)),x81914))+~P22(f312(f312(f228(x81911),f312(f312(f90(x81911),x81912),x81914)),f312(f312(f90(x81911),x81913),x81914)))
% 155.94/155.63 [8192]~P123(x81921)+P22(f312(f312(f228(x81921),x81922),x81923))+~P22(f312(f312(f227(x81921),f2(x81921)),x81924))+~P22(f312(f312(f228(x81921),f312(f312(f90(x81921),x81922),x81924)),f312(f312(f90(x81921),x81923),x81924)))
% 155.94/155.63 [8193]~P122(x81931)+P22(f312(f312(f227(x81931),x81932),x81933))+~P22(f312(f312(f228(x81931),f2(x81931)),x81934))+~P22(f312(f312(f227(x81931),f312(f312(f90(x81931),x81934),x81932)),f312(f312(f90(x81931),x81934),x81933)))
% 155.94/155.63 [8194]~P118(x81941)+P22(f312(f312(f227(x81941),x81942),x81943))+~P22(f312(f312(f228(x81941),f2(x81941)),x81944))+~P22(f312(f312(f227(x81941),f312(f312(f90(x81941),x81944),x81942)),f312(f312(f90(x81941),x81944),x81943)))
% 155.94/155.63 [8195]~P122(x81951)+P22(f312(f312(f227(x81951),x81952),x81953))+~P22(f312(f312(f228(x81951),f2(x81951)),x81954))+~P22(f312(f312(f227(x81951),f312(f312(f90(x81951),x81952),x81954)),f312(f312(f90(x81951),x81953),x81954)))
% 155.94/155.63 [8242]P22(f312(f312(f314(x82421),x82422),x82423))+~P22(f312(f312(f227(f861(x82421,a846)),x82423),x82424))+~P22(f312(f312(f228(f861(x82421,a846)),x82423),x82424))+P22(f312(f312(f228(f861(x82421,a846)),x82423),f312(f312(f289(x82421),x82422),x82424)))
% 155.94/155.63 [8616]E(f312(f312(f21(a1),f471(x86161,x86162,x86163,x86164)),f472(x86161,x86162,x86163,x86164)),x86164)+~P22(f312(f312(f228(a1),f2(a1)),x86163))+~P22(f312(f312(f227(a1),x86161),x86164))+P22(f312(f312(f227(a1),x86161),f312(f312(f89(a1),x86164),x86163)))
% 155.94/155.63 [8617]E(f312(f312(f21(a1),f479(x86171,x86172,x86173,x86174)),f480(x86171,x86172,x86173,x86174)),x86174)+~P22(f312(f312(f228(a1),f2(a1)),x86173))+~P22(f312(f312(f228(a1),x86171),x86174))+P22(f312(f312(f228(a1),x86171),f312(f312(f89(a1),x86174),x86173)))
% 155.94/155.63 [8752]~E(f312(f312(f161(x87521),x87523),f618(x87524,x87523,x87521,x87522)),f312(f312(f161(x87521),x87524),f618(x87524,x87523,x87521,x87522)))+E(f312(f312(f169(x87521),x87522),x87523),f312(f312(f169(x87521),x87522),x87524))+~P22(f312(f312(f227(a853),x87522),f312(f190(f854(x87521)),x87523)))+~P22(f312(f312(f227(a853),x87522),f312(f190(f854(x87521)),x87524)))
% 155.94/155.63 [8820]~P22(f312(f312(f228(a1),f2(a1)),x88203))+~P22(f312(f312(f227(a1),x88201),x88204))+P22(f312(f312(f314(a1),f471(x88201,x88202,x88203,x88204)),x88202))+P22(f312(f312(f227(a1),x88201),f312(f312(f89(a1),x88204),x88203)))
% 155.94/155.63 [8821]~P22(f312(f312(f228(a1),f2(a1)),x88213))+~P22(f312(f312(f228(a1),x88211),x88214))+P22(f312(f312(f314(a1),f479(x88211,x88212,x88213,x88214)),x88212))+P22(f312(f312(f228(a1),x88211),f312(f312(f89(a1),x88214),x88213)))
% 155.94/155.63 [8864]~P99(x88641)+~P22(f312(f70(x88641),x88643))+~P22(f312(f312(f314(x88641),x88644),x88643))+P22(f312(f312(f227(x88641),f312(f312(f73(x88641,x88641,f115(x88641)),x88642),x88643)),f312(f312(f115(x88641),x88644),x88642)))
% 155.94/155.63 [8865]~P103(x88651)+~P22(f312(f70(x88651),x88653))+~P22(f312(f312(f314(x88651),x88654),x88653))+P22(f312(f312(f227(x88651),f312(f312(f73(x88651,x88651,f225(x88651)),x88652),x88653)),f312(f312(f225(x88651),x88654),x88652)))
% 155.94/155.63 [8915]E(f312(f312(f169(x89151),x89152),x89153),f312(f312(f169(x89151),x89152),x89154))+P22(f312(f312(f228(a853),f618(x89153,x89154,x89151,x89152)),x89152))+~P22(f312(f312(f227(a853),x89152),f312(f190(f854(x89151)),x89153)))+~P22(f312(f312(f227(a853),x89152),f312(f190(f854(x89151)),x89154)))
% 155.94/155.63 [8920]~P22(f312(f312(f228(a1),f2(a1)),x89203))+~P22(f312(f312(f228(a1),x89201),x89202))+P22(f312(f312(f314(a1),f480(x89201,x89204,x89203,x89202)),f283(a1,f87(a1),x89203)))+P22(f312(f312(f228(a1),x89201),f312(f312(f89(a1),x89202),x89203)))
% 155.94/155.63 [8921]~P22(f312(f312(f228(a1),f2(a1)),x89213))+~P22(f312(f312(f227(a1),x89211),x89212))+P22(f312(f312(f314(a1),f472(x89211,x89214,x89213,x89212)),f283(a1,f87(a1),x89213)))+P22(f312(f312(f227(a1),x89211),f312(f312(f89(a1),x89212),x89213)))
% 155.94/155.63 [9079]~E(f312(f173(x90791,x90792),x90793),f312(f173(x90791,x90792),x90794))+E(f312(f168(f860(x90791,x90792)),x90793),f312(f168(f860(x90791,x90792)),x90794))+~P22(f312(f133(x90791),f312(f312(f150(f860(x90791,x90792),x90791),f246(x90791,x90792)),x90794)))+~P22(f312(f133(x90791),f312(f312(f150(f860(x90791,x90792),x90791),f246(x90791,x90792)),x90793)))
% 155.94/155.63 [9091]E(f312(f173(x90911,x90912),x90913),f312(f173(x90911,x90912),x90914))+~E(f312(f168(f860(x90911,x90912)),x90913),f312(f168(f860(x90911,x90912)),x90914))+~P22(f312(f133(x90911),f312(f312(f150(f860(x90911,x90912),x90911),f246(x90911,x90912)),x90914)))+~P22(f312(f133(x90911),f312(f312(f150(f860(x90911,x90912),x90911),f246(x90911,x90912)),x90913)))
% 155.94/155.63 [9361]~P22(f312(f312(f228(a1),f2(a1)),x93613))+~P22(f312(f312(f227(a1),f2(a1)),x93614))+~P22(f312(f312(f228(a1),x93614),x93611))+P22(f312(f312(f228(a1),f312(f312(f89(a1),f312(f312(f90(a1),x93611),f54(a1,x93612,x93613))),x93614)),f312(f312(f90(a1),x93611),x93613)))
% 155.94/155.63 [9750]E(x97501,x97502)+P22(f312(f312(f314(f860(f854(x97503),f854(x97503))),f312(f312(f239(f854(x97503),f854(x97503)),x97502),x97501)),f143(x97503,x97504)))+P22(f312(f312(f314(f860(f854(x97503),f854(x97503))),f312(f312(f239(f854(x97503),f854(x97503)),x97501),x97502)),f143(x97503,x97504)))+~P22(f312(f312(f314(f860(x97503,x97503)),f312(f312(f239(x97503,x97503),f605(x97501,x97502,x97504,x97503)),f610(x97501,x97502,x97504,x97503))),x97504))
% 155.94/155.63 [9751]E(x97511,x97512)+P22(f312(f312(f314(f860(f854(x97513),f854(x97513))),f312(f312(f239(f854(x97513),f854(x97513)),x97512),x97511)),f143(x97513,x97514)))+P22(f312(f312(f314(f860(f854(x97513),f854(x97513))),f312(f312(f239(f854(x97513),f854(x97513)),x97511),x97512)),f143(x97513,x97514)))+~P22(f312(f312(f314(f860(x97513,x97513)),f312(f312(f239(x97513,x97513),f610(x97511,x97512,x97514,x97513)),f605(x97511,x97512,x97514,x97513))),x97514))
% 155.94/155.63 [7321]~P103(x73211)+~P22(f312(f312(f228(x73211),x73213),x73214))+~P22(f312(f312(f228(x73211),x73212),x73214))+P22(f312(f312(f228(x73211),f312(f312(f226(x73211),x73212),x73213)),x73214))
% 155.94/155.63 [7324]~P98(x73241)+~P22(f312(f312(f227(x73241),x73243),x73244))+~P22(f312(f312(f227(x73241),x73242),x73244))+P22(f312(f312(f227(x73241),f312(f312(f124(x73241),x73242),x73243)),x73244))
% 155.94/155.63 [7327]~P103(x73271)+~P22(f312(f312(f227(x73271),x73273),x73274))+~P22(f312(f312(f227(x73271),x73272),x73274))+P22(f312(f312(f227(x73271),f312(f312(f226(x73271),x73272),x73273)),x73274))
% 155.94/155.63 [7645]~E(x76451,x76453)+E(f135(a853,f312(f282(a853,x76451),x76452)),f312(f312(f147(a853),x76453),x76454))+~E(f135(a853,f312(f282(a853,f312(f312(f89(a853),x76451),f87(a853))),x76452)),x76454)+~P22(f312(f312(f228(a853),x76451),x76452))
% 155.94/155.63 [7656]~P103(x76561)+P22(f312(f312(f228(x76561),x76562),x76563))+P22(f312(f312(f228(x76561),x76564),x76563))+~P22(f312(f312(f228(x76561),f312(f312(f225(x76561),x76564),x76562)),x76563))
% 155.94/155.63 [7657]~P103(x76571)+P22(f312(f312(f227(x76571),x76572),x76573))+P22(f312(f312(f227(x76571),x76574),x76573))+~P22(f312(f312(f227(x76571),f312(f312(f225(x76571),x76574),x76572)),x76573))
% 155.94/155.63 [7928]~P66(x79281)+~P22(f312(f312(f228(x79281),f2(x79281)),x79283))+~P22(f312(f312(f228(x79281),x79282),f312(f312(f268(x79281),x79284),x79283)))+P22(f312(f312(f228(x79281),f312(f312(f90(x79281),x79282),x79283)),x79284))
% 155.94/155.63 [7929]~P67(x79291)+~P22(f312(f312(f228(x79291),f2(x79291)),x79293))+~P22(f312(f312(f228(x79291),x79292),f312(f312(f268(x79291),x79294),x79293)))+P22(f312(f312(f228(x79291),f312(f312(f90(x79291),x79292),x79293)),x79294))
% 155.94/155.63 [7931]~P66(x79311)+~P22(f312(f312(f228(x79311),f2(x79311)),x79313))+~P22(f312(f312(f228(x79311),x79312),f312(f312(f90(x79311),x79314),x79313)))+P22(f312(f312(f228(x79311),f312(f312(f268(x79311),x79312),x79313)),x79314))
% 155.94/155.63 [7932]~P67(x79321)+~P22(f312(f312(f228(x79321),f2(x79321)),x79323))+~P22(f312(f312(f228(x79321),x79322),f312(f312(f90(x79321),x79324),x79323)))+P22(f312(f312(f228(x79321),f312(f312(f268(x79321),x79322),x79323)),x79324))
% 155.94/155.63 [7933]~P66(x79331)+~P22(f312(f312(f228(x79331),f2(x79331)),x79333))+~P22(f312(f312(f227(x79331),x79332),f312(f312(f268(x79331),x79334),x79333)))+P22(f312(f312(f227(x79331),f312(f312(f90(x79331),x79332),x79333)),x79334))
% 155.94/155.63 [7934]~P67(x79341)+~P22(f312(f312(f228(x79341),f2(x79341)),x79343))+~P22(f312(f312(f227(x79341),x79342),f312(f312(f268(x79341),x79344),x79343)))+P22(f312(f312(f227(x79341),f312(f312(f90(x79341),x79342),x79343)),x79344))
% 155.94/155.63 [7936]~P66(x79361)+~P22(f312(f312(f228(x79361),f2(x79361)),x79363))+~P22(f312(f312(f227(x79361),x79362),f312(f312(f90(x79361),x79364),x79363)))+P22(f312(f312(f227(x79361),f312(f312(f268(x79361),x79362),x79363)),x79364))
% 155.94/155.63 [7937]~P67(x79371)+~P22(f312(f312(f228(x79371),f2(x79371)),x79373))+~P22(f312(f312(f227(x79371),x79372),f312(f312(f90(x79371),x79374),x79373)))+P22(f312(f312(f227(x79371),f312(f312(f268(x79371),x79372),x79373)),x79374))
% 155.94/155.63 [8073]~P66(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))
% 155.94/155.63 [8075]~P66(x80751)+~P22(f312(f312(f228(x80751),f2(x80751)),x80754))+P22(f312(f312(f228(x80751),x80752),f312(f312(f268(x80751),x80753),x80754)))+~P22(f312(f312(f228(x80751),f312(f312(f90(x80751),x80752),x80754)),x80753))
% 155.94/155.63 [8076]~P67(x80761)+~P22(f312(f312(f228(x80761),f2(x80761)),x80764))+P22(f312(f312(f228(x80761),x80762),f312(f312(f90(x80761),x80763),x80764)))+~P22(f312(f312(f228(x80761),f312(f312(f268(x80761),x80762),x80764)),x80763))
% 155.94/155.63 [8077]~P67(x80771)+~P22(f312(f312(f228(x80771),f2(x80771)),x80774))+P22(f312(f312(f228(x80771),x80772),f312(f312(f268(x80771),x80773),x80774)))+~P22(f312(f312(f228(x80771),f312(f312(f90(x80771),x80772),x80774)),x80773))
% 155.94/155.63 [8078]~P66(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))
% 155.94/155.63 [8080]~P66(x80801)+~P22(f312(f312(f228(x80801),f2(x80801)),x80804))+P22(f312(f312(f227(x80801),x80802),f312(f312(f268(x80801),x80803),x80804)))+~P22(f312(f312(f227(x80801),f312(f312(f90(x80801),x80802),x80804)),x80803))
% 155.94/155.63 [8081]~P67(x80811)+~P22(f312(f312(f228(x80811),f2(x80811)),x80814))+P22(f312(f312(f227(x80811),x80812),f312(f312(f90(x80811),x80813),x80814)))+~P22(f312(f312(f227(x80811),f312(f312(f268(x80811),x80812),x80814)),x80813))
% 155.94/155.63 [8082]~P67(x80821)+~P22(f312(f312(f228(x80821),f2(x80821)),x80824))+P22(f312(f312(f227(x80821),x80822),f312(f312(f268(x80821),x80823),x80824)))+~P22(f312(f312(f227(x80821),f312(f312(f90(x80821),x80822),x80824)),x80823))
% 155.94/155.63 [8241]~P22(f312(x82411,x82414))+P22(f312(x82411,f312(f47(a853,x82412),x82413)))+~P22(f312(f312(f228(a853),x82412),f312(f312(f90(a853),x82413),f312(a126,x82414))))+~P22(f312(f312(f227(a853),f312(f312(f90(a853),x82413),x82414)),x82412))
% 155.94/155.63 [8247]~P67(x82471)+~P22(f312(f312(f228(x82471),x82473),f2(x82471)))+~P22(f312(f312(f228(x82471),f312(f312(f268(x82471),x82474),x82473)),x82472))+P22(f312(f312(f228(x82471),f312(f312(f90(x82471),x82472),x82473)),x82474))
% 155.94/155.63 [8248]~P67(x82481)+~P22(f312(f312(f228(x82481),x82483),f2(x82481)))+~P22(f312(f312(f228(x82481),f312(f312(f90(x82481),x82484),x82483)),x82482))+P22(f312(f312(f228(x82481),f312(f312(f268(x82481),x82482),x82483)),x82484))
% 155.94/155.63 [8249]~P67(x82491)+~P22(f312(f312(f228(x82491),x82493),f2(x82491)))+~P22(f312(f312(f227(x82491),f312(f312(f268(x82491),x82494),x82493)),x82492))+P22(f312(f312(f227(x82491),f312(f312(f90(x82491),x82492),x82493)),x82494))
% 155.94/155.63 [8250]~P67(x82501)+~P22(f312(f312(f228(x82501),x82503),f2(x82501)))+~P22(f312(f312(f227(x82501),f312(f312(f90(x82501),x82504),x82503)),x82502))+P22(f312(f312(f227(x82501),f312(f312(f268(x82501),x82502),x82503)),x82504))
% 155.94/155.63 [8481]~P98(x84811)+~P22(f312(f70(x84811),x84814))+~P22(f312(f312(f314(x84811),x84812),x84814))+P22(f312(f312(f227(x84811),f312(f312(f124(x84811),x84812),x84813)),f312(f312(f73(x84811,x84811,f124(x84811)),x84813),x84814)))
% 155.94/155.63 [8482]~P103(x84821)+~P22(f312(f70(x84821),x84824))+~P22(f312(f312(f314(x84821),x84822),x84824))+P22(f312(f312(f227(x84821),f312(f312(f226(x84821),x84822),x84823)),f312(f312(f73(x84821,x84821,f226(x84821)),x84823),x84824)))
% 155.94/155.63 [8618]~P22(f312(f70(x86181),x86182))+E(f312(f53(x86181),f312(f312(f21(f861(x86181,a846)),x86182),f312(f312(f289(x86181),x86183),x86184))),f312(f312(f21(a853),f312(f53(x86181),f312(f312(f21(f861(x86181,a846)),x86182),x86184))),f87(a853)))+P22(f312(f312(f314(x86181),x86183),x86184))+~P22(f312(f312(f314(x86181),x86183),x86182))
% 155.94/155.63 [8689]E(f312(f312(f89(a1),f473(x86891,x86892,x86893,x86894)),f474(x86891,x86892,x86893,x86894)),x86894)+~P22(f312(f312(f228(a1),f2(a1)),x86893))+~P22(f312(f312(f227(a1),x86894),x86891))+P22(f312(f312(f227(a1),f312(f312(f21(a1),x86894),x86893)),x86891))
% 155.94/155.63 [8690]E(f312(f312(f89(a1),f481(x86901,x86902,x86903,x86904)),f482(x86901,x86902,x86903,x86904)),x86904)+~P22(f312(f312(f228(a1),f2(a1)),x86903))+~P22(f312(f312(f228(a1),x86904),x86901))+P22(f312(f312(f228(a1),f312(f312(f21(a1),x86904),x86903)),x86901))
% 155.94/155.63 [8900]~P22(f312(f312(f228(a1),f2(a1)),x89003))+~P22(f312(f312(f227(a1),x89004),x89001))+P22(f312(f312(f314(a1),f473(x89001,x89002,x89003,x89004)),x89002))+P22(f312(f312(f227(a1),f312(f312(f21(a1),x89004),x89003)),x89001))
% 155.94/155.63 [8901]~P22(f312(f312(f228(a1),f2(a1)),x89013))+~P22(f312(f312(f228(a1),x89014),x89011))+P22(f312(f312(f314(a1),f481(x89011,x89012,x89013,x89014)),x89012))+P22(f312(f312(f228(a1),f312(f312(f21(a1),x89014),x89013)),x89011))
% 155.94/155.63 [8983]~P22(f312(f312(f228(a1),f2(a1)),x89832))+~P22(f312(f312(f228(a1),x89831),x89833))+P22(f312(f312(f314(a1),f482(x89833,x89834,x89832,x89831)),f283(a1,f87(a1),x89832)))+P22(f312(f312(f228(a1),f312(f312(f21(a1),x89831),x89832)),x89833))
% 155.94/155.63 [8984]~P22(f312(f312(f228(a1),f2(a1)),x89842))+~P22(f312(f312(f227(a1),x89841),x89843))+P22(f312(f312(f314(a1),f474(x89843,x89844,x89842,x89841)),f283(a1,f87(a1),x89842)))+P22(f312(f312(f227(a1),f312(f312(f21(a1),x89841),x89842)),x89843))
% 155.94/155.63 [9000]~P22(f312(f312(f228(a1),f2(a1)),x90003))+~P22(f312(f312(f227(a1),f2(a1)),x90004))+~P22(f312(f312(f228(a1),x90004),x90001))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),f312(f312(f90(a1),x90001),f54(a1,x90002,x90003))),x90004)))
% 155.94/155.63 [9078]~P22(f312(f312(f227(a1),x90784),f2(a1)))+~P22(f312(f312(f228(a1),f2(a1)),x90782))+~P22(f312(f312(f228(a1),x90781),x90784))+P22(f312(f312(f228(a1),f312(f312(f90(a1),x90781),x90782)),f312(f312(f89(a1),f312(f312(f90(a1),x90781),f54(a1,x90783,x90782))),x90784)))
% 155.94/155.63 [9100]P22(f312(f70(x91001),x91002))+~P22(f312(f70(x91001),x91003))+~P22(f312(f312(f314(f861(x91001,a846)),x91002),f312(f312(f69(x91001),x91003),x91004)))+~P22(f312(f312(f227(f861(f860(x91001,x91001),a846)),x91004),f312(f312(f247(x91001,x91001),x91003),f312(f16(f861(x91001,a846),x91001),x91003))))
% 155.94/155.63 [9138]~P49(f861(x91381,a846),f861(x91381,a846),x91383)+~P22(f312(f312(f314(x91381),x91382),x91384))+P22(f312(f312(f314(x91381),x91382),f110(f861(x91381,a846),x91383)))+~P22(f312(f312(f227(f861(x91381,a846)),x91384),f312(x91383,f312(f312(f124(f861(x91381,a846)),x91384),f110(f861(x91381,a846),x91383)))))
% 155.94/155.63 [9313]~P49(f861(x93133,a846),f861(x93133,a846),x93134)+P22(f312(x93131,x93132))+~P22(f312(f312(f314(x93133),x93132),f109(f861(x93133,a846),x93134)))+P22(f312(f312(f314(x93133),f558(x93131,x93134,x93132,x93133)),f312(x93134,f312(f312(f115(f861(x93133,a846)),f109(f861(x93133,a846),x93134)),f312(f233(x93133),x93131)))))
% 155.94/155.63 [9523]~P22(f312(f70(x95232),x95234))+~P22(f312(f70(x95231),x95233))+~P22(f312(f312(f227(a853),f312(f53(x95232),x95234)),f312(f53(x95231),x95233)))+P22(f312(f312(f227(f861(x95231,a846)),f312(f290(x95232,x95231,f388(x95233,x95231,x95234,x95232)),x95234)),x95233))
% 155.94/155.63 [9178]~P22(f312(f312(f314(x91781),x91782),x91784))+P22(f312(f312(f314(x91781),x91782),x91783))+~P22(f312(f312(f228(f861(x91781,a846)),x91784),f312(f312(f289(x91781),x91782),x91783)))+P22(f312(f312(f228(f861(x91781,a846)),f312(f312(f21(f861(x91781,a846)),x91784),f312(f312(f289(x91781),x91782),f189(f861(x91781,a846))))),x91783))
% 155.94/155.63 [9338]~P22(f312(f312(f314(x93381),x93382),x93384))+P22(f312(f312(f314(x93381),x93382),x93383))+P22(f312(f312(f228(f861(x93381,a846)),x93384),f312(f312(f289(x93381),x93382),x93383)))+~P22(f312(f312(f228(f861(x93381,a846)),f312(f312(f21(f861(x93381,a846)),x93384),f312(f312(f289(x93381),x93382),f189(f861(x93381,a846))))),x93383))
% 155.94/155.63 [9364]P22(f312(f312(f314(x93641),x93642),x93643))+~P22(f312(f312(f227(f861(x93641,a846)),x93644),x93643))+P22(f312(f312(f228(f861(x93641,a846)),x93644),f312(f312(f289(x93641),x93642),x93643)))+~P22(f312(f312(f228(f861(x93641,a846)),f312(f312(f21(f861(x93641,a846)),x93644),f312(f312(f289(x93641),x93642),f189(f861(x93641,a846))))),x93643))
% 155.94/155.63 [9369]~P22(f312(f312(f314(x93691),x93693),x93692))+~P22(f312(f312(f228(f861(x93691,a846)),x93692),x93694))+P22(f312(f312(f228(f861(x93691,a846)),x93692),f312(f312(f289(x93691),x93693),x93694)))+~P22(f312(f312(f228(f861(x93691,a846)),f312(f312(f21(f861(x93691,a846)),x93692),f312(f312(f289(x93691),x93693),f189(f861(x93691,a846))))),x93694))
% 155.94/155.63 [9381]~P22(f312(f312(f227(f861(x93811,a846)),x93812),x93814))+~P22(f312(f312(f228(f861(x93811,a846)),x93812),x93814))+P22(f312(f312(f228(f861(x93811,a846)),x93812),f312(f312(f289(x93811),x93813),x93814)))+~P22(f312(f312(f228(f861(x93811,a846)),f312(f312(f21(f861(x93811,a846)),x93812),f312(f312(f289(x93811),x93813),f189(f861(x93811,a846))))),x93814))
% 155.94/155.63 [9427]~P105(x94272)+~P63(x94271)+~P22(f312(f312(f227(f861(x94271,x94272)),x94273),x94274))+P22(f312(f67(x94271),f312(f312(f18(x94271,x94272,a846),f312(f312(f8(x94272,f861(x94272,a846),x94271),f227(x94272)),x94273)),x94274)))
% 155.94/155.63 [9567]~P105(x95672)+~P63(x95671)+P22(f312(f312(f227(f861(x95671,x95672)),x95673),x95674))+~P22(f312(f67(x95671),f312(f312(f18(x95671,x95672,a846),f312(f312(f8(x95672,f861(x95672,a846),x95671),f227(x95672)),x95673)),x95674)))
% 155.94/155.63 [10053]~P49(f861(x100531,a846),f861(x100531,a846),x100533)+~P22(f312(f312(f314(x100531),x100532),x100534))+P22(f312(f312(f314(x100531),x100532),f110(f861(x100531,a846),x100533)))+~P22(f312(f312(f227(f861(x100531,a846)),x100534),f312(x100533,f109(f861(x100531,a846),f312(f312(f7(f861(x100531,a846),f861(x100531,a846),f861(x100531,a846)),f312(f312(f8(f861(x100531,a846),f861(f861(x100531,a846),f861(x100531,a846)),f861(x100531,a846)),f124(f861(x100531,a846))),f312(f312(f7(f861(x100531,a846),f861(x100531,a846),f861(x100531,a846)),f312(f312(f8(f861(x100531,a846),f861(f861(x100531,a846),f861(x100531,a846)),f861(x100531,a846)),f124(f861(x100531,a846))),x100533)),x100534))),f110(f861(x100531,a846),x100533))))))
% 155.94/155.63 [9733]E(f312(f312(f161(x97331),f312(f312(f161(f854(x97331)),f175(x97331,x97332)),x97333)),x97334),f312(f312(f161(x97331),f312(f312(f161(f854(x97331)),x97332),x97334)),x97333))+~P22(f312(f312(f228(a853),x97333),f312(f190(f854(f854(x97331))),f175(x97331,x97332))))+~P33(a853,f312(f165(a853),f312(f312(f150(f854(x97331),a853),f190(f854(x97331))),x97332)))+~P22(f312(f312(f228(a853),x97334),f312(f190(f854(f854(x97331))),f312(f132(f854(x97331),f312(f312(f8(a853,a846,f854(x97331)),f312(f228(a853),x97333)),f190(f854(x97331)))),x97332))))
% 155.94/155.63 [9762]~P22(f312(f312(f314(f860(a853,a853)),x97624),x97621))+~P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),x97624),x97622)),a45))+~P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),x97621),x97623)),a77))+P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),x97621),f312(f312(f289(f860(a853,a853)),x97622),x97623))),a77))
% 155.94/155.63 [9763]~P22(f312(f312(f314(f860(a853,a853)),x97634),x97631))+~P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),x97634),x97632)),a79))+~P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),x97631),x97633)),a80))+P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),x97631),f312(f312(f289(f860(a853,a853)),x97632),x97633))),a80))
% 155.94/155.63 [9651]~P105(x96512)+~P63(x96511)+~P22(f312(f312(f228(f861(x96511,x96512)),x96513),x96514))+P22(f312(f66(x96511),f312(f312(f8(a846,a846,x96511),a307),f312(f312(f18(x96511,x96512,a846),f312(f312(f8(x96512,f861(x96512,a846),x96511),a309),x96513)),x96514))))
% 155.94/155.63 [9776]~P22(f312(f312(f314(f860(a853,a853)),x97764),x97763))+~P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),x97761),x97764)),a45))+~P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),x97762),x97763)),a46))+P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),f312(f312(f289(f860(a853,a853)),x97761),x97762)),x97763)),a46))
% 155.94/155.63 [9777]~P22(f312(f312(f314(f860(a853,a853)),x97774),x97773))+~P22(f312(f312(f314(f860(f860(a853,a853),f860(a853,a853))),f312(f312(f239(f860(a853,a853),f860(a853,a853)),x97771),x97774)),a79))+~P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),x97772),x97773)),a78))+P22(f312(f312(f314(f860(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846))),f312(f312(f239(f861(f860(a853,a853),a846),f861(f860(a853,a853),a846)),f312(f312(f289(f860(a853,a853)),x97771),x97772)),x97773)),a78))
% 155.94/155.63 [8827]~P36(x88271,x88272,x88274,x88275)+~P36(x88271,x88272,x88273,x88275)+~P36(x88271,x88272,x88273,f180(x88271,x88272,x88273,x88274))+P36(x88271,x88272,f180(x88271,x88272,x88273,x88274),x88275)
% 155.94/155.63 [5949]~P2(x59494,x59491)+~P22(f312(f312(x59491,x59492),x59495))+P22(f312(f312(x59491,x59492),x59493))+~P22(f312(f312(x59491,x59495),x59493))
% 155.94/155.63 [5222]~P30(x52225)+E(x52221,x52222)+~E(x52223,x52224)+~E(f312(f312(f21(x52225),x52223),x52224),f312(f312(f21(x52225),x52221),x52222))
% 155.94/155.63 [6049]~P12(x60495,x60491,x60493)+E(f312(f312(x60491,x60492),f312(x60493,x60494)),f312(x60493,x60494))+~P22(f312(f70(x60495),x60494))+~P22(f312(f312(f314(x60495),x60492),x60494))
% 155.94/155.63 [6238]~P76(x62381)+~E(f312(f312(f21(x62381),x62384),x62385),f312(f312(f21(x62381),x62382),x62383))+~P22(f312(f312(f228(x62381),x62384),x62385))+P22(f312(f312(f228(x62381),x62382),x62383))
% 155.94/155.63 [6240]~P76(x62401)+~E(f312(f312(f21(x62401),x62404),x62405),f312(f312(f21(x62401),x62402),x62403))+~P22(f312(f312(f227(x62401),x62404),x62405))+P22(f312(f312(f227(x62401),x62402),x62403))
% 155.94/155.63 [7189]~E(x71892,f312(f312(f147(x71891),x71894),x71895))+P22(f312(f312(f314(f854(x71891)),x71892),f157(x71891,x71893)))+~P22(f312(f312(f314(f854(x71891)),x71895),f157(x71891,x71893)))+~P22(f312(f312(f314(x71891),x71894),x71893))
% 155.94/155.63 [7596]~E(f312(f190(f854(x75961)),x75963),f312(f190(f854(x75962)),x75964))+~E(f312(f312(f150(f860(x75961,x75962),x75962),f248(x75961,x75962)),x75965),x75964)+~E(f312(f312(f150(f860(x75961,x75962),x75961),f246(x75961,x75962)),x75965),x75963)+E(f312(f312(f177(x75961,x75962),x75963),x75964),x75965)
% 155.94/155.63 [7925]~P105(x79251)+P22(f312(f312(f228(f861(x79251,a846)),f283(x79251,x79252,x79253)),f283(x79251,x79254,x79255)))+~P22(f312(f312(f227(x79251),x79254),x79255))+P22(f312(f312(f227(x79251),x79252),x79253))
% 155.94/155.63 [8024]~P105(x80241)+P22(f312(f312(f227(f861(x80241,a846)),f283(x80241,x80242,x80243)),f283(x80241,x80244,x80245)))+~P22(f312(f312(f227(x80241),x80243),x80245))+~P22(f312(f312(f227(x80241),x80244),x80242))
% 155.94/155.63 [8149]~P103(x81491)+P22(f312(f312(f227(x81491),x81492),x81493))+P22(f312(f312(f227(x81491),x81494),x81493))+~P22(f312(f312(f227(f861(x81491,a846)),f312(f282(x81491,x81493),x81492)),f312(f282(x81491,x81494),x81495)))
% 155.94/155.63 [8150]~P103(x81501)+P22(f312(f312(f227(x81501),x81502),x81503))+P22(f312(f312(f227(x81501),x81502),x81504))+~P22(f312(f312(f227(f861(x81501,a846)),f312(f282(x81501,x81503),x81502)),f312(f282(x81501,x81505),x81504)))
% 155.94/155.63 [8322]~P99(x83223)+~P99(x83221)+~P49(x83223,x83221,x83222)+P22(f312(f312(f227(x83221),f312(x83222,f312(f312(f115(x83223),x83224),x83225))),f312(f312(f115(x83221),f312(x83222,x83224)),f312(x83222,x83225))))
% 155.94/155.63 [8323]~P99(x83231)+~P103(x83233)+~P49(x83233,x83231,x83232)+P22(f312(f312(f227(x83231),f312(x83232,f312(f312(f225(x83233),x83234),x83235))),f312(f312(f115(x83231),f312(x83232,x83234)),f312(x83232,x83235))))
% 155.94/155.63 [8399]~P105(x83991)+~P22(f312(f312(f228(f861(x83991,a846)),f283(x83991,x83994,x83992)),f283(x83991,x83995,x83993)))+P22(f312(f312(f227(x83991),x83992),x83993))+~P22(f312(f312(f227(x83991),x83994),x83992))
% 155.94/155.63 [8400]~P105(x84001)+~P22(f312(f312(f227(f861(x84001,a846)),f283(x84001,x84004,x84002)),f283(x84001,x84005,x84003)))+P22(f312(f312(f227(x84001),x84002),x84003))+~P22(f312(f312(f227(x84001),x84004),x84002))
% 155.94/155.63 [8401]~P105(x84011)+~P22(f312(f312(f228(f861(x84011,a846)),f283(x84011,x84013,x84014)),f283(x84011,x84012,x84015)))+P22(f312(f312(f227(x84011),x84012),x84013))+~P22(f312(f312(f227(x84011),x84013),x84014))
% 155.94/155.63 [8402]~P105(x84021)+~P22(f312(f312(f227(f861(x84021,a846)),f283(x84021,x84023,x84024)),f283(x84021,x84022,x84025)))+P22(f312(f312(f227(x84021),x84022),x84023))+~P22(f312(f312(f227(x84021),x84023),x84024))
% 155.94/155.63 [5897]~P103(x58975)+~P103(x58971)+~P49(x58975,x58971,x58972)+E(f312(f312(f225(x58971),f312(x58972,x58973)),f312(x58972,x58974)),f312(x58972,f312(f312(f225(x58975),x58973),x58974)))
% 155.94/155.63 [5898]~P103(x58985)+~P103(x58981)+~P49(x58985,x58981,x58982)+E(f312(f312(f226(x58981),f312(x58982,x58983)),f312(x58982,x58984)),f312(x58982,f312(f312(f226(x58985),x58983),x58984)))
% 155.94/155.63 [5948]~P12(x59482,x59485,x59483)+E(x59481,f189(f861(x59482,a846)))+~P22(f312(f70(x59482),x59481))+E(f312(x59483,f312(f312(f289(x59482),x59484),x59481)),f312(f312(x59485,x59484),f312(x59483,x59481)))
% 155.94/155.63 [6697]~E(x66971,x66972)+~E(f312(f312(f115(f861(x66973,a846)),x66974),x66975),f189(f861(x66973,a846)))+~P22(f312(f312(f314(x66973),x66972),x66975))+~P22(f312(f312(f314(x66973),x66971),x66974))
% 155.94/155.63 [6838]~P72(x68382)+~P22(f312(f70(x68381),x68385))+E(f312(f312(f9(x68381,x68382),x68383),f312(f312(f289(x68381),x68384),x68385)),f312(f312(f90(x68382),f312(x68383,x68384)),f312(f312(f9(x68381,x68382),x68383),x68385)))+P22(f312(f312(f314(x68381),x68384),x68385))
% 155.94/155.63 [6840]~P26(x68402)+~P22(f312(f70(x68401),x68405))+E(f312(f312(f6(x68401,x68402),x68403),f312(f312(f289(x68401),x68404),x68405)),f312(f312(f89(x68402),f312(x68403,x68404)),f312(f312(f6(x68401,x68402),x68403),x68405)))+P22(f312(f312(f314(x68401),x68404),x68405))
% 155.94/155.63 [7338]~P13(x73382,x73385,x73381)+~P22(f312(f70(x73382),x73384))+E(f312(x73381,f312(f312(f289(x73382),x73383),x73384)),x73383)+~E(f312(f312(f21(f861(x73382,a846)),x73384),f312(f312(f289(x73382),x73383),f189(f861(x73382,a846)))),f189(f861(x73382,a846)))
% 155.94/155.63 [7650]~P22(f312(x76501,x76503))+~P22(f312(f312(f195(x76502),x76503),x76505))+~P22(f312(f312(f195(f35(x76501,x76502)),x76505),x76504))+P22(f312(f312(f195(f35(x76501,x76502)),x76503),x76504))
% 155.94/155.63 [7701]~P80(x77011)+~P22(f312(f312(f228(x77011),x77013),x77015))+~P22(f312(f312(f228(x77011),x77012),x77014))+P22(f312(f312(f228(x77011),f312(f312(f89(x77011),x77012),x77013)),f312(f312(f89(x77011),x77014),x77015)))
% 155.94/155.63 [7702]~P80(x77021)+~P22(f312(f312(f227(x77021),x77022),x77024))+~P22(f312(f312(f228(x77021),x77023),x77025))+P22(f312(f312(f228(x77021),f312(f312(f89(x77021),x77022),x77023)),f312(f312(f89(x77021),x77024),x77025)))
% 155.94/155.63 [7703]~P80(x77031)+~P22(f312(f312(f227(x77031),x77033),x77035))+~P22(f312(f312(f228(x77031),x77032),x77034))+P22(f312(f312(f228(x77031),f312(f312(f89(x77031),x77032),x77033)),f312(f312(f89(x77031),x77034),x77035)))
% 155.94/155.63 [7704]~P82(x77041)+~P22(f312(f312(f227(x77041),x77043),x77045))+~P22(f312(f312(f227(x77041),x77042),x77044))+P22(f312(f312(f227(x77041),f312(f312(f89(x77041),x77042),x77043)),f312(f312(f89(x77041),x77044),x77045)))
% 155.94/155.63 [7705]~P98(x77051)+~P22(f312(f312(f227(x77051),x77053),x77055))+~P22(f312(f312(f227(x77051),x77052),x77054))+P22(f312(f312(f227(x77051),f312(f312(f124(x77051),x77052),x77053)),f312(f312(f124(x77051),x77054),x77055)))
% 155.94/155.63 [7706]~P99(x77061)+~P22(f312(f312(f227(x77061),x77063),x77065))+~P22(f312(f312(f227(x77061),x77062),x77064))+P22(f312(f312(f227(x77061),f312(f312(f115(x77061),x77062),x77063)),f312(f312(f115(x77061),x77064),x77065)))
% 155.94/155.63 [7707]~P103(x77071)+~P22(f312(f312(f227(x77071),x77073),x77075))+~P22(f312(f312(f227(x77071),x77072),x77074))+P22(f312(f312(f227(x77071),f312(f312(f225(x77071),x77072),x77073)),f312(f312(f225(x77071),x77074),x77075)))
% 155.94/155.63 [7708]~P103(x77081)+~P22(f312(f312(f227(x77081),x77083),x77085))+~P22(f312(f312(f227(x77081),x77082),x77084))+P22(f312(f312(f227(x77081),f312(f312(f226(x77081),x77082),x77083)),f312(f312(f226(x77081),x77084),x77085)))
% 155.94/155.63 [7838]~P136(x78385)+E(x78381,x78382)+E(x78383,x78384)+~E(f312(f312(f89(x78385),f312(f312(f90(x78385),x78383),x78381)),f312(f312(f90(x78385),x78384),x78382)),f312(f312(f89(x78385),f312(f312(f90(x78385),x78383),x78382)),f312(f312(f90(x78385),x78384),x78381)))
% 155.94/155.63 [7976]P34(x79761,x79762,x79763)+~P21(x79761,x79764,x79765)+~P34(x79761,x79762,f639(x79765,x79764,x79761,x79762))+~P22(f312(f312(f314(f852(x79761)),x79763),x79765))
% 155.94/155.63 [8047]~P103(x80474)+~P22(f312(f133(x80471),x80473))+P22(f312(f312(f314(x80471),x80472),f312(f168(x80471),x80473)))+P22(f312(f133(x80471),f312(f312(f145(x80471,x80474,x80475),x80472),x80473)))
% 155.94/155.63 [8196]~P26(x81961)+E(f312(f312(f89(x81961),f312(f312(f6(a853,x81961),x81962),f312(f282(a853,x81963),x81964))),f312(f312(f6(a853,x81961),x81962),f312(f282(a853,x81964),x81965))),f312(f312(f6(a853,x81961),x81962),f312(f282(a853,x81963),x81965)))+~P22(f312(f312(f227(a853),x81964),x81965))+~P22(f312(f312(f227(a853),x81963),x81964))
% 155.94/155.63 [8197]~P30(x81971)+E(f312(f312(f21(x81971),f312(f312(f6(a853,x81971),x81972),f312(f282(a853,x81973),x81974))),f312(f312(f6(a853,x81971),x81972),f312(f282(a853,x81973),x81975))),f312(f312(f6(a853,x81971),x81972),f312(f282(a853,x81975),x81974)))+~P22(f312(f312(f227(a853),x81975),x81974))+~P22(f312(f312(f227(a853),x81973),x81975))
% 155.94/155.63 [8535]~P65(x85352)+E(x85351,f2(x85352))+E(x85353,f2(x85352))+E(f312(f312(f268(x85352),f312(f312(f89(x85352),f312(f312(f90(x85352),x85354),x85351)),f312(f312(f90(x85352),x85355),x85353))),f312(f312(f90(x85352),x85353),x85351)),f312(f312(f89(x85352),f312(f312(f268(x85352),x85354),x85353)),f312(f312(f268(x85352),x85355),x85351)))
% 155.94/155.63 [8536]~P65(x85362)+E(x85361,f2(x85362))+E(x85363,f2(x85362))+E(f312(f312(f268(x85362),f312(f312(f21(x85362),f312(f312(f90(x85362),x85364),x85361)),f312(f312(f90(x85362),x85365),x85363))),f312(f312(f90(x85362),x85363),x85361)),f312(f312(f21(x85362),f312(f312(f268(x85362),x85364),x85363)),f312(f312(f268(x85362),x85365),x85361)))
% 155.94/155.63 [8545]~E(x85452,f312(x85453,x85451))+E(x85451,f825(x85452,x85453,x85454,x85455))+~P19(x85455,x85454,x85453,f235(f861(x85455,a846)))+~P22(f312(f312(f314(x85454),x85452),f312(f290(x85455,x85454,x85453),f235(f861(x85455,a846)))))
% 155.94/155.63 [8737]~P112(x87371)+~P22(f312(f312(f228(x87371),f312(f84(x87371),x87372)),x87374))+P22(f312(f312(f228(x87371),f312(f312(f90(x87371),f312(f84(x87371),x87372)),f312(f84(x87371),x87373))),f312(f312(f90(x87371),x87374),x87375)))+~P22(f312(f312(f228(x87371),f312(f84(x87371),x87373)),x87375))
% 155.94/155.63 [8754]~P21(x87541,x87545,x87544)+P34(x87541,x87542,x87543)+P22(f312(f312(f314(f852(x87541)),f639(x87544,x87545,x87541,x87542)),x87545))+~P22(f312(f312(f314(f852(x87541)),x87543),x87544))
% 155.94/155.63 [8856]~P19(x88561,x88563,x88565,x88562)+~P22(f312(f70(x88563),x88564))+P22(f312(f312(f227(a853),f312(f53(x88561),x88562)),f312(f53(x88563),x88564)))+~P22(f312(f312(f227(f861(x88563,a846)),f312(f290(x88561,x88563,x88565),x88562)),x88564))
% 155.94/155.63 [8929]~P72(x89292)+~P19(x89291,x89291,x89294,x89295)+~P22(f312(f70(x89291),x89295))+E(f312(f312(f9(x89291,x89292),f312(f82(x89291,x89292,x89291,x89293),x89294)),x89295),f312(f312(f9(x89291,x89292),x89293),f312(f290(x89291,x89291,x89294),x89295)))
% 155.94/155.63 [8930]~P26(x89302)+~P19(x89301,x89301,x89304,x89305)+~P22(f312(f70(x89301),x89305))+E(f312(f312(f6(x89301,x89302),f312(f82(x89301,x89302,x89301,x89303),x89304)),x89305),f312(f312(f6(x89301,x89302),x89303),f312(f290(x89301,x89301,x89304),x89305)))
% 155.94/155.63 [9077]~P19(x90772,x90773,x90775,x90771)+E(x90771,f189(f861(x90772,a846)))+E(f312(f290(x90773,x90772,f830(x90774,x90773,x90772,x90771)),x90774),x90771)+~P22(f312(f312(f227(f861(x90773,a846)),f312(f290(x90772,x90773,x90775),x90771)),x90774))
% 155.94/155.63 [9548]~P103(x95485)+~P31(x95485)+P22(f312(f312(f314(x95481),f408(x95482,x95483,x95481,x95484,x95485)),x95483))+~P22(f312(f312(f228(x95485),x95484),f312(f312(f50(x95481,x95485),x95483),x95482)))
% 155.94/155.63 [9552]~P103(x95521)+~P31(x95521)+P22(f312(f312(f228(x95521),x95522),f312(x95523,f408(x95523,x95524,x95525,x95522,x95521))))+~P22(f312(f312(f228(x95521),x95522),f312(f312(f50(x95525,x95521),x95524),x95523)))
% 155.94/155.63 [9631]~P68(x96311)+~P22(f312(f75(x96311,x96311,f90(x96311),x96312,x96313),x96315))+P22(f312(f312(f314(x96311),x96312),x96313))+P22(f312(f75(x96311,x96311,f90(x96311),x96314,f312(f312(f289(x96311),x96312),x96313)),f312(f312(f90(x96311),x96314),x96315)))
% 155.94/155.63 [9849]~P72(x98492)+~P22(f312(f70(x98491),x98495))+E(f312(f312(f9(x98491,x98492),f312(f312(f7(x98491,x98492,x98492),f312(f312(f18(x98491,x98492,f861(x98492,x98492)),f312(f312(f8(a846,f861(x98492,f861(x98492,x98492)),x98491),f108(x98492)),f312(a309,x98493))),x98494)),f87(x98492))),x98495),f87(x98492))+P22(f312(f312(f314(x98491),x98493),x98495))
% 155.94/155.63 [9850]~P26(x98502)+~P22(f312(f70(x98501),x98505))+E(f312(f312(f6(x98501,x98502),f312(f312(f7(x98501,x98502,x98502),f312(f312(f18(x98501,x98502,f861(x98502,x98502)),f312(f312(f8(a846,f861(x98502,f861(x98502,x98502)),x98501),f108(x98502)),f312(a309,x98503))),x98504)),f2(x98502))),x98505),f2(x98502))+P22(f312(f312(f314(x98501),x98503),x98505))
% 155.94/155.63 [9851]~P72(x98512)+~P22(f312(f70(x98511),x98515))+E(f312(f312(f9(x98511,x98512),f312(f312(f7(x98511,x98512,x98512),f312(f312(f18(x98511,x98512,f861(x98512,x98512)),f312(f312(f8(a846,f861(x98512,f861(x98512,x98512)),x98511),f108(x98512)),f312(a309,x98513))),x98514)),f87(x98512))),x98515),f312(x98514,x98513))+~P22(f312(f312(f314(x98511),x98513),x98515))
% 155.94/155.63 [9852]~P26(x98522)+~P22(f312(f70(x98521),x98525))+E(f312(f312(f6(x98521,x98522),f312(f312(f7(x98521,x98522,x98522),f312(f312(f18(x98521,x98522,f861(x98522,x98522)),f312(f312(f8(a846,f861(x98522,f861(x98522,x98522)),x98521),f108(x98522)),f312(a309,x98523))),x98524)),f2(x98522))),x98525),f312(x98524,x98523))+~P22(f312(f312(f314(x98521),x98523),x98525))
% 155.94/155.63 [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,f861(x99122,x99122)),f312(f312(f8(a846,f861(x99122,f861(x99122,x99122)),x99121),f108(x99122)),f312(f312(f7(x99121,x99121,a846),a309),x99123))),x99124)),f87(x99122))),x99125),f87(x99122))+P22(f312(f312(f314(x99121),x99123),x99125))
% 155.94/155.63 [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,f861(x99132,x99132)),f312(f312(f8(a846,f861(x99132,f861(x99132,x99132)),x99131),f108(x99132)),f312(f312(f7(x99131,x99131,a846),a309),x99133))),x99134)),f2(x99132))),x99135),f2(x99132))+P22(f312(f312(f314(x99131),x99133),x99135))
% 155.94/155.63 [9915]~P72(x99152)+~P22(f312(f70(x99151),x99155))+E(f312(f312(f9(x99151,x99152),f312(f312(f7(x99151,x99152,x99152),f312(f312(f18(x99151,x99152,f861(x99152,x99152)),f312(f312(f8(a846,f861(x99152,f861(x99152,x99152)),x99151),f108(x99152)),f312(f312(f7(x99151,x99151,a846),a309),x99153))),x99154)),f87(x99152))),x99155),f312(x99154,x99153))+~P22(f312(f312(f314(x99151),x99153),x99155))
% 155.94/155.63 [9916]~P26(x99162)+~P22(f312(f70(x99161),x99165))+E(f312(f312(f6(x99161,x99162),f312(f312(f7(x99161,x99162,x99162),f312(f312(f18(x99161,x99162,f861(x99162,x99162)),f312(f312(f8(a846,f861(x99162,f861(x99162,x99162)),x99161),f108(x99162)),f312(f312(f7(x99161,x99161,a846),a309),x99163))),x99164)),f2(x99162))),x99165),f312(x99164,x99163))+~P22(f312(f312(f314(x99161),x99163),x99165))
% 155.94/155.63 [7700]~P30(x77002)+~P22(f312(f70(x77001),x77004))+E(f312(f312(f6(x77001,x77002),x77003),f312(f312(f21(f861(x77001,a846)),x77004),f312(f312(f289(x77001),x77005),f189(f861(x77001,a846))))),f312(f312(f6(x77001,x77002),x77003),x77004))+P22(f312(f312(f314(x77001),x77005),x77004))
% 155.94/155.63 [8203]~P120(x82032)+~P22(f312(f70(x82031),x82034))+E(f312(f312(f6(x82031,x82032),x82033),f312(f312(f21(f861(x82031,a846)),x82034),f312(f312(f289(x82031),x82035),f189(f861(x82031,a846))))),f312(f312(f21(x82032),f312(f312(f6(x82031,x82032),x82033),x82034)),f312(x82033,x82035)))+~P22(f312(f312(f314(x82031),x82035),x82034))
% 155.94/155.63 [8204]~P30(x82042)+~P22(f312(f70(x82041),x82044))+E(f312(f312(f6(x82041,x82042),x82043),f312(f312(f21(f861(x82041,a846)),x82044),f312(f312(f289(x82041),x82045),f189(f861(x82041,a846))))),f312(f312(f21(x82042),f312(f312(f6(x82041,x82042),x82043),x82044)),f312(x82043,x82045)))+~P22(f312(f312(f314(x82041),x82045),x82044))
% 155.94/155.63 [8237]~P30(x82371)+~P22(f312(f70(x82372),x82374))+E(f312(f312(f21(x82371),f312(f312(f6(x82372,x82371),x82373),x82374)),f312(f312(f6(x82372,x82371),x82373),x82375)),f312(f312(f6(x82372,x82371),x82373),f312(f312(f21(f861(x82372,a846)),x82374),x82375)))+~P22(f312(f312(f227(f861(x82372,a846)),x82375),x82374))
% 155.94/155.63 [8259]P22(f312(f70(x82591),f312(x82592,x82593)))+~P22(f312(f70(x82594),x82595))+~P22(f312(f312(f314(x82594),x82593),x82595))+~P22(f312(f70(x82591),f312(f312(f50(x82594,f861(x82591,a846)),x82595),x82592)))
% 155.94/155.63 [8377]~P98(x83775)+~P98(x83771)+~P49(x83775,x83771,x83772)+P22(f312(f312(f227(x83771),f312(f312(f124(x83771),f312(x83772,x83773)),f312(x83772,x83774))),f312(x83772,f312(f312(f124(x83775),x83773),x83774))))
% 155.94/155.63 [8378]~P98(x83781)+~P103(x83785)+~P49(x83785,x83781,x83782)+P22(f312(f312(f227(x83781),f312(f312(f124(x83781),f312(x83782,x83783)),f312(x83782,x83784))),f312(x83782,f312(f312(f226(x83785),x83783),x83784))))
% 155.94/155.63 [8700]~P3(x87001,x87005,x87004)+~E(f312(f264(x87001,x87001,x87004),f312(f312(f289(x87001),x87002),f189(f861(x87001,a846)))),f312(f264(x87001,x87001,x87004),f312(f312(f289(x87001),x87003),f189(f861(x87001,a846)))))+~P22(f312(f312(f314(x87001),x87003),x87005))+P22(f312(f312(f314(f860(x87001,x87001)),f312(f312(f239(x87001,x87001),x87002),x87003)),x87004))
% 155.94/155.63 [8998]~P22(f312(x89981,x89985))+P22(f312(x89981,f808(x89981,x89982,x89983,x89984)))+P22(f312(x89981,f807(x89981,x89982,x89983,x89984)))+~P22(f312(f312(f314(x89984),x89985),f312(f312(f124(f861(x89984,a846)),x89983),x89982)))
% 155.94/155.63 [9183]~P22(f312(x91831,x91835))+P22(f312(x91831,f807(x91831,x91832,x91833,x91834)))+P22(f312(f312(f314(x91834),f808(x91831,x91832,x91833,x91834)),x91832))+~P22(f312(f312(f314(x91834),x91835),f312(f312(f124(f861(x91834,a846)),x91833),x91832)))
% 155.94/155.63 [9184]~P22(f312(x91841,x91845))+P22(f312(x91841,f808(x91841,x91842,x91843,x91844)))+P22(f312(f312(f314(x91844),f807(x91841,x91842,x91843,x91844)),x91843))+~P22(f312(f312(f314(x91844),x91845),f312(f312(f124(f861(x91844,a846)),x91843),x91842)))
% 155.94/155.63 [9190]P22(f312(x91901,x91902))+~P22(f312(x91901,f811(x91901,x91903,x91904,x91905)))+~P22(f312(x91901,f810(x91901,x91903,x91904,x91905)))+~P22(f312(f312(f314(x91905),x91902),f312(f312(f124(f861(x91905,a846)),x91904),x91903)))
% 155.94/155.63 [9231]E(x92311,x92312)+~P22(f312(f312(f314(f860(x92313,x92313)),f312(f312(f239(x92313,x92313),x92311),x92312)),f287(x92313,x92315)))+P22(f312(f312(f314(x92313),x92311),x92314))+~P22(f312(f312(f227(f861(f860(x92313,x92313),a846)),x92315),f312(f312(f247(x92313,x92313),x92314),f312(f16(f861(x92313,a846),x92313),x92314))))
% 155.94/155.63 [9248]P22(f312(x92481,x92482))+~P22(f312(x92481,f810(x92481,x92484,x92485,x92483)))+P22(f312(f312(f314(x92483),f811(x92481,x92484,x92485,x92483)),x92484))+~P22(f312(f312(f314(x92483),x92482),f312(f312(f124(f861(x92483,a846)),x92485),x92484)))
% 155.94/155.63 [9249]P22(f312(x92491,x92492))+~P22(f312(x92491,f811(x92491,x92494,x92495,x92493)))+P22(f312(f312(f314(x92493),f810(x92491,x92494,x92495,x92493)),x92495))+~P22(f312(f312(f314(x92493),x92492),f312(f312(f124(f861(x92493,a846)),x92495),x92494)))
% 155.94/155.63 [9309]P22(f312(x93091,x93092))+P22(f312(f312(f314(x93093),f811(x93091,x93094,x93095,x93093)),x93094))+P22(f312(f312(f314(x93093),f810(x93091,x93094,x93095,x93093)),x93095))+~P22(f312(f312(f314(x93093),x93092),f312(f312(f124(f861(x93093,a846)),x93095),x93094)))
% 155.94/155.63 [9311]~P22(f312(x93112,x93115))+P22(f312(f312(f314(x93111),f808(x93112,x93113,x93114,x93111)),x93113))+P22(f312(f312(f314(x93111),f807(x93112,x93113,x93114,x93111)),x93114))+~P22(f312(f312(f314(x93111),x93115),f312(f312(f124(f861(x93111,a846)),x93114),x93113)))
% 155.94/155.63 [9459]~P3(x94591,x94595,x94594)+~P22(f312(f312(f314(x94591),x94593),x94595))+P22(f312(f312(f314(f860(x94591,x94591)),f312(f312(f239(x94591,x94591),x94592),x94593)),x94594))+~P22(f312(f312(f227(f861(x94591,a846)),f312(f264(x94591,x94591,x94594),f312(f312(f289(x94591),x94593),f189(f861(x94591,a846))))),f312(f264(x94591,x94591,x94594),f312(f312(f289(x94591),x94592),f189(f861(x94591,a846))))))
% 155.94/155.63 [9577]~P103(x95775)+~P31(x95775)+P22(f312(f312(f314(x95771),f641(x95772,x95773,x95774,x95771,x95775)),x95774))+~P22(f312(f312(f228(x95775),f312(f312(f51(x95771,x95775),x95774),x95773)),x95772))
% 155.94/155.63 [9609]~P25(x96095)+~P82(x96095)+P22(f312(f312(f314(x96091),f613(x96092,x96093,x96094,x96091,x96095)),f312(f168(x96091),x96094)))+P22(f312(f312(f227(x96095),f312(f162(x96095),f312(f312(f150(x96091,x96095),x96093),x96094))),f312(f162(x96095),f312(f312(f150(x96091,x96095),x96092),x96094))))
% 155.94/155.63 [9721]~P103(x97211)+~P31(x97211)+P22(f312(f312(f228(x97211),f312(x97212,f641(x97213,x97212,x97214,x97215,x97211))),x97213))+~P22(f312(f312(f228(x97211),f312(f312(f51(x97215,x97211),x97214),x97212)),x97213))
% 155.94/155.63 [9868]~P25(x98681)+~P82(x98681)+~P22(f312(f312(f227(x98681),f312(x98683,f613(x98685,x98683,x98684,x98682,x98681))),f312(x98685,f613(x98685,x98683,x98684,x98682,x98681))))+P22(f312(f312(f227(x98681),f312(f162(x98681),f312(f312(f150(x98682,x98681),x98683),x98684))),f312(f162(x98681),f312(f312(f150(x98682,x98681),x98685),x98684))))
% 155.94/155.63 [8552]~P72(x85521)+~P22(f312(f70(x85524),x85525))+~P22(f312(f312(f314(x85524),x85523),x85525))+E(f312(f312(f90(x85521),f312(x85522,x85523)),f312(f312(f9(x85524,x85521),x85522),f312(f312(f21(f861(x85524,a846)),x85525),f312(f312(f289(x85524),x85523),f189(f861(x85524,a846)))))),f312(f312(f9(x85524,x85521),x85522),x85525))
% 155.94/155.63 [8554]~P26(x85541)+~P22(f312(f70(x85544),x85545))+~P22(f312(f312(f314(x85544),x85543),x85545))+E(f312(f312(f89(x85541),f312(x85542,x85543)),f312(f312(f6(x85544,x85541),x85542),f312(f312(f21(f861(x85544,a846)),x85545),f312(f312(f289(x85544),x85543),f189(f861(x85544,a846)))))),f312(f312(f6(x85544,x85541),x85542),x85545))
% 155.94/155.63 [8607]~P13(x86071,x86074,x86075)+~P22(f312(f70(x86071),x86072))+E(f312(f312(f21(f861(x86071,a846)),x86072),f312(f312(f289(x86071),x86073),f189(f861(x86071,a846)))),f189(f861(x86071,a846)))+E(f312(f312(x86074,x86073),f312(x86075,f312(f312(f21(f861(x86071,a846)),x86072),f312(f312(f289(x86071),x86073),f189(f861(x86071,a846)))))),f312(x86075,f312(f312(f289(x86071),x86073),x86072)))
% 155.94/155.63 [8978]~P26(x89781)+~P22(f312(f70(x89782),x89785))+~P22(f312(f70(x89782),x89784))+E(f312(f312(f89(x89781),f312(f312(f6(x89782,x89781),x89783),f312(f312(f124(f861(x89782,a846)),x89784),x89785))),f312(f312(f6(x89782,x89781),x89783),f312(f312(f115(f861(x89782,a846)),x89784),x89785))),f312(f312(f89(x89781),f312(f312(f6(x89782,x89781),x89783),x89784)),f312(f312(f6(x89782,x89781),x89783),x89785)))
% 155.94/155.63 [8980]~P72(x89801)+~P22(f312(f70(x89802),x89805))+~P22(f312(f70(x89802),x89804))+E(f312(f312(f90(x89801),f312(f312(f9(x89802,x89801),x89803),f312(f312(f124(f861(x89802,a846)),x89804),x89805))),f312(f312(f9(x89802,x89801),x89803),f312(f312(f115(f861(x89802,a846)),x89804),x89805))),f312(f312(f90(x89801),f312(f312(f9(x89802,x89801),x89803),x89804)),f312(f312(f9(x89802,x89801),x89803),x89805)))
% 155.94/155.63 [9119]~P30(x91191)+~P22(f312(f70(x91192),x91195))+~P22(f312(f70(x91192),x91194))+E(f312(f312(f21(x91191),f312(f312(f89(x91191),f312(f312(f6(x91192,x91191),x91193),x91194)),f312(f312(f6(x91192,x91191),x91193),x91195))),f312(f312(f6(x91192,x91191),x91193),f312(f312(f115(f861(x91192,a846)),x91194),x91195))),f312(f312(f6(x91192,x91191),x91193),f312(f312(f124(f861(x91192,a846)),x91194),x91195)))
% 155.94/155.63 [9321]~P19(x93211,x93212,x93213,x93215)+~P19(x93211,x93212,x93213,x93214)+P19(x93211,x93212,x93213,f312(f312(f124(f861(x93211,a846)),x93214),x93215))+~E(f312(f312(f115(f861(x93212,a846)),f312(f290(x93211,x93212,x93213),f312(f312(f21(f861(x93211,a846)),x93214),x93215))),f312(f290(x93211,x93212,x93213),f312(f312(f21(f861(x93211,a846)),x93215),x93214))),f189(f861(x93212,a846)))
% 155.94/155.63 [9428]E(x94281,f2(a1))+~P22(f312(f312(f228(a1),f2(a1)),x94283))+~P22(f312(f57(x94282,x94281),f312(f312(f239(a1,a1),x94284),x94285)))+P22(f312(f57(x94282,f312(f312(f90(a1),x94281),x94283)),f312(f312(f239(a1,a1),f312(f47(a1,x94284),x94283)),f312(f312(f89(a1),f312(f312(f90(a1),x94281),f54(a1,x94284,x94283))),x94285))))
% 155.94/155.63 [9436]~P22(f312(f312(f228(a853),f2(a853)),x94363))+~P22(f312(f312(f228(a853),f2(a853)),x94362))+~P22(f312(f56(x94361,x94362),f312(f312(f239(a853,a853),x94364),x94365)))+P22(f312(f56(x94361,f312(f312(f90(a853),x94362),x94363)),f312(f312(f239(a853,a853),f312(f47(a853,x94364),x94363)),f312(f312(f89(a853),f312(f312(f90(a853),x94362),f54(a853,x94364,x94363))),x94365))))
% 155.94/155.63 [9493]~P72(x94931)+~P22(f312(f70(x94932),x94935))+~P22(f312(f70(x94932),x94934))+E(f312(f312(f90(x94931),f312(f312(f312(f74(x94931,x94932,f90(x94931)),x94933),f87(x94931)),f312(f312(f124(f861(x94932,a846)),x94934),x94935))),f312(f312(f312(f74(x94931,x94932,f90(x94931)),x94933),f87(x94931)),f312(f312(f115(f861(x94932,a846)),x94934),x94935))),f312(f312(f90(x94931),f312(f312(f312(f74(x94931,x94932,f90(x94931)),x94933),f87(x94931)),x94934)),f312(f312(f312(f74(x94931,x94932,f90(x94931)),x94933),f87(x94931)),x94935)))
% 155.94/155.63 [9495]~E(f312(f312(f169(x94951),x94955),x94952),f312(f312(f169(x94951),x94955),x94953))+P22(f312(f312(f314(f860(f854(x94951),f854(x94951))),f312(f312(f239(f854(x94951),f854(x94951)),x94952),x94953)),f143(x94951,x94954)))+~P22(f312(f312(f228(a853),x94955),f312(f312(f225(a853),f312(f190(f854(x94951)),x94952)),f312(f190(f854(x94951)),x94953))))+~P22(f312(f312(f314(f860(x94951,x94951)),f312(f312(f239(x94951,x94951),f312(f312(f161(x94951),x94952),x94955)),f312(f312(f161(x94951),x94953),x94955))),x94954))
% 155.94/155.63 [9597]~P23(x95975)+~P82(x95975)+P22(f312(f312(f314(x95971),f487(x95972,x95973,x95974,x95971,x95975)),x95974))+P22(f312(f312(f227(x95975),f312(f312(f6(x95971,x95975),x95973),x95974)),f312(f312(f90(x95975),f312(f114(x95975),f312(f53(x95971),x95974))),x95972)))
% 155.94/155.63 [9794]~P23(x97941)+~P82(x97941)+~P22(f312(f312(f227(x97941),f312(x97943,f487(x97945,x97943,x97944,x97942,x97941))),x97945))+P22(f312(f312(f227(x97941),f312(f312(f6(x97942,x97941),x97943),x97944)),f312(f312(f90(x97941),f312(f114(x97941),f312(f53(x97942),x97944))),x97945)))
% 155.94/155.63 [8579]E(f312(f312(f129(x85791),x85792),x85793),f312(f312(f129(x85791),x85794),x85795))+~E(f312(f312(f169(x85791),f312(f190(f854(x85791)),x85792)),x85794),x85792)+~E(f312(f312(f129(x85791),f312(f312(f134(x85791),f312(f190(f854(x85791)),x85792)),x85794)),x85795),x85793)+P22(f312(f312(f227(a853),f312(f190(f854(x85791)),x85794)),f312(f190(f854(x85791)),x85792)))
% 155.94/155.63 [8699]E(f312(f312(f129(x86991),x86992),x86993),f312(f312(f129(x86991),x86994),x86995))+~E(f312(f312(f169(x86991),f312(f190(f854(x86991)),x86992)),x86994),x86992)+~E(x86993,f312(f312(f129(x86991),f312(f312(f134(x86991),f312(f190(f854(x86991)),x86992)),x86994)),x86995))+~P22(f312(f312(f227(a853),f312(f190(f854(x86991)),x86992)),f312(f190(f854(x86991)),x86994)))
% 155.94/155.63 [9934]~P22(f312(x99345,x99344))+~P22(f312(f70(x99342),f312(f233(x99342),x99345)))+P22(f312(f70(x99341),f312(f233(x99341),f312(f312(f7(x99341,x99342,a846),x99343),x99344))))+~P22(f312(f70(x99341),f312(f233(x99341),f312(f312(f8(f861(x99342,a846),a846,x99341),f96(x99342)),f312(f312(f8(f861(x99342,a846),f861(x99342,a846),x99341),f312(f18(x99342,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99342),a310),x99345))),x99343)))))
% 155.94/155.63 [8374]~P14(x83745,x83741,x83746,x83742)+E(f312(f82(x83741,x83741,x83741,f312(x83742,x83743)),f312(x83742,x83744)),f312(f82(x83741,x83741,x83741,f312(x83742,x83744)),f312(x83742,x83743)))+~P22(f312(f70(x83745),x83744))+~P22(f312(f70(x83745),x83743))
% 155.94/155.63 [7758]~P19(x77581,x77582,x77584,x77583)+~E(f312(x77584,x77586),x77585)+E(f312(f86(x77581,x77582,x77583,x77584),x77585),x77586)+~P22(f312(f312(f314(x77581),x77586),x77583))
% 155.94/155.63 [7945]~P15(x79456,x79451,x79454,x79452)+E(f312(f82(x79451,x79451,x79451,f312(x79452,x79453)),f312(x79454,x79455)),f312(x79452,x79453))+~P22(f312(f70(x79456),x79453))+~P22(f312(f312(f314(x79456),x79455),x79453))
% 155.94/155.63 [9167]~P14(x91673,x91671,x91676,x91672)+E(f312(f82(x91671,x91671,x91671,f312(x91672,f312(f312(f21(f861(x91673,a846)),x91674),f312(f312(f289(x91673),x91675),f189(f861(x91673,a846)))))),f312(x91676,x91675)),f312(x91672,x91674))+~P22(f312(f70(x91673),x91674))+~P22(f312(f312(f314(x91673),x91675),x91674))
% 155.94/155.63 [6844]~P60(x68441)+~E(f54(x68441,x68443,x68444),f54(x68441,x68446,x68444))+~E(f54(x68441,x68442,x68444),f54(x68441,x68445,x68444))+E(f54(x68441,f312(f312(f89(x68441),x68442),x68443),x68444),f54(x68441,f312(f312(f89(x68441),x68445),x68446),x68444))
% 155.94/155.63 [6845]~P61(x68451)+~E(f54(x68451,x68453,x68454),f54(x68451,x68456,x68454))+~E(f54(x68451,x68452,x68454),f54(x68451,x68455,x68454))+E(f54(x68451,f312(f312(f21(x68451),x68452),x68453),x68454),f54(x68451,f312(f312(f21(x68451),x68455),x68456),x68454))
% 155.94/155.63 [6846]~P60(x68461)+~E(f54(x68461,x68463,x68464),f54(x68461,x68466,x68464))+~E(f54(x68461,x68462,x68464),f54(x68461,x68465,x68464))+E(f54(x68461,f312(f312(f90(x68461),x68462),x68463),x68464),f54(x68461,f312(f312(f90(x68461),x68465),x68466),x68464))
% 155.94/155.63 [7715]~P31(x77151)+P22(f312(f312(f227(x77151),x77152),f312(x77153,x77154)))+~P22(f312(f312(f314(x77155),x77154),x77156))+~P22(f312(f312(f227(x77151),x77152),f312(f312(f51(x77155,x77151),x77156),x77153)))
% 155.94/155.63 [7961]~P103(x79613)+~P22(f312(x79612,x79615))+~P33(x79613,f312(f312(f150(x79611,x79613),x79614),x79616))+E(f312(f132(x79611,x79612),f312(f312(f145(x79611,x79613,x79614),x79615),x79616)),f312(f312(f145(x79611,x79613,x79614),x79615),f312(f132(x79611,x79612),x79616)))
% 155.94/155.63 [7984]E(x79841,x79842)+E(x79843,f2(a1))+~P22(f312(f57(x79844,x79843),f312(f312(f239(a1,a1),x79845),x79842)))+~P22(f312(f57(x79844,x79843),f312(f312(f239(a1,a1),x79846),x79841)))
% 155.94/155.63 [7985]E(x79851,x79852)+E(x79853,f2(a1))+~P22(f312(f57(x79854,x79853),f312(f312(f239(a1,a1),x79852),x79855)))+~P22(f312(f57(x79854,x79853),f312(f312(f239(a1,a1),x79851),x79856)))
% 155.94/155.63 [8005]~P14(x80052,x80055,x80056,x80051)+~P22(f312(f70(x80052),x80054))+E(f312(x80051,f312(f312(f289(x80052),x80053),x80054)),f312(f82(x80055,x80055,x80055,f312(x80051,x80054)),f312(x80056,x80053)))+P22(f312(f312(f314(x80052),x80053),x80054))
% 155.94/155.63 [8240]~P15(x82405,x82401,x82406,x82402)+E(f312(f82(x82401,x82401,x82401,f312(x82402,x82403)),f312(x82402,x82404)),f312(x82402,x82403))+~P22(f312(f70(x82405),x82403))+~P22(f312(f312(f227(f861(x82405,a846)),x82404),x82403))
% 155.94/155.63 [9366]~P19(x93661,x93662,x93664,x93663)+~P22(f312(f312(f314(x93662),x93665),f312(f290(x93661,x93662,x93664),x93663)))+P22(f312(f312(f314(x93661),f312(f86(x93661,x93662,x93663,x93664),x93665)),x93666))+~P22(f312(f312(f227(f861(x93661,a846)),x93663),x93666))
% 155.94/155.63 [9736]~P26(x97362)+~E(f502(x97361,x97363,x97365,x97366,x97364,x97362),f503(x97361,x97363,x97365,x97366,x97364,x97362))+~P22(f312(f70(x97364),x97366))+E(f312(f312(f6(x97361,x97362),x97363),f312(f290(x97364,x97361,x97365),x97366)),f312(f312(f6(x97364,x97362),f312(f82(x97361,x97362,x97364,x97363),x97365)),x97366))
% 155.94/155.63 [9772]~P26(x97726)+E(f312(x97721,f502(x97722,x97723,x97721,x97724,x97725,x97726)),f312(x97721,f503(x97722,x97723,x97721,x97724,x97725,x97726)))+E(f312(f312(f6(x97722,x97726),x97723),f312(f290(x97725,x97722,x97721),x97724)),f312(f312(f6(x97725,x97726),f312(f82(x97722,x97726,x97725,x97723),x97721)),x97724))+~P22(f312(f70(x97725),x97724))
% 155.94/155.63 [9817]~P26(x98172)+~E(f312(x98173,f312(x98175,f503(x98171,x98173,x98175,x98176,x98174,x98172))),f2(x98172))+~P22(f312(f70(x98174),x98176))+E(f312(f312(f6(x98171,x98172),x98173),f312(f290(x98174,x98171,x98175),x98176)),f312(f312(f6(x98174,x98172),f312(f82(x98171,x98172,x98174,x98173),x98175)),x98176))
% 155.94/155.63 [9878]~P26(x98782)+~P22(f312(f70(x98784),x98786))+E(f312(f312(f6(x98781,x98782),x98783),f312(f290(x98784,x98781,x98785),x98786)),f312(f312(f6(x98784,x98782),f312(f82(x98781,x98782,x98784,x98783),x98785)),x98786))+P22(f312(f312(f314(x98784),f503(x98781,x98783,x98785,x98786,x98784,x98782)),x98786))
% 155.94/155.63 [9879]~P26(x98792)+~P22(f312(f70(x98794),x98796))+E(f312(f312(f6(x98791,x98792),x98793),f312(f290(x98794,x98791,x98795),x98796)),f312(f312(f6(x98794,x98792),f312(f82(x98791,x98792,x98794,x98793),x98795)),x98796))+P22(f312(f312(f314(x98794),f502(x98791,x98793,x98795,x98796,x98794,x98792)),x98796))
% 155.94/155.63 [9956]~P49(f861(f860(x99564,x99565),a846),f861(f860(x99564,x99565),a846),x99566)+~P22(f312(f312(x99561,f564(x99561,x99566,x99563,x99562,x99565,x99564)),f565(x99561,x99566,x99563,x99562,x99565,x99564)))+P22(f312(f312(x99561,x99562),x99563))+~P22(f312(f312(f314(f860(x99564,x99565)),f312(f312(f239(x99564,x99565),x99562),x99563)),f109(f861(f860(x99564,x99565),a846),x99566)))
% 155.94/155.63 [9993]~P72(x99931)+~P22(f312(f70(x99932),x99936))+E(f312(f312(f312(f74(x99931,x99932,f90(x99931)),f312(f312(f18(x99932,f861(x99933,a846),x99931),f312(f312(f7(x99932,x99931,f861(f861(x99933,a846),x99931)),f312(f312(f8(f861(x99933,x99931),f861(x99931,f861(f861(x99933,a846),x99931)),x99932),f74(x99931,x99933,f90(x99931))),x99934)),f87(x99931))),x99935)),f87(x99931)),x99936),f312(f312(f312(f74(x99931,f860(x99932,x99933),f90(x99931)),f312(f249(x99932,x99933,x99931),x99934)),f87(x99931)),f312(f312(f247(x99932,x99933),x99936),x99935)))+P22(f312(f312(f314(x99932),f530(x99934,x99935,x99933,x99936,x99932,x99931)),x99936))
% 155.94/155.63 [10013]~P72(x100131)+~P22(f312(f70(x100132),x100136))+E(f312(f312(f312(f74(x100131,x100132,f90(x100131)),f312(f312(f18(x100132,f861(x100133,a846),x100131),f312(f312(f7(x100132,x100131,f861(f861(x100133,a846),x100131)),f312(f312(f8(f861(x100133,x100131),f861(x100131,f861(f861(x100133,a846),x100131)),x100132),f74(x100131,x100133,f90(x100131))),x100134)),f87(x100131))),x100135)),f87(x100131)),x100136),f312(f312(f312(f74(x100131,f860(x100132,x100133),f90(x100131)),f312(f249(x100132,x100133,x100131),x100134)),f87(x100131)),f312(f312(f247(x100132,x100133),x100136),x100135)))+~P22(f312(f70(x100133),f312(x100135,f530(x100134,x100135,x100133,x100136,x100132,x100131))))
% 155.94/155.63 [8148]~P15(x81482,x81485,x81486,x81481)+~P22(f312(f70(x81482),x81484))+~P22(f312(f70(x81482),x81483))+E(f312(x81481,f312(f312(f124(f861(x81482,a846)),x81483),x81484)),f312(f82(x81485,x81485,x81485,f312(x81481,x81483)),f312(x81481,x81484)))
% 155.94/155.63 [8375]~P31(x83751)+P22(f312(f312(f227(x83751),f312(x83752,x83753)),x83754))+~P22(f312(f312(f314(x83755),x83753),x83756))+~P22(f312(f312(f227(x83751),f312(f312(f50(x83755,x83751),x83756),x83752)),x83754))
% 155.94/155.63 [8777]~P19(x87772,x87771,x87773,x87776)+E(f312(f312(f21(f861(x87771,a846)),f312(f290(x87772,x87771,x87773),x87774)),f312(f290(x87772,x87771,x87773),x87775)),f312(f290(x87772,x87771,x87773),f312(f312(f21(f861(x87772,a846)),x87774),x87775)))+~P22(f312(f312(f227(f861(x87772,a846)),x87775),x87776))+~P22(f312(f312(f227(f861(x87772,a846)),x87774),x87776))
% 155.94/155.63 [8778]~P19(x87782,x87781,x87783,x87786)+E(f312(f312(f115(f861(x87781,a846)),f312(f290(x87782,x87781,x87783),x87784)),f312(f290(x87782,x87781,x87783),x87785)),f312(f290(x87782,x87781,x87783),f312(f312(f115(f861(x87782,a846)),x87784),x87785)))+~P22(f312(f312(f227(f861(x87782,a846)),x87785),x87786))+~P22(f312(f312(f227(f861(x87782,a846)),x87784),x87786))
% 155.94/155.63 [8813]~P22(f312(x88131,x88133))+~P22(f312(f312(f312(f312(a198,x88132),x88133),x88134),x88136))+~P22(f312(f312(f312(f312(a198,f35(x88131,x88132)),x88136),x88134),x88135))+P22(f312(f312(f312(f312(a198,f35(x88131,x88132)),x88133),x88134),x88135))
% 155.94/155.63 [9044]E(x90441,x90442)+~P54(x90443,x90444,x90445)+~P22(f312(f312(f314(f860(x90443,x90444)),f312(f312(f239(x90443,x90444),x90446),x90442)),x90445))+~P22(f312(f312(f314(f860(x90443,x90444)),f312(f312(f239(x90443,x90444),x90446),x90441)),x90445))
% 155.94/155.63 [9812]~P68(x98121)+~E(f312(x98123,f747(x98124,x98126,x98123,x98125,x98122,x98121)),f312(x98126,f747(x98124,x98126,x98123,x98125,x98122,x98121)))+~P22(f312(f70(x98122),x98125))+E(f312(f312(f312(f74(x98121,x98122,f90(x98121)),x98123),x98124),x98125),f312(f312(f312(f74(x98121,x98122,f90(x98121)),x98126),x98124),x98125))
% 155.94/155.63 [9875]~P68(x98751)+~P22(f312(f70(x98752),x98755))+E(f312(f312(f312(f74(x98751,x98752,f90(x98751)),x98753),x98754),x98755),f312(f312(f312(f74(x98751,x98752,f90(x98751)),x98756),x98754),x98755))+P22(f312(f312(f314(x98752),f747(x98754,x98753,x98756,x98755,x98752,x98751)),x98755))
% 155.94/155.63 [8592]~P68(x85921)+~P22(f312(f70(x85922),x85926))+P22(f312(f312(f314(x85922),x85925),x85926))+E(f312(f312(f312(f74(x85921,x85922,f90(x85921)),x85923),x85924),f312(f312(f289(x85922),x85925),x85926)),f312(f312(f90(x85921),f312(x85923,x85925)),f312(f312(f312(f74(x85921,x85922,f90(x85921)),x85923),x85924),x85926)))
% 155.94/155.63 [8639]~P3(x86391,x86396,x86393)+~P9(x86391,f861(x86392,a846),x86393,x86395)+~P22(f312(f312(f314(x86391),x86394),x86396))+E(f312(f312(f50(x86391,f861(x86392,a846)),f312(f264(x86391,x86391,x86393),f312(f312(f289(x86391),x86394),f189(f861(x86391,a846))))),x86395),f312(x86395,x86394))
% 155.94/155.63 [9056]~P14(x90563,x90561,x90566,x90562)+~P22(f312(f70(x90563),x90565))+~P22(f312(f70(x90563),x90564))+E(f312(f82(x90561,x90561,x90561,f312(x90562,f312(f312(f124(f861(x90563,a846)),x90564),x90565))),f312(x90562,f312(f312(f115(f861(x90563,a846)),x90564),x90565))),f312(f82(x90561,x90561,x90561,f312(x90562,x90564)),f312(x90562,x90565)))
% 155.94/155.63 [10015]~P49(f861(f860(x100154,x100155),a846),f861(f860(x100154,x100155),a846),x100156)+P22(f312(f312(x100151,x100152),x100153))+~P22(f312(f312(f314(f860(x100154,x100155)),f312(f312(f239(x100154,x100155),x100152),x100153)),f109(f861(f860(x100154,x100155),a846),x100156)))+P22(f312(f312(f314(f860(x100154,x100155)),f312(f312(f239(x100154,x100155),f564(x100151,x100156,x100153,x100152,x100155,x100154)),f565(x100151,x100156,x100153,x100152,x100155,x100154))),f312(x100156,f312(f312(f115(f861(f860(x100154,x100155),a846)),f109(f861(f860(x100154,x100155),a846),x100156)),f312(f233(f860(x100154,x100155)),f312(f249(x100154,x100155,a846),x100151))))))
% 155.94/155.63 [9385]~E(x93853,f312(f312(f155(x93851,x93852),x93855),x93856))+P22(f312(f312(f314(f860(f854(x93851),f854(x93851))),f312(f312(f239(f854(x93851),f854(x93851)),x93852),x93853)),f153(x93851,x93854)))+~P22(f312(f312(f228(a853),x93855),f312(f190(f854(x93851)),x93852)))+~P22(f312(f312(f314(f860(x93851,x93851)),f312(f312(f239(x93851,x93851),f312(f312(f161(x93851),x93852),x93855)),x93856)),x93854))
% 155.94/155.63 [9892]~P72(x98922)+~P22(f312(f70(x98921),x98926))+P22(f312(f312(f314(x98921),f529(x98924,x98925,x98923,x98926,x98921,x98922)),x98926))+E(f312(f312(f9(x98921,x98922),f312(f312(f18(x98921,f861(x98923,a846),x98922),f312(f312(f8(f861(x98923,x98922),f861(f861(x98923,a846),x98922),x98921),f9(x98923,x98922)),x98924)),x98925)),x98926),f312(f312(f9(f860(x98921,x98923),x98922),f312(f249(x98921,x98923,x98922),x98924)),f312(f312(f247(x98921,x98923),x98926),x98925)))
% 155.94/155.63 [9893]~P26(x98932)+~P22(f312(f70(x98931),x98936))+P22(f312(f312(f314(x98931),f531(x98934,x98935,x98933,x98936,x98931,x98932)),x98936))+E(f312(f312(f6(x98931,x98932),f312(f312(f18(x98931,f861(x98933,a846),x98932),f312(f312(f8(f861(x98933,x98932),f861(f861(x98933,a846),x98932),x98931),f6(x98933,x98932)),x98934)),x98935)),x98936),f312(f312(f6(f860(x98931,x98933),x98932),f312(f249(x98931,x98933,x98932),x98934)),f312(f312(f247(x98931,x98933),x98936),x98935)))
% 155.94/155.63 [9931]~P72(x99312)+~P22(f312(f70(x99311),x99316))+~P22(f312(f70(x99313),f312(x99315,f529(x99314,x99315,x99313,x99316,x99311,x99312))))+E(f312(f312(f9(x99311,x99312),f312(f312(f18(x99311,f861(x99313,a846),x99312),f312(f312(f8(f861(x99313,x99312),f861(f861(x99313,a846),x99312),x99311),f9(x99313,x99312)),x99314)),x99315)),x99316),f312(f312(f9(f860(x99311,x99313),x99312),f312(f249(x99311,x99313,x99312),x99314)),f312(f312(f247(x99311,x99313),x99316),x99315)))
% 155.94/155.63 [9932]~P26(x99322)+~P22(f312(f70(x99321),x99326))+~P22(f312(f70(x99323),f312(x99325,f531(x99324,x99325,x99323,x99326,x99321,x99322))))+E(f312(f312(f6(x99321,x99322),f312(f312(f18(x99321,f861(x99323,a846),x99322),f312(f312(f8(f861(x99323,x99322),f861(f861(x99323,a846),x99322),x99321),f6(x99323,x99322)),x99324)),x99325)),x99326),f312(f312(f6(f860(x99321,x99323),x99322),f312(f249(x99321,x99323,x99322),x99324)),f312(f312(f247(x99321,x99323),x99326),x99325)))
% 155.94/155.63 [9914]~P72(x99142)+~P22(f312(f70(x99141),x99146))+P22(f312(f312(f314(x99141),x99143),x99146))+E(f312(f312(f9(x99141,x99142),f312(f312(f7(x99141,x99142,x99142),f312(f312(f18(x99141,x99142,f861(x99142,x99142)),f312(f312(f8(a846,f861(x99142,f861(x99142,x99142)),x99141),f108(x99142)),f312(f312(f7(x99141,x99141,a846),a309),x99143))),x99144)),x99145)),x99146),f312(f312(f240(x99142),x99145),f312(f53(x99141),x99146)))
% 155.94/155.63 [9919]~P72(x99192)+~P22(f312(f70(x99191),x99196))+~P22(f312(f312(f314(x99191),x99193),x99196))+E(f312(f312(f9(x99191,x99192),f312(f312(f7(x99191,x99192,x99192),f312(f312(f18(x99191,x99192,f861(x99192,x99192)),f312(f312(f8(a846,f861(x99192,f861(x99192,x99192)),x99191),f108(x99192)),f312(f312(f7(x99191,x99191,a846),a309),x99193))),x99194)),x99195)),x99196),f312(f312(f90(x99192),f312(x99194,x99193)),f312(f312(f240(x99192),x99195),f312(f312(f21(a853),f312(f53(x99191),x99196)),f87(a853)))))
% 155.94/155.63 [9985]~P22(f312(f70(x99851),x99855))+~P22(f312(f70(x99852),x99853))+P22(f312(f312(f314(x99852),f561(x99856,x99854,x99853,x99852,x99855,x99851)),x99853))+E(f312(f312(f6(x99851,a853),f312(f312(f8(f861(x99852,a846),a853,x99851),f53(x99852)),f312(f312(f8(f861(x99852,a846),f861(x99852,a846),x99851),f233(x99852)),f312(f312(f8(f861(x99852,a846),f861(x99852,a846),x99851),f312(f18(x99852,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99852),a310),f312(f312(f7(x99852,f861(x99852,a846),a846),f314(x99852)),x99853)))),x99854)))),x99855),f312(f312(f90(a853),x99856),f312(f53(x99852),x99853)))
% 155.94/155.63 [9986]~P22(f312(f70(x99861),x99865))+~P22(f312(f70(x99862),x99863))+P22(f312(f312(f314(x99862),f566(x99866,x99864,x99863,x99862,x99865,x99861)),x99863))+E(f312(f312(f6(x99861,a853),f312(f312(f8(f861(x99862,a846),a853,x99861),f53(x99862)),f312(f312(f8(f861(x99862,a846),f861(x99862,a846),x99861),f233(x99862)),f312(f312(f8(f861(x99862,a846),f861(x99862,a846),x99861),f312(f18(x99862,a846,a846),f312(f312(f8(a846,f861(a846,a846),x99862),a310),f312(f312(f7(x99862,f861(x99862,a846),a846),f314(x99862)),x99863)))),x99864)))),x99865),f312(f312(f6(x99862,a853),x99866),x99863))
% 155.94/155.63 [10018]~P22(f312(f70(x100182),x100183))+~P22(f312(f70(x100181),x100185))+~E(f312(f53(x100181),f312(f233(x100181),f312(f312(f18(x100181,a846,a846),f312(f312(f8(a846,f861(a846,a846),x100181),a310),f312(f312(f7(x100181,f861(x100181,a846),a846),f314(x100181)),x100185))),f312(f312(f7(x100181,x100182,a846),x100184),f561(x100186,x100184,x100183,x100182,x100185,x100181))))),x100186)+E(f312(f312(f6(x100181,a853),f312(f312(f8(f861(x100182,a846),a853,x100181),f53(x100182)),f312(f312(f8(f861(x100182,a846),f861(x100182,a846),x100181),f233(x100182)),f312(f312(f8(f861(x100182,a846),f861(x100182,a846),x100181),f312(f18(x100182,a846,a846),f312(f312(f8(a846,f861(a846,a846),x100182),a310),f312(f312(f7(x100182,f861(x100182,a846),a846),f314(x100182)),x100183)))),x100184)))),x100185),f312(f312(f90(a853),x100186),f312(f53(x100182),x100183)))
% 155.94/155.63 [10020]~P22(f312(f70(x100202),x100203))+~P22(f312(f70(x100201),x100205))+~E(f312(f53(x100201),f312(f233(x100201),f312(f312(f18(x100201,a846,a846),f312(f312(f8(a846,f861(a846,a846),x100201),a310),f312(f312(f7(x100201,f861(x100201,a846),a846),f314(x100201)),x100205))),f312(f312(f7(x100201,x100202,a846),x100204),f566(x100206,x100204,x100203,x100202,x100205,x100201))))),f312(x100206,f566(x100206,x100204,x100203,x100202,x100205,x100201)))+E(f312(f312(f6(x100201,a853),f312(f312(f8(f861(x100202,a846),a853,x100201),f53(x100202)),f312(f312(f8(f861(x100202,a846),f861(x100202,a846),x100201),f233(x100202)),f312(f312(f8(f861(x100202,a846),f861(x100202,a846),x100201),f312(f18(x100202,a846,a846),f312(f312(f8(a846,f861(a846,a846),x100202),a310),f312(f312(f7(x100202,f861(x100202,a846),a846),f314(x100202)),x100203)))),x100204)))),x100205),f312(f312(f6(x100202,a853),x100206),x100203))
% 155.94/155.63 [9462]P22(f312(x94621,x94622))+~P22(f312(f312(f314(x94627),x94622),f312(x94626,x94624)))+~P22(f312(x94621,f404(x94621,x94626,x94625,x94623,x94627)))+~P22(f312(f312(f314(x94623),x94624),x94625))
% 155.94/155.63 [9362]~P68(x93621)+~P19(x93625,x93622,x93626,x93627)+~P22(f312(f70(x93625),x93627))+E(f312(f312(f312(f74(x93621,x93622,f90(x93621)),x93623),x93624),f312(f290(x93625,x93622,x93626),x93627)),f312(f312(f312(f74(x93621,x93625,f90(x93621)),f312(f82(x93622,x93621,x93625,x93623),x93626)),x93624),x93627))
% 155.94/155.63 [9487]~E(f312(f312(f289(x94871),x94875),x94876),f312(f312(f289(x94871),x94872),x94873))+~P22(f312(f75(x94871,x94871,x94874,x94872,x94873),x94877))+P22(f312(f312(f314(x94871),x94872),x94873))+P22(f312(f71(x94871,x94874,f312(f312(f289(x94871),x94875),x94876)),x94877))
% 155.94/155.63 [9566]P22(f312(x95661,x95662))+~P22(f312(f312(f314(x95663),x95662),f312(x95664,x95667)))+~P22(f312(f312(f314(x95666),x95667),x95665))+P22(f312(f312(f314(x95663),f404(x95661,x95664,x95665,x95666,x95663)),f312(f312(f50(x95666,f861(x95663,a846)),x95665),x95664)))
% 155.94/155.63 [9578]~P19(x95782,x95781,x95785,x95784)+~P19(x95781,x95783,x95786,f312(f290(x95782,x95781,x95785),x95784))+E(f312(f312(f82(x95781,x95782,x95783,f86(x95782,x95781,x95784,x95785)),f86(x95781,x95783,f312(f290(x95782,x95781,x95785),x95784),x95786)),x95787),f312(f86(x95782,x95783,x95784,f312(f82(x95781,x95783,x95782,x95786),x95785)),x95787))+~P22(f312(f312(f314(x95783),x95787),f312(f290(x95781,x95783,x95786),f312(f290(x95782,x95781,x95785),x95784))))
% 155.94/155.63 [9639]E(x96391,f2(a1))+~P22(f312(f57(x96393,x96391),f312(f312(f239(a1,a1),x96395),x96397)))+~P22(f312(f57(x96392,x96391),f312(f312(f239(a1,a1),x96394),x96396)))+P22(f312(f57(f312(f312(f89(a1),x96392),x96393),x96391),f312(f312(f239(a1,a1),f312(f312(f89(a1),f312(f312(f89(a1),x96394),x96395)),f312(f47(a1,f312(f312(f89(a1),x96396),x96397)),x96391))),f54(a1,f312(f312(f89(a1),x96396),x96397),x96391))))
% 155.94/155.63 [9645]~P22(f312(f312(f228(a853),f2(a853)),x96453))+~P22(f312(f56(x96452,x96453),f312(f312(f239(a853,a853),x96455),x96457)))+~P22(f312(f56(x96451,x96453),f312(f312(f239(a853,a853),x96454),x96456)))+P22(f312(f56(f312(f312(f89(a853),x96451),x96452),x96453),f312(f312(f239(a853,a853),f312(f312(f89(a853),f312(f312(f89(a853),x96454),x96455)),f312(f47(a853,f312(f312(f89(a853),x96456),x96457)),x96453))),f54(a853,f312(f312(f89(a853),x96456),x96457),x96453))))
% 155.94/155.63 [10017]~P26(x100172)+~P22(f312(f70(x100173),x100175))+~P22(f312(f70(x100171),x100177))+E(f312(f312(f6(x100171,x100172),f312(f312(f18(x100171,f861(x100173,a846),x100172),f312(f312(f8(f861(x100173,x100172),f861(f861(x100173,a846),x100172),x100171),f6(x100173,x100172)),x100174)),f312(f312(f8(f861(x100173,a846),f861(x100173,a846),x100171),f233(x100173)),f312(f312(f8(f861(x100173,a846),f861(x100173,a846),x100171),f312(f18(x100173,a846,a846),f312(f312(f8(a846,f861(a846,a846),x100173),a310),f312(f312(f7(x100173,f861(x100173,a846),a846),f314(x100173)),x100175)))),x100176)))),x100177),f312(f312(f6(x100173,x100172),f312(f312(f18(x100173,f861(x100171,a846),x100172),f312(f312(f8(f861(x100171,x100172),f861(f861(x100171,a846),x100172),x100173),f6(x100171,x100172)),f312(f7(x100171,x100173,x100172),x100174))),f312(f312(f8(f861(x100171,a846),f861(x100171,a846),x100173),f233(x100171)),f312(f312(f8(f861(x100171,a846),f861(x100171,a846),x100173),f312(f18(x100171,a846,a846),f312(f312(f8(a846,f861(a846,a846),x100171),a310),f312(f312(f7(x100171,f861(x100171,a846),a846),f314(x100171)),x100177)))),f312(f7(x100171,x100173,a846),x100176))))),x100175))
% 155.94/155.63 [9526]~P10(x95266,x95261,x95262,x95268,x95263,x95264)+~P3(x95266,x95267,x95268)+P9(x95261,x95262,x95263,f312(x95264,x95265))+~P22(f312(f312(f314(x95266),x95265),x95267))
% 155.94/155.63 [7962]~P34(x79628,x79627,f312(f312(f312(f100(x79628),x79624),x79626),x79621))+P22(f312(f312(x79621,x79622),x79623))+~P22(f312(f312(x79624,x79622),x79625))+~P22(f312(f312(f312(f312(a198,x79626),x79625),x79627),x79623))
% 155.94/155.63 [9150]~P14(x91507,x91501,x91508,x91503)+~P22(f312(f70(x91507),x91505))+~P22(f312(f70(x91507),x91504))+E(f312(f82(x91501,x91501,x91502,f312(x91503,x91504)),f312(f82(x91501,x91501,x91502,f312(x91503,x91505)),x91506)),f312(f82(x91501,x91501,x91502,f312(x91503,x91505)),f312(f82(x91501,x91501,x91502,f312(x91503,x91504)),x91506)))
% 155.94/155.63 [9157]~P39(x91571,x91572,x91573,x91574,x91577)+P39(x91571,x91572,x91573,f312(f312(f155(x91571,x91574),x91575),x91576),f312(f312(f155(x91572,x91577),x91575),x91578))+~P22(f312(f312(x91573,x91576),x91578))+~P22(f312(f312(f228(a853),x91575),f312(f190(f854(x91571)),x91574)))
% 155.94/155.63 [9158]~P39(x91581,x91582,x91583,x91584,x91587)+P39(x91581,x91582,x91583,f312(f312(f155(x91581,x91584),x91585),x91586),f312(f312(f155(x91582,x91587),x91585),x91588))+~P22(f312(f312(x91583,x91586),x91588))+~P22(f312(f312(f228(a853),x91585),f312(f190(f854(x91582)),x91587)))
% 155.94/155.63 [9236]~P19(x92362,x92362,x92365,x92366)+~P16(x92363,x92362,x92367,x92368,x92361)+~P22(f312(f70(x92362),x92366))+E(f312(f312(x92361,f312(f82(x92362,x92363,x92362,x92364),x92365)),x92366),f312(f312(x92361,x92364),f312(f290(x92362,x92362,x92365),x92366)))
% 155.94/155.63 [9524]~P17(x95247,x95242,x95245,x95248,x95246,x95241)+~P22(f312(f70(x95242),x95244))+E(f312(x95241,f312(f312(f289(x95242),x95243),x95244)),f312(f312(x95245,f312(x95246,x95243)),f312(x95241,x95244)))+P22(f312(f312(f314(x95242),x95243),x95244))
% 155.94/155.63 [9135]P22(f312(f312(f314(f860(f854(x91351),f854(x91351))),f312(f312(f239(f854(x91351),f854(x91351)),x91352),x91353)),f153(x91351,x91354)))+~E(x91353,f312(f312(f129(x91351),x91355),f312(f312(f147(x91351),x91356),x91357)))+~E(x91352,f312(f312(f129(x91351),x91355),f312(f312(f147(x91351),x91358),x91357)))+~P22(f312(f312(f314(f860(x91351,x91351)),f312(f312(f239(x91351,x91351),x91358),x91356)),x91354))
% 155.94/155.63 [10059]~P19(x100594,x100592,x100595,x100598)+E(f312(f312(f51(x100591,f861(x100592,a846)),x100593),f312(f312(f8(f861(x100594,a846),f861(x100592,a846),x100591),f290(x100594,x100592,x100595)),x100596)),f312(f290(x100594,x100592,x100595),f312(f312(f51(x100591,f861(x100594,a846)),x100593),x100596)))+~P22(f312(f312(f314(x100591),x100597),x100593))+P22(f312(f312(f314(x100591),f674(x100597,x100596,x100593,x100591,x100598,x100595,x100592,x100594)),x100593))
% 155.94/155.63 [10082]~P19(x100824,x100822,x100825,x100827)+E(f312(f312(f51(x100821,f861(x100822,a846)),x100823),f312(f312(f8(f861(x100824,a846),f861(x100822,a846),x100821),f290(x100824,x100822,x100825)),x100826)),f312(f290(x100824,x100822,x100825),f312(f312(f51(x100821,f861(x100824,a846)),x100823),x100826)))+~P22(f312(f312(f314(x100821),x100828),x100823))+~P22(f312(f312(f227(f861(x100824,a846)),f312(x100826,f674(x100828,x100826,x100823,x100821,x100827,x100825,x100822,x100824))),x100827))
% 155.94/155.63 [9586]~P17(x95867,x95865,x95861,x95868,x95862,x95864)+~P22(f312(f70(x95865),x95866))+~P22(f312(f312(f314(x95865),x95863),x95866))+E(f312(f312(x95861,f312(x95862,x95863)),f312(x95864,f312(f312(f21(f861(x95865,a846)),x95866),f312(f312(f289(x95865),x95863),f189(f861(x95865,a846)))))),f312(x95864,x95866))
% 155.94/155.63 [9594]~P17(x95946,x95943,x95941,x95947,x95948,x95942)+~P22(f312(f70(x95943),x95945))+~P22(f312(f70(x95943),x95944))+E(f312(f312(x95941,f312(x95942,f312(f312(f124(f861(x95943,a846)),x95944),x95945))),f312(x95942,f312(f312(f115(f861(x95943,a846)),x95944),x95945))),f312(f312(x95941,f312(x95942,x95944)),f312(x95942,x95945)))
% 155.94/155.63 [9686]P45(x96861,x96862,x96863,x96864,x96865,f312(f312(x96863,x96866),x96867))+~P45(x96861,x96862,x96863,x96864,f312(f312(f21(f861(x96861,a846)),x96865),f312(f312(f289(x96861),x96868),f189(f861(x96861,a846)))),x96869)+~E(f312(f312(x96863,x96866),x96867),f312(f312(x96863,x96868),x96869))+~P22(f312(f312(f314(x96861),x96868),x96865))
% 155.94/155.63 [10097]P18(x100971,x100972,f312(f312(f289(f852(x100971)),f312(f312(f312(f100(x100971),f312(x100973,f370(x100974,x100975,x100976,x100977,x100973,x100972,x100971,x100978,x100979))),f312(x100977,f370(x100974,x100975,x100976,x100977,x100973,x100972,x100971,x100978,x100979))),f312(x100976,f370(x100974,x100975,x100976,x100977,x100973,x100972,x100971,x100978,x100979)))),f189(f861(f852(x100971),a846))))+~P22(f312(f70(x100979),x100978))+~P18(x100971,x100972,f312(f290(x100979,f852(x100971),f312(f312(f18(x100979,f861(x100971,f861(a848,a846)),f852(x100971)),f312(f312(f18(x100979,a847,f861(f861(x100971,f861(a848,a846)),f852(x100971))),f312(f312(f8(f861(x100971,f861(a848,a846)),f861(a847,f861(f861(x100971,f861(a848,a846)),f852(x100971))),x100979),f100(x100971)),x100973)),x100977)),x100976)),x100978))+P18(x100971,x100972,f312(f290(x100979,f852(x100971),f312(f312(f18(x100979,f861(x100971,f861(a848,a846)),f852(x100971)),f312(f312(f18(x100979,a847,f861(f861(x100971,f861(a848,a846)),f852(x100971))),f312(f312(f8(f861(x100971,f861(a848,a846)),f861(a847,f861(f861(x100971,f861(a848,a846)),f852(x100971))),x100979),f100(x100971)),x100975)),x100977)),x100974)),x100978))
% 155.94/155.63 [10098]~P18(x100981,x100982,f312(f312(f289(f852(x100981)),f312(f312(f312(f100(x100981),f312(x100984,f370(x100986,x100984,x100988,x100985,x100989,x100982,x100981,x100987,x100983))),f312(x100985,f370(x100986,x100984,x100988,x100985,x100989,x100982,x100981,x100987,x100983))),f312(x100986,f370(x100986,x100984,x100988,x100985,x100989,x100982,x100981,x100987,x100983)))),f189(f861(f852(x100981),a846))))+~P22(f312(f70(x100983),x100987))+~P18(x100981,x100982,f312(f290(x100983,f852(x100981),f312(f312(f18(x100983,f861(x100981,f861(a848,a846)),f852(x100981)),f312(f312(f18(x100983,a847,f861(f861(x100981,f861(a848,a846)),f852(x100981))),f312(f312(f8(f861(x100981,f861(a848,a846)),f861(a847,f861(f861(x100981,f861(a848,a846)),f852(x100981))),x100983),f100(x100981)),x100989)),x100985)),x100988)),x100987))+P18(x100981,x100982,f312(f290(x100983,f852(x100981),f312(f312(f18(x100983,f861(x100981,f861(a848,a846)),f852(x100981)),f312(f312(f18(x100983,a847,f861(f861(x100981,f861(a848,a846)),f852(x100981))),f312(f312(f8(f861(x100981,f861(a848,a846)),f861(a847,f861(f861(x100981,f861(a848,a846)),f852(x100981))),x100983),f100(x100981)),x100984)),x100985)),x100986)),x100987))
% 155.94/155.63 [9622]~P10(x96226,x96227,x96228,x96229,x962210,x96221)+E(f312(f312(x96221,x96222),x96223),f312(f312(x96221,x96224),x96225))+~P22(f312(f312(f314(f860(x96227,x96227)),f312(f312(f239(x96227,x96227),x96223),x96225)),x962210))+~P22(f312(f312(f314(f860(x96226,x96226)),f312(f312(f239(x96226,x96226),x96222),x96224)),x96229))
% 155.94/155.63 [9238]~P87(x92382)+E(x92381,f189(f861(x92382,a846)))+~P22(f312(f70(x92382),x92381))+P22(f312(f312(f314(x92382),f11(x92382,x92381)),x92381))+~P22(f312(f312(f314(x92382),f312(f312(f115(x92382),f374(x92381,x92382)),f375(x92381,x92382))),f312(f312(f289(x92382),f374(x92381,x92382)),f312(f312(f289(x92382),f375(x92381,x92382)),f189(f861(x92382,a846))))))
% 155.94/155.63 [9239]~P87(x92392)+E(x92391,f189(f861(x92392,a846)))+~P22(f312(f70(x92392),x92391))+P22(f312(f312(f314(x92392),f10(x92392,x92391)),x92391))+~P22(f312(f312(f314(x92392),f312(f312(f124(x92392),f377(x92391,x92392)),f382(x92391,x92392))),f312(f312(f289(x92392),f377(x92391,x92392)),f312(f312(f289(x92392),f382(x92391,x92392)),f189(f861(x92392,a846))))))
% 155.94/155.63 [9270]~P68(x92702)+E(x92701,f189(f861(x92702,a846)))+~P22(f312(f70(x92702),x92701))+P22(f312(f312(f314(x92702),f312(f72(x92702,f90(x92702)),x92701)),x92701))+~P22(f312(f312(f314(x92702),f312(f312(f90(x92702),f545(x92701,x92702)),f546(x92701,x92702))),f312(f312(f289(x92702),f545(x92701,x92702)),f312(f312(f289(x92702),f546(x92701,x92702)),f189(f861(x92702,a846))))))
% 155.94/155.63 [9276]~P103(x92762)+E(x92761,f189(f861(x92762,a846)))+~P22(f312(f70(x92762),x92761))+P22(f312(f312(f314(x92762),f12(x92762,f226(x92762),x92761)),x92761))+~P22(f312(f312(f314(x92762),f312(f312(f226(x92762),f389(x92761,x92762)),f390(x92761,x92762))),f312(f312(f289(x92762),f389(x92761,x92762)),f312(f312(f289(x92762),f390(x92761,x92762)),f189(f861(x92762,a846))))))
% 155.94/155.63 [9277]~P103(x92772)+E(x92771,f189(f861(x92772,a846)))+~P22(f312(f70(x92772),x92771))+P22(f312(f312(f314(x92772),f13(x92772,f225(x92772),x92771)),x92771))+~P22(f312(f312(f314(x92772),f312(f312(f225(x92772),f391(x92771,x92772)),f392(x92771,x92772))),f312(f312(f289(x92772),f391(x92771,x92772)),f312(f312(f289(x92772),f392(x92771,x92772)),f189(f861(x92772,a846))))))
% 155.94/155.63 [6424]~P84(x64242)+E(x64241,f2(x64242))+~E(f312(f312(f89(x64242),x64243),x64241),f2(x64242))+~P22(f312(f312(f227(x64242),f2(x64242)),x64243))+~P22(f312(f312(f227(x64242),f2(x64242)),x64241))
% 155.94/155.63 [6425]~P84(x64252)+E(x64251,f2(x64252))+~E(f312(f312(f89(x64252),x64251),x64253),f2(x64252))+~P22(f312(f312(f227(x64252),f2(x64252)),x64253))+~P22(f312(f312(f227(x64252),f2(x64252)),x64251))
% 155.94/155.63 [6950]~P103(x69502)+~P33(x69502,x69501)+E(x69501,f127(x69502))+~P22(f312(f312(f314(x69502),x69503),f312(f168(x69502),f650(x69501,x69502))))+P22(f312(f312(f227(x69502),f689(x69501,x69502)),x69503))
% 155.94/155.63 [7117]~P103(x71171)+E(f15(x71171,x71172),x71173)+~P22(f312(f70(x71171),x71172))+~P22(f312(f312(f227(x71171),x71173),f746(x71173,x71172,x71171)))+~P22(f312(f312(f314(x71171),x71173),x71172))
% 155.94/155.63 [7146]~P103(x71461)+~P33(x71461,x71462)+~P33(x71461,x71463)+P33(x71461,f312(f312(f129(x71461),x71462),x71463))+P22(f312(f312(f314(x71461),f647(x71463,x71462,x71461)),f312(f168(x71461),x71462)))
% 155.94/155.63 [7147]~P103(x71471)+~P33(x71471,x71472)+~P33(x71471,x71473)+P33(x71471,f312(f312(f129(x71471),x71472),x71473))+P22(f312(f312(f314(x71471),f648(x71473,x71472,x71471)),f312(f168(x71471),x71473)))
% 155.94/155.63 [7193]~P103(x71931)+E(f14(x71931,x71932),x71933)+~P22(f312(f70(x71931),x71932))+P22(f312(f312(f314(x71931),f748(x71933,x71932,x71931)),x71932))+~P22(f312(f312(f314(x71931),x71933),x71932))
% 155.94/155.63 [7194]~P103(x71941)+E(f15(x71941,x71942),x71943)+~P22(f312(f70(x71941),x71942))+P22(f312(f312(f314(x71941),f746(x71943,x71942,x71941)),x71942))+~P22(f312(f312(f314(x71941),x71943),x71942))
% 155.94/155.63 [7773]~P103(x77731)+E(f14(x77731,x77732),x77733)+~P22(f312(f70(x77731),x77732))+~P22(f312(f312(f314(x77731),x77733),x77732))+~P22(f312(f312(f227(x77731),f748(x77733,x77732,x77731)),x77733))
% 155.94/155.63 [8095]~P103(x80951)+~P33(x80951,x80952)+~P33(x80951,x80953)+P33(x80951,f312(f312(f129(x80951),x80952),x80953))+~P22(f312(f312(f227(x80951),f647(x80953,x80952,x80951)),f648(x80953,x80952,x80951)))
% 155.94/155.63 [8882]~P87(x88822)+E(x88821,f189(f861(x88822,a846)))+~E(f312(f312(f115(x88822),f312(x88823,f433(x88821,x88823,x88822))),f312(x88823,f440(x88821,x88823,x88822))),f312(x88823,f312(f312(f115(x88822),f433(x88821,x88823,x88822)),f440(x88821,x88823,x88822))))+E(f11(x88822,f312(f290(x88822,x88822,x88823),x88821)),f312(x88823,f11(x88822,x88821)))+~P22(f312(f70(x88822),x88821))
% 155.94/155.63 [8883]~P87(x88832)+E(x88831,f189(f861(x88832,a846)))+~E(f312(f312(f124(x88832),f312(x88833,f441(x88831,x88833,x88832))),f312(x88833,f442(x88831,x88833,x88832))),f312(x88833,f312(f312(f124(x88832),f441(x88831,x88833,x88832)),f442(x88831,x88833,x88832))))+E(f10(x88832,f312(f290(x88832,x88832,x88833),x88831)),f312(x88833,f10(x88832,x88831)))+~P22(f312(f70(x88832),x88831))
% 155.94/155.63 [8884]~P103(x88842)+E(x88841,f189(f861(x88842,a846)))+~E(f312(f312(f226(x88842),f312(x88843,f434(x88841,x88843,x88842))),f312(x88843,f437(x88841,x88843,x88842))),f312(x88843,f312(f312(f226(x88842),f434(x88841,x88843,x88842)),f437(x88841,x88843,x88842))))+E(f14(x88842,f312(f290(x88842,x88842,x88843),x88841)),f312(x88843,f14(x88842,x88841)))+~P22(f312(f70(x88842),x88841))
% 155.94/155.63 [8885]~P103(x88852)+E(x88851,f189(f861(x88852,a846)))+~E(f312(f312(f225(x88852),f312(x88853,f438(x88851,x88853,x88852))),f312(x88853,f439(x88851,x88853,x88852))),f312(x88853,f312(f312(f225(x88852),f438(x88851,x88853,x88852)),f439(x88851,x88853,x88852))))+E(f15(x88852,f312(f290(x88852,x88852,x88853),x88851)),f312(x88853,f15(x88852,x88851)))+~P22(f312(f70(x88852),x88851))
% 155.94/155.63 [8956]~P103(x89562)+E(x89561,f189(f861(x89562,a846)))+~E(f312(f312(f226(x89562),f312(x89563,f426(x89561,x89563,x89562))),f312(x89563,f428(x89561,x89563,x89562))),f312(x89563,f312(f312(f226(x89562),f426(x89561,x89563,x89562)),f428(x89561,x89563,x89562))))+E(f12(x89562,f226(x89562),f312(f290(x89562,x89562,x89563),x89561)),f312(x89563,f12(x89562,f226(x89562),x89561)))+~P22(f312(f70(x89562),x89561))
% 155.94/155.63 [8957]~P103(x89572)+E(x89571,f189(f861(x89572,a846)))+~E(f312(f312(f225(x89572),f312(x89573,f435(x89571,x89573,x89572))),f312(x89573,f436(x89571,x89573,x89572))),f312(x89573,f312(f312(f225(x89572),f435(x89571,x89573,x89572)),f436(x89571,x89573,x89572))))+E(f13(x89572,f225(x89572),f312(f290(x89572,x89572,x89573),x89571)),f312(x89573,f13(x89572,f225(x89572),x89571)))+~P22(f312(f70(x89572),x89571))
% 155.94/155.63 [6436]~P68(x64362)+E(x64361,f189(f861(x64362,a846)))+~P22(f312(f70(x64362),x64361))+E(f312(f72(x64362,f90(x64362)),f312(f312(f289(x64362),x64363),x64361)),f312(f312(f90(x64362),x64363),f312(f72(x64362,f90(x64362)),x64361)))+P22(f312(f312(f314(x64362),x64363),x64361))
% 155.94/155.63 [6955]~P87(x69552)+E(f312(f312(f124(x69552),f10(x69552,x69551)),f10(x69552,x69553)),f10(x69552,x69553))+E(x69551,f189(f861(x69552,a846)))+~P22(f312(f70(x69552),x69553))+~P22(f312(f312(f227(f861(x69552,a846)),x69551),x69553))
% 155.94/155.63 [6956]~P87(x69562)+E(f312(f312(f115(x69562),f11(x69562,x69561)),f11(x69562,x69563)),f11(x69562,x69563))+E(x69561,f189(f861(x69562,a846)))+~P22(f312(f70(x69562),x69563))+~P22(f312(f312(f227(f861(x69562,a846)),x69561),x69563))
% 155.94/155.63 [6957]~P103(x69572)+E(f312(f312(f225(x69572),f15(x69572,x69571)),f15(x69572,x69573)),f15(x69572,x69573))+E(x69571,f189(f861(x69572,a846)))+~P22(f312(f70(x69572),x69573))+~P22(f312(f312(f227(f861(x69572,a846)),x69571),x69573))
% 155.94/155.63 [6958]~P103(x69582)+E(f312(f312(f226(x69582),f14(x69582,x69581)),f14(x69582,x69583)),f14(x69582,x69583))+E(x69581,f189(f861(x69582,a846)))+~P22(f312(f70(x69582),x69583))+~P22(f312(f312(f227(f861(x69582,a846)),x69581),x69583))
% 155.94/155.63 [7249]~P103(x72492)+E(x72491,f189(f861(x72492,a846)))+~P22(f312(f70(x72492),x72493))+P22(f312(f312(f227(x72492),f14(x72492,x72491)),f14(x72492,x72493)))+~P22(f312(f312(f227(f861(x72492,a846)),x72491),x72493))
% 155.94/155.63 [7250]~P103(x72502)+E(x72501,f189(f861(x72502,a846)))+~P22(f312(f70(x72502),x72503))+P22(f312(f312(f227(x72502),f15(x72502,x72503)),f15(x72502,x72501)))+~P22(f312(f312(f227(f861(x72502,a846)),x72501),x72503))
% 155.94/155.63 [7307]~P87(x73071)+E(f11(x73071,x73072),x73073)+~P22(f312(f70(x73071),x73072))+~E(f312(f312(f21(f861(x73071,a846)),x73072),f312(f312(f289(x73071),x73073),f189(f861(x73071,a846)))),f189(f861(x73071,a846)))+~P22(f312(f312(f314(x73071),x73073),x73072))
% 155.94/155.63 [7308]~P87(x73081)+E(f10(x73081,x73082),x73083)+~P22(f312(f70(x73081),x73082))+~E(f312(f312(f21(f861(x73081,a846)),x73082),f312(f312(f289(x73081),x73083),f189(f861(x73081,a846)))),f189(f861(x73081,a846)))+~P22(f312(f312(f314(x73081),x73083),x73082))
% 155.94/155.63 [7309]~P103(x73091)+E(f14(x73091,x73092),x73093)+~P22(f312(f70(x73091),x73092))+~E(f312(f312(f21(f861(x73091,a846)),x73092),f312(f312(f289(x73091),x73093),f189(f861(x73091,a846)))),f189(f861(x73091,a846)))+~P22(f312(f312(f314(x73091),x73093),x73092))
% 155.94/155.63 [7310]~P103(x73101)+E(f15(x73101,x73102),x73103)+~P22(f312(f70(x73101),x73102))+~E(f312(f312(f21(f861(x73101,a846)),x73102),f312(f312(f289(x73101),x73103),f189(f861(x73101,a846)))),f189(f861(x73101,a846)))+~P22(f312(f312(f314(x73101),x73103),x73102))
% 155.94/155.63 [7404]~P103(x74041)+E(f12(x74041,f226(x74041),x74042),x74043)+~P22(f312(f70(x74041),x74042))+~E(f312(f312(f21(f861(x74041,a846)),x74042),f312(f312(f289(x74041),x74043),f189(f861(x74041,a846)))),f189(f861(x74041,a846)))+~P22(f312(f312(f314(x74041),x74043),x74042))
% 155.94/155.63 [7405]~P103(x74051)+E(f13(x74051,f225(x74051),x74052),x74053)+~P22(f312(f70(x74051),x74052))+~E(f312(f312(f21(f861(x74051,a846)),x74052),f312(f312(f289(x74051),x74053),f189(f861(x74051,a846)))),f189(f861(x74051,a846)))+~P22(f312(f312(f314(x74051),x74053),x74052))
% 155.94/155.63 [7441]~P103(x74412)+E(x74411,f189(f861(x74412,a846)))+~P22(f312(f70(x74412),x74411))+~P22(f312(f312(f228(x74412),x74413),f540(x74413,x74411,x74412)))+P22(f312(f312(f228(x74412),x74413),f312(f72(x74412,f225(x74412)),x74411)))
% 155.94/155.63 [7442]~P99(x74422)+E(x74421,f189(f861(x74422,a846)))+~P22(f312(f70(x74422),x74421))+~P22(f312(f312(f227(x74422),x74423),f524(x74423,x74421,x74422)))+P22(f312(f312(f227(x74422),x74423),f312(f72(x74422,f115(x74422)),x74421)))
% 155.94/155.63 [7443]~P103(x74432)+E(x74431,f189(f861(x74432,a846)))+~P22(f312(f70(x74432),x74431))+~P22(f312(f312(f227(x74432),x74433),f536(x74433,x74431,x74432)))+P22(f312(f312(f227(x74432),x74433),f312(f72(x74432,f225(x74432)),x74431)))
% 155.94/155.63 [7530]~P99(x75302)+E(x75301,f189(f861(x75302,a846)))+~P22(f312(f70(x75302),x75301))+P22(f312(f312(f314(x75302),f524(x75303,x75301,x75302)),x75301))+P22(f312(f312(f227(x75302),x75303),f312(f72(x75302,f115(x75302)),x75301)))
% 155.94/155.63 [7531]~P103(x75312)+E(x75311,f189(f861(x75312,a846)))+~P22(f312(f70(x75312),x75311))+P22(f312(f312(f314(x75312),f536(x75313,x75311,x75312)),x75311))+P22(f312(f312(f227(x75312),x75313),f312(f72(x75312,f225(x75312)),x75311)))
% 155.94/155.63 [7532]~P103(x75322)+E(x75321,f189(f861(x75322,a846)))+~P22(f312(f70(x75322),x75321))+P22(f312(f312(f314(x75322),f540(x75323,x75321,x75322)),x75321))+P22(f312(f312(f228(x75322),x75323),f312(f72(x75322,f225(x75322)),x75321)))
% 155.94/155.63 [7654]~P103(x76542)+E(x76541,f189(f861(x76542,a846)))+E(f312(f312(f225(x76542),f13(x76542,f225(x76542),x76541)),f13(x76542,f225(x76542),x76543)),f13(x76542,f225(x76542),x76543))+~P22(f312(f70(x76542),x76543))+~P22(f312(f312(f227(f861(x76542,a846)),x76541),x76543))
% 155.94/155.63 [7655]~P103(x76552)+E(x76551,f189(f861(x76552,a846)))+E(f312(f312(f226(x76552),f12(x76552,f226(x76552),x76551)),f12(x76552,f226(x76552),x76553)),f12(x76552,f226(x76552),x76553))+~P22(f312(f70(x76552),x76553))+~P22(f312(f312(f227(f861(x76552,a846)),x76551),x76553))
% 155.94/155.63 [7846]~E(f691(x78461,x78463,x78462),f692(x78461,x78463,x78462))+~E(f312(f53(x78462),f693(x78461,x78463,x78462)),x78461)+E(f312(f312(f90(a853),x78461),f312(f53(f861(x78462,a846)),x78463)),f312(f53(x78462),f48(f861(x78462,a846),x78463)))+~P22(f312(f70(x78462),f48(f861(x78462,a846),x78463)))+~P22(f312(f70(f861(x78462,a846)),x78463))
% 155.94/155.63 [8029]~P103(x80292)+E(x80291,f189(f861(x80292,a846)))+~P22(f312(f70(x80292),x80293))+P22(f312(f312(f227(x80292),f312(f72(x80292,f225(x80292)),x80293)),f312(f72(x80292,f225(x80292)),x80291)))+~P22(f312(f312(f227(f861(x80292,a846)),x80291),x80293))
% 155.94/155.63 [8344]~E(f691(x83441,x83443,x83442),f692(x83441,x83443,x83442))+E(f312(f312(f90(a853),x83441),f312(f53(f861(x83442,a846)),x83443)),f312(f53(x83442),f48(f861(x83442,a846),x83443)))+P22(f312(f312(f314(f861(x83442,a846)),f693(x83441,x83443,x83442)),x83443))+~P22(f312(f70(x83442),f48(f861(x83442,a846),x83443)))+~P22(f312(f70(f861(x83442,a846)),x83443))
% 155.94/155.63 [8371]~E(f312(f53(x83712),f693(x83711,x83713,x83712)),x83711)+E(f312(f312(f90(a853),x83711),f312(f53(f861(x83712,a846)),x83713)),f312(f53(x83712),f48(f861(x83712,a846),x83713)))+P22(f312(f312(f314(f861(x83712,a846)),f692(x83711,x83713,x83712)),x83713))+~P22(f312(f70(x83712),f48(f861(x83712,a846),x83713)))+~P22(f312(f70(f861(x83712,a846)),x83713))
% 155.94/155.63 [8372]~E(f312(f53(x83722),f693(x83721,x83723,x83722)),x83721)+E(f312(f312(f90(a853),x83721),f312(f53(f861(x83722,a846)),x83723)),f312(f53(x83722),f48(f861(x83722,a846),x83723)))+P22(f312(f312(f314(f861(x83722,a846)),f691(x83721,x83723,x83722)),x83723))+~P22(f312(f70(x83722),f48(f861(x83722,a846),x83723)))+~P22(f312(f70(f861(x83722,a846)),x83723))
% 155.94/155.63 [8403]~E(f312(f53(x84032),f693(x84031,x84033,x84032)),x84031)+~E(f312(f312(f115(f861(x84032,a846)),f692(x84031,x84033,x84032)),f691(x84031,x84033,x84032)),f189(f861(x84032,a846)))+E(f312(f312(f90(a853),x84031),f312(f53(f861(x84032,a846)),x84033)),f312(f53(x84032),f48(f861(x84032,a846),x84033)))+~P22(f312(f70(f861(x84032,a846)),x84033))+~P22(f312(f70(x84032),f48(f861(x84032,a846),x84033)))
% 155.94/155.63 [8645]E(f312(f312(f90(a853),x86451),f312(f53(f861(x86452,a846)),x86453)),f312(f53(x86452),f48(f861(x86452,a846),x86453)))+P22(f312(f312(f314(f861(x86452,a846)),f693(x86451,x86453,x86452)),x86453))+P22(f312(f312(f314(f861(x86452,a846)),f692(x86451,x86453,x86452)),x86453))+~P22(f312(f70(f861(x86452,a846)),x86453))+~P22(f312(f70(x86452),f48(f861(x86452,a846),x86453)))
% 155.94/155.63 [8646]E(f312(f312(f90(a853),x86461),f312(f53(f861(x86462,a846)),x86463)),f312(f53(x86462),f48(f861(x86462,a846),x86463)))+P22(f312(f312(f314(f861(x86462,a846)),f693(x86461,x86463,x86462)),x86463))+P22(f312(f312(f314(f861(x86462,a846)),f691(x86461,x86463,x86462)),x86463))+~P22(f312(f70(f861(x86462,a846)),x86463))+~P22(f312(f70(x86462),f48(f861(x86462,a846),x86463)))
% 155.94/155.63 [8671]~E(f312(f312(f115(f861(x86712,a846)),f692(x86711,x86713,x86712)),f691(x86711,x86713,x86712)),f189(f861(x86712,a846)))+E(f312(f312(f90(a853),x86711),f312(f53(f861(x86712,a846)),x86713)),f312(f53(x86712),f48(f861(x86712,a846),x86713)))+~P22(f312(f70(f861(x86712,a846)),x86713))+P22(f312(f312(f314(f861(x86712,a846)),f693(x86711,x86713,x86712)),x86713))+~P22(f312(f70(x86712),f48(f861(x86712,a846),x86713)))
% 155.94/155.63 [8931]~P93(x89312)+E(x89311,f189(f861(x89312,a846)))+~E(f312(f312(f90(x89312),f312(x89313,f544(x89311,x89313,x89312))),f312(x89313,f547(x89311,x89313,x89312))),f312(x89313,f312(f312(f90(x89312),f544(x89311,x89313,x89312)),f547(x89311,x89313,x89312))))+~P22(f312(f70(x89312),x89311))+E(f312(f72(x89312,f90(x89312)),f312(f290(x89312,x89312,x89313),x89311)),f312(x89313,f312(f72(x89312,f90(x89312)),x89311)))
% 155.94/155.63 [9847]P22(f312(f312(x98471,x98472),x98473))+P22(f312(f312(f228(a1),f349(x98471,x98473,x98472)),f354(x98471,x98473,x98472)))+P22(f312(f312(f227(a1),f354(x98471,x98473,x98472)),f2(a1)))+P22(f312(f312(x98471,f349(x98471,x98473,x98472)),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(x98471,x98473,x98472))))+~P22(f312(f300(f860(a1,a1),a65),f312(f312(f239(a1,a1),x98472),x98473)))
% 155.94/155.63 [9853]P22(f312(f312(x98531,x98532),x98533))+P22(f312(f312(f227(a1),f348(x98531,x98533,x98532)),f2(a1)))+P22(f312(f312(x98531,f347(x98531,x98533,x98532)),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(x98531,x98533,x98532))))+P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),f347(x98531,x98533,x98532)),f348(x98531,x98533,x98532))))+~P22(f312(f300(f860(a1,a1),a60),f312(f312(f239(a1,a1),x98532),x98533)))
% 155.94/155.63 [7818]~P112(x78181)+~P22(f312(f312(f227(x78181),x78182),f87(x78181)))+~P22(f312(f312(f227(x78181),f2(x78181)),x78182))+~P22(f312(f312(f227(x78181),f2(x78181)),x78183))+P22(f312(f312(f227(x78181),f312(f312(f90(x78181),x78182),x78183)),x78183))
% 155.94/155.63 [7819]~P112(x78191)+~P22(f312(f312(f227(x78191),x78193),f87(x78191)))+~P22(f312(f312(f227(x78191),f2(x78191)),x78193))+~P22(f312(f312(f227(x78191),f2(x78191)),x78192))+P22(f312(f312(f227(x78191),f312(f312(f90(x78191),x78192),x78193)),x78192))
% 155.94/155.63 [8181]~P103(x81812)+E(x81811,f189(f861(x81812,a846)))+~P22(f312(f70(x81812),x81811))+P22(f312(f312(f314(x81812),f537(x81813,x81811,x81812)),x81811))+~P22(f312(f312(f227(x81812),f312(f72(x81812,f225(x81812)),x81811)),x81813))
% 155.94/155.63 [8182]~P103(x81822)+E(x81821,f189(f861(x81822,a846)))+~P22(f312(f70(x81822),x81821))+P22(f312(f312(f314(x81822),f543(x81823,x81821,x81822)),x81821))+~P22(f312(f312(f228(x81822),f312(f72(x81822,f225(x81822)),x81821)),x81823))
% 155.94/155.63 [8183]~P103(x81832)+E(x81831,f189(f861(x81832,a846)))+~P22(f312(f70(x81832),x81831))+P22(f312(f312(f228(x81832),f543(x81833,x81831,x81832)),x81833))+~P22(f312(f312(f228(x81832),f312(f72(x81832,f225(x81832)),x81831)),x81833))
% 155.94/155.63 [8184]~P103(x81842)+E(x81841,f189(f861(x81842,a846)))+~P22(f312(f70(x81842),x81841))+P22(f312(f312(f227(x81842),f537(x81843,x81841,x81842)),x81843))+~P22(f312(f312(f227(x81842),f312(f72(x81842,f225(x81842)),x81841)),x81843))
% 155.94/155.63 [8270]~P22(f312(x82701,x82703))+P22(f312(x82701,f475(x82701,x82702)))+P22(f312(x82701,f470(x82701,x82702)))+~P22(f312(f312(f228(a1),f2(a1)),x82702))+P22(f312(x82701,f312(f312(f21(a1),f470(x82701,x82702)),f312(f312(f90(a1),f476(x82701,x82702)),x82702))))
% 155.94/155.63 [8503]~P22(f312(x85031,x85033))+P22(f312(x85031,f470(x85031,x85032)))+~P22(f312(f312(f228(a1),f2(a1)),x85032))+P22(f312(f312(f314(a1),f475(x85031,x85032)),f283(a1,f87(a1),x85032)))+P22(f312(x85031,f312(f312(f21(a1),f470(x85031,x85032)),f312(f312(f90(a1),f476(x85031,x85032)),x85032))))
% 155.94/155.63 [8692]~P22(f312(x86921,x86923))+~P22(f312(x86921,f470(x86921,x86922)))+P22(f312(x86921,f475(x86921,x86922)))+~P22(f312(f312(f228(a1),f2(a1)),x86922))+~P22(f312(x86921,f312(f312(f21(a1),f470(x86921,x86922)),f312(f312(f90(a1),f476(x86921,x86922)),x86922))))
% 155.94/155.63 [8811]~P22(f312(x88111,x88113))+~P22(f312(x88111,f470(x88111,x88112)))+~P22(f312(f312(f228(a1),f2(a1)),x88112))+P22(f312(f312(f314(a1),f475(x88111,x88112)),f283(a1,f87(a1),x88112)))+~P22(f312(x88111,f312(f312(f21(a1),f470(x88111,x88112)),f312(f312(f90(a1),f476(x88111,x88112)),x88112))))
% 155.94/155.63 [8603]~P87(x86031)+~P22(f312(f70(x86031),x86032))+E(f312(f312(f21(f861(x86031,a846)),x86032),f312(f312(f289(x86031),x86033),f189(f861(x86031,a846)))),f189(f861(x86031,a846)))+~P22(f312(f312(f314(x86031),x86033),x86032))+E(f312(f312(f115(x86031),x86033),f11(x86031,f312(f312(f21(f861(x86031,a846)),x86032),f312(f312(f289(x86031),x86033),f189(f861(x86031,a846)))))),f11(x86031,x86032))
% 155.94/155.63 [8604]~P87(x86041)+~P22(f312(f70(x86041),x86042))+E(f312(f312(f21(f861(x86041,a846)),x86042),f312(f312(f289(x86041),x86043),f189(f861(x86041,a846)))),f189(f861(x86041,a846)))+~P22(f312(f312(f314(x86041),x86043),x86042))+E(f312(f312(f124(x86041),x86043),f10(x86041,f312(f312(f21(f861(x86041,a846)),x86042),f312(f312(f289(x86041),x86043),f189(f861(x86041,a846)))))),f10(x86041,x86042))
% 155.94/155.63 [8605]~P103(x86051)+~P22(f312(f70(x86051),x86052))+E(f312(f312(f21(f861(x86051,a846)),x86052),f312(f312(f289(x86051),x86053),f189(f861(x86051,a846)))),f189(f861(x86051,a846)))+~P22(f312(f312(f314(x86051),x86053),x86052))+E(f312(f312(f226(x86051),x86053),f14(x86051,f312(f312(f21(f861(x86051,a846)),x86052),f312(f312(f289(x86051),x86053),f189(f861(x86051,a846)))))),f14(x86051,x86052))
% 155.94/155.63 [8606]~P103(x86061)+~P22(f312(f70(x86061),x86062))+E(f312(f312(f21(f861(x86061,a846)),x86062),f312(f312(f289(x86061),x86063),f189(f861(x86061,a846)))),f189(f861(x86061,a846)))+~P22(f312(f312(f314(x86061),x86063),x86062))+E(f312(f312(f225(x86061),x86063),f15(x86061,f312(f312(f21(f861(x86061,a846)),x86062),f312(f312(f289(x86061),x86063),f189(f861(x86061,a846)))))),f15(x86061,x86062))
% 155.94/155.63 [8665]~P103(x86651)+~P22(f312(f70(x86651),x86652))+E(f312(f312(f21(f861(x86651,a846)),x86652),f312(f312(f289(x86651),x86653),f189(f861(x86651,a846)))),f189(f861(x86651,a846)))+~P22(f312(f312(f314(x86651),x86653),x86652))+E(f312(f312(f226(x86651),x86653),f12(x86651,f226(x86651),f312(f312(f21(f861(x86651,a846)),x86652),f312(f312(f289(x86651),x86653),f189(f861(x86651,a846)))))),f12(x86651,f226(x86651),x86652))
% 155.94/155.63 [8666]~P103(x86661)+~P22(f312(f70(x86661),x86662))+E(f312(f312(f21(f861(x86661,a846)),x86662),f312(f312(f289(x86661),x86663),f189(f861(x86661,a846)))),f189(f861(x86661,a846)))+~P22(f312(f312(f314(x86661),x86663),x86662))+E(f312(f312(f225(x86661),x86663),f13(x86661,f225(x86661),f312(f312(f21(f861(x86661,a846)),x86662),f312(f312(f289(x86661),x86663),f189(f861(x86661,a846)))))),f13(x86661,f225(x86661),x86662))
% 155.94/155.63 [8679]~P87(x86791)+~P22(f312(f70(x86791),x86793))+~P22(f312(f70(x86791),x86792))+E(f312(f312(f115(f861(x86791,a846)),x86792),x86793),f189(f861(x86791,a846)))+E(f312(f312(f124(x86791),f10(x86791,f312(f312(f124(f861(x86791,a846)),x86792),x86793))),f10(x86791,f312(f312(f115(f861(x86791,a846)),x86792),x86793))),f312(f312(f124(x86791),f10(x86791,x86792)),f10(x86791,x86793)))
% 155.94/155.63 [8680]~P87(x86801)+~P22(f312(f70(x86801),x86803))+~P22(f312(f70(x86801),x86802))+E(f312(f312(f115(f861(x86801,a846)),x86802),x86803),f189(f861(x86801,a846)))+E(f312(f312(f115(x86801),f11(x86801,f312(f312(f124(f861(x86801,a846)),x86802),x86803))),f11(x86801,f312(f312(f115(f861(x86801,a846)),x86802),x86803))),f312(f312(f115(x86801),f11(x86801,x86802)),f11(x86801,x86803)))
% 155.94/155.63 [8681]~P103(x86811)+~P22(f312(f70(x86811),x86813))+~P22(f312(f70(x86811),x86812))+E(f312(f312(f115(f861(x86811,a846)),x86812),x86813),f189(f861(x86811,a846)))+E(f312(f312(f225(x86811),f15(x86811,f312(f312(f124(f861(x86811,a846)),x86812),x86813))),f15(x86811,f312(f312(f115(f861(x86811,a846)),x86812),x86813))),f312(f312(f225(x86811),f15(x86811,x86812)),f15(x86811,x86813)))
% 155.94/155.63 [8682]~P103(x86821)+~P22(f312(f70(x86821),x86823))+~P22(f312(f70(x86821),x86822))+E(f312(f312(f115(f861(x86821,a846)),x86822),x86823),f189(f861(x86821,a846)))+E(f312(f312(f226(x86821),f14(x86821,f312(f312(f124(f861(x86821,a846)),x86822),x86823))),f14(x86821,f312(f312(f115(f861(x86821,a846)),x86822),x86823))),f312(f312(f226(x86821),f14(x86821,x86822)),f14(x86821,x86823)))
% 155.94/155.63 [8903]~P103(x89031)+~P22(f312(f70(x89031),x89033))+~P22(f312(f70(x89031),x89032))+E(f312(f312(f115(f861(x89031,a846)),x89032),x89033),f189(f861(x89031,a846)))+E(f312(f312(f225(x89031),f13(x89031,f225(x89031),f312(f312(f124(f861(x89031,a846)),x89032),x89033))),f13(x89031,f225(x89031),f312(f312(f115(f861(x89031,a846)),x89032),x89033))),f312(f312(f225(x89031),f13(x89031,f225(x89031),x89032)),f13(x89031,f225(x89031),x89033)))
% 155.94/155.63 [8904]~P103(x89041)+~P22(f312(f70(x89041),x89043))+~P22(f312(f70(x89041),x89042))+E(f312(f312(f115(f861(x89041,a846)),x89042),x89043),f189(f861(x89041,a846)))+E(f312(f312(f226(x89041),f12(x89041,f226(x89041),f312(f312(f124(f861(x89041,a846)),x89042),x89043))),f12(x89041,f226(x89041),f312(f312(f115(f861(x89041,a846)),x89042),x89043))),f312(f312(f226(x89041),f12(x89041,f226(x89041),x89042)),f12(x89041,f226(x89041),x89043)))
% 155.94/155.63 [9683]~P117(x96833)+E(x96831,x96832)+~P22(f312(f312(f227(x96833),f2(x96833)),x96832))+~P22(f312(f312(f227(x96833),f2(x96833)),x96831))+~E(f312(f312(f240(x96833),x96831),f312(f117(a853),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(x96833),x96832),f312(f117(a853),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)))))
% 155.94/155.63 [6242]E(f495(x62421,x62422,x62423),x62424)+E(f312(x62421,x62424),f2(a853))+~E(f312(f312(f6(x62423,a853),x62421),x62422),f87(a853))+~P22(f312(f70(x62423),x62422))+~P22(f312(f312(f314(x62423),x62424),x62422))
% 155.94/155.63 [6306]E(f492(x63061,x63062,x63063),x63064)+E(f312(x63061,x63064),f2(a853))+~E(f312(f312(f6(x63063,a853),x63061),x63062),f312(a126,f2(a853)))+~P22(f312(f70(x63063),x63062))+~P22(f312(f312(f314(x63063),x63064),x63062))
% 155.94/155.63 [6409]~P103(x64091)+~P31(x64091)+P22(f312(f312(f228(x64091),x64092),f48(x64091,x64093)))+~P22(f312(f312(f228(x64091),x64092),x64094))+~P22(f312(f312(f314(x64091),x64094),x64093))
% 155.94/155.63 [6577]~P103(x65771)+~P31(x65771)+~P22(f312(f312(f228(x65771),x65774),x65773))+P22(f312(f312(f228(x65771),f49(x65771,x65772)),x65773))+~P22(f312(f312(f314(x65771),x65774),x65772))
% 155.94/155.63 [6829]~P117(x68293)+E(x68291,x68292)+~E(f312(f312(f240(x68293),x68291),f312(a126,x68294)),f312(f312(f240(x68293),x68292),f312(a126,x68294)))+~P22(f312(f312(f227(x68293),f2(x68293)),x68292))+~P22(f312(f312(f227(x68293),f2(x68293)),x68291))
% 155.94/155.63 [7043]~E(f496(x70432,x70433,x70431,x70434),x70434)+~E(f312(x70432,x70434),f87(a853))+E(f312(f312(f6(x70431,a853),x70432),x70433),f87(a853))+~P22(f312(f70(x70431),x70433))+~P22(f312(f312(f314(x70431),x70434),x70433))
% 155.94/155.63 [7050]~P107(x70504)+~P127(x70504)+E(f312(x70501,f396(x70501,x70502,x70503,x70504)),f2(x70504))+~E(f312(f312(f9(x70503,x70504),x70501),x70502),f2(x70504))+~P22(f312(f70(x70503),x70502))
% 155.94/155.63 [7137]~E(f493(x71372,x71373,x71371,x71374),x71374)+~E(f312(x71372,x71374),f312(a126,f2(a853)))+E(f312(f312(f6(x71371,a853),x71372),x71373),f312(a126,f2(a853)))+~P22(f312(f70(x71371),x71373))+~P22(f312(f312(f314(x71371),x71374),x71373))
% 155.94/155.63 [7857]~E(f312(x78572,x78574),f87(a853))+~E(f312(x78572,f496(x78572,x78573,x78571,x78574)),f2(a853))+E(f312(f312(f6(x78571,a853),x78572),x78573),f87(a853))+~P22(f312(f70(x78571),x78573))+~P22(f312(f312(f314(x78571),x78574),x78573))
% 155.94/155.63 [7900]~E(f312(x79002,x79004),f312(a126,f2(a853)))+~E(f312(x79002,f493(x79002,x79003,x79001,x79004)),f2(a853))+E(f312(f312(f6(x79001,a853),x79002),x79003),f312(a126,f2(a853)))+~P22(f312(f70(x79001),x79003))+~P22(f312(f312(f314(x79001),x79004),x79003))
% 155.94/155.63 [8471]~P103(x84711)+~P33(x84711,x84714)+P33(x84711,x84712)+~E(x84712,f312(f312(f147(x84711),x84713),x84714))+~P22(f312(f312(f227(x84711),x84713),f694(x84712,x84711,x84714,x84713)))
% 155.94/155.63 [8507]E(x85071,x85072)+E(f312(f312(f89(a1),f459(x85073,x85072,x85074,x85071)),f460(x85073,x85072,x85074,x85071)),x85071)+~E(f312(f312(f21(a1),x85071),x85074),x85072)+~P22(f312(f312(f228(a1),f2(a1)),x85074))+~P22(f312(f312(f314(a1),x85072),x85073))
% 155.94/155.63 [8508]E(x85081,x85082)+E(f312(f312(f21(a1),f447(x85083,x85082,x85084,x85081)),f448(x85083,x85082,x85084,x85081)),x85081)+~E(f312(f312(f89(a1),x85081),x85084),x85082)+~P22(f312(f312(f228(a1),f2(a1)),x85084))+~P22(f312(f312(f314(a1),x85082),x85083))
% 155.94/155.63 [8677]E(f312(x86771,f323(x86772,x86771,x86773,x86774)),x86772)+P22(f312(f312(f227(a853),x86774),f324(x86772,x86771,x86773,x86774)))+~P22(f312(f312(f227(a1),x86772),f312(x86771,x86773)))+~P22(f312(f312(f228(a853),x86774),x86773))+~P22(f312(f312(f227(a1),f312(x86771,x86774)),x86772))
% 155.94/155.63 [8678]~P103(x86781)+~P33(x86781,x86783)+P33(x86781,x86782)+~E(x86782,f312(f312(f147(x86781),x86784),x86783))+P22(f312(f312(f314(x86781),f694(x86782,x86781,x86783,x86784)),f312(f168(x86781),x86783)))
% 155.94/155.63 [8695]~P107(x86954)+~P127(x86954)+~E(f312(f312(f9(x86951,x86954),x86952),x86953),f2(x86954))+~P22(f312(f70(x86951),x86953))+P22(f312(f312(f314(x86951),f396(x86952,x86953,x86951,x86954)),x86953))
% 155.94/155.63 [8730]~E(f312(x87302,x87304),f87(a853))+E(f312(f312(f6(x87301,a853),x87302),x87303),f87(a853))+~P22(f312(f70(x87301),x87303))+~P22(f312(f312(f314(x87301),x87304),x87303))+P22(f312(f312(f314(x87301),f496(x87302,x87303,x87301,x87304)),x87303))
% 155.94/155.63 [8738]E(x87381,x87382)+~E(f312(f312(f89(a1),x87382),x87384),x87381)+~P22(f312(f312(f228(a1),f2(a1)),x87384))+~P22(f312(f312(f314(a1),x87381),x87383))+P22(f312(f312(f314(a1),f447(x87383,x87381,x87384,x87382)),x87383))
% 155.94/155.63 [8739]E(x87391,x87392)+~E(f312(f312(f21(a1),x87392),x87394),x87391)+~P22(f312(f312(f228(a1),f2(a1)),x87394))+~P22(f312(f312(f314(a1),x87391),x87393))+P22(f312(f312(f314(a1),f459(x87393,x87391,x87394,x87392)),x87393))
% 155.94/155.63 [8741]~E(f312(x87412,x87414),f312(a126,f2(a853)))+E(f312(f312(f6(x87411,a853),x87412),x87413),f312(a126,f2(a853)))+~P22(f312(f70(x87411),x87413))+~P22(f312(f312(f314(x87411),x87414),x87413))+P22(f312(f312(f314(x87411),f493(x87412,x87413,x87411,x87414)),x87413))
% 155.94/155.63 [8746]P58(x87462,x87463,x87464,x87461)+E(x87461,f189(f861(x87462,a846)))+~P22(f312(f70(x87462),x87464))+~P22(f312(f70(x87462),x87461))+P22(f312(f312(f314(x87462),f511(x87461,x87464,x87463,x87462)),x87464))
% 155.94/155.63 [8825]E(x88251,x88252)+~E(f312(f312(f89(a1),x88252),x88254),x88251)+~P22(f312(f312(f228(a1),f2(a1)),x88254))+~P22(f312(f312(f314(a1),x88251),x88253))+P22(f312(f312(f314(a1),f448(x88253,x88251,x88254,x88252)),f283(a1,f87(a1),x88254)))
% 155.94/155.63 [8826]E(x88261,x88262)+~E(f312(f312(f21(a1),x88262),x88264),x88261)+~P22(f312(f312(f228(a1),f2(a1)),x88264))+~P22(f312(f312(f314(a1),x88261),x88263))+P22(f312(f312(f314(a1),f460(x88263,x88261,x88264,x88262)),f283(a1,f87(a1),x88264)))
% 155.94/155.63 [8909]P22(f312(f312(f227(a853),x89091),f323(x89092,x89093,x89094,x89091)))+~P22(f312(f312(f227(a1),x89092),f312(x89093,x89094)))+P22(f312(f312(f227(a853),x89091),f324(x89092,x89093,x89094,x89091)))+~P22(f312(f312(f228(a853),x89091),x89094))+~P22(f312(f312(f227(a1),f312(x89093,x89091)),x89092))
% 155.94/155.63 [9017]E(f312(x90171,f323(x90172,x90171,x90173,x90174)),x90172)+~P22(f312(f312(f227(a1),x90172),f312(x90171,x90173)))+P22(f312(f312(f228(a853),f324(x90172,x90171,x90173,x90174)),x90173))+~P22(f312(f312(f228(a853),x90174),x90173))+~P22(f312(f312(f227(a1),f312(x90171,x90174)),x90172))
% 155.94/155.63 [9147]~P22(f312(f312(f227(a1),x91472),f312(x91473,x91474)))+P22(f312(f312(f227(a853),x91471),f324(x91472,x91473,x91474,x91471)))+P22(f312(f312(f227(a853),f323(x91472,x91473,x91474,x91471)),x91474))+~P22(f312(f312(f228(a853),x91471),x91474))+~P22(f312(f312(f227(a1),f312(x91473,x91471)),x91472))
% 155.94/155.63 [9148]~P22(f312(f312(f227(a1),x91482),f312(x91483,x91484)))+P22(f312(f312(f227(a853),x91481),f323(x91482,x91483,x91484,x91481)))+P22(f312(f312(f228(a853),f324(x91482,x91483,x91484,x91481)),x91484))+~P22(f312(f312(f228(a853),x91481),x91484))+~P22(f312(f312(f227(a1),f312(x91483,x91481)),x91482))
% 155.94/155.63 [9253]~P22(f312(f312(f227(a1),x92531),f312(x92532,x92533)))+P22(f312(f312(f227(a853),f323(x92531,x92532,x92533,x92534)),x92533))+~P22(f312(f312(f228(a853),x92534),x92533))+~P22(f312(f312(f227(a1),f312(x92532,x92534)),x92531))+P22(f312(f312(f228(a853),f324(x92531,x92532,x92533,x92534)),x92533))
% 155.94/155.63 [9332]E(x93321,f189(f861(x93322,a846)))+~P22(f312(f70(x93322),x93324))+~P22(f312(f70(x93322),x93321))+P22(f312(f312(f314(f860(f861(x93322,a846),f861(x93322,a846))),f312(f312(f239(f861(x93322,a846),f861(x93322,a846)),x93324),x93321)),f303(x93322,x93323)))+P22(f312(f312(f314(x93322),f516(x93323,x93321,x93324,x93322)),x93324))
% 155.94/155.63 [9333]E(x93331,f189(f861(x93332,a846)))+~P22(f312(f70(x93332),x93334))+~P22(f312(f70(x93332),x93331))+P22(f312(f312(f314(f860(f861(x93332,a846),f861(x93332,a846))),f312(f312(f239(f861(x93332,a846),f861(x93332,a846)),x93334),x93331)),f303(x93332,x93333)))+P22(f312(f312(f314(x93332),f741(x93333,x93331,x93334,x93332)),x93334))
% 155.94/155.63 [9994]E(f312(x99941,f323(x99942,x99941,x99943,x99944)),x99942)+~P22(f312(f312(f227(a1),x99942),f312(x99941,x99943)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x99941,f312(f312(f89(a853),f324(x99942,x99941,x99943,x99944)),f87(a853)))),f312(x99941,f324(x99942,x99941,x99943,x99944))))),f87(a1)))+~P22(f312(f312(f228(a853),x99944),x99943))+~P22(f312(f312(f227(a1),f312(x99941,x99944)),x99942))
% 155.94/155.63 [9995]~P22(f312(f312(f227(a1),x99952),f312(x99953,x99954)))+P22(f312(f312(f227(a853),x99951),f323(x99952,x99953,x99954,x99951)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x99953,f312(f312(f89(a853),f324(x99952,x99953,x99954,x99951)),f87(a853)))),f312(x99953,f324(x99952,x99953,x99954,x99951))))),f87(a1)))+~P22(f312(f312(f228(a853),x99951),x99954))+~P22(f312(f312(f227(a1),f312(x99953,x99951)),x99952))
% 155.94/155.63 [9996]~P22(f312(f312(f227(a1),x99961),f312(x99962,x99963)))+~P22(f312(f312(f227(a1),f312(f84(a1),f312(f312(f21(a1),f312(x99962,f312(f312(f89(a853),f324(x99961,x99962,x99963,x99964)),f87(a853)))),f312(x99962,f324(x99961,x99962,x99963,x99964))))),f87(a1)))+~P22(f312(f312(f228(a853),x99964),x99963))+~P22(f312(f312(f227(a1),f312(x99962,x99964)),x99961))+P22(f312(f312(f227(a853),f323(x99961,x99962,x99963,x99964)),x99963))
% 155.94/155.63 [7107]~P66(x71071)+P22(f312(f312(f228(x71071),x71072),f2(x71071)))+~P22(f312(f312(f228(x71071),x71073),f2(x71071)))+P22(f312(f312(f228(x71071),f2(x71071)),x71072))+P22(f312(f312(f228(x71071),x71073),f312(f312(f268(x71071),x71074),x71072)))
% 155.94/155.63 [7108]~P66(x71081)+P22(f312(f312(f228(x71081),x71082),f2(x71081)))+~P22(f312(f312(f227(x71081),x71083),f2(x71081)))+P22(f312(f312(f228(x71081),f2(x71081)),x71082))+P22(f312(f312(f227(x71081),x71083),f312(f312(f268(x71081),x71084),x71082)))
% 155.94/155.63 [7344]~P66(x73441)+P22(f312(f312(f228(x73441),x73442),f2(x73441)))+P22(f312(f312(f228(x73441),x73443),f2(x73441)))+P22(f312(f312(f228(x73441),f2(x73441)),x73443))+~P22(f312(f312(f228(x73441),x73442),f312(f312(f268(x73441),x73444),x73443)))
% 155.94/155.63 [7345]~P66(x73451)+P22(f312(f312(f228(x73451),x73452),f2(x73451)))+P22(f312(f312(f227(x73451),x73453),f2(x73451)))+P22(f312(f312(f228(x73451),f2(x73451)),x73452))+~P22(f312(f312(f227(x73451),x73453),f312(f312(f268(x73451),x73454),x73452)))
% 155.94/155.63 [7462]E(x74621,x74622)+~E(f312(f312(f161(x74623),x74624),x74621),f312(f312(f161(x74623),x74624),x74622))+~P22(f312(f133(x74623),x74624))+~P22(f312(f312(f228(a853),x74622),f312(f190(f854(x74623)),x74624)))+~P22(f312(f312(f228(a853),x74621),f312(f190(f854(x74623)),x74624)))
% 155.94/155.63 [7820]~P66(x78201)+~P22(f312(f312(f228(x78201),x78203),f2(x78201)))+P22(f312(f312(f228(x78201),f2(x78201)),x78202))+~P22(f312(f312(f228(x78201),x78204),f312(f312(f90(x78201),x78203),x78202)))+P22(f312(f312(f228(x78201),x78203),f312(f312(f268(x78201),x78204),x78202)))
% 155.94/155.63 [7821]~P66(x78211)+~P22(f312(f312(f227(x78211),x78213),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)))
% 155.94/155.63 [7822]~P66(x78221)+~P22(f312(f312(f228(x78221),x78222),f2(x78221)))+P22(f312(f312(f228(x78221),f2(x78221)),x78222))+~P22(f312(f312(f228(x78221),x78224),f312(f312(f90(x78221),x78223),x78222)))+P22(f312(f312(f228(x78221),x78223),f312(f312(f268(x78221),x78224),x78222)))
% 155.94/155.63 [7823]~P66(x78231)+~P22(f312(f312(f228(x78231),x78232),f2(x78231)))+P22(f312(f312(f228(x78231),f2(x78231)),x78232))+~P22(f312(f312(f228(x78231),x78234),f312(f312(f268(x78231),x78233),x78232)))+P22(f312(f312(f228(x78231),x78233),f312(f312(f90(x78231),x78234),x78232)))
% 155.94/155.63 [7824]~P66(x78241)+~P22(f312(f312(f228(x78241),x78242),f2(x78241)))+P22(f312(f312(f228(x78241),f2(x78241)),x78242))+~P22(f312(f312(f227(x78241),x78244),f312(f312(f90(x78241),x78243),x78242)))+P22(f312(f312(f227(x78241),x78243),f312(f312(f268(x78241),x78244),x78242)))
% 155.94/155.63 [7825]~P66(x78251)+~P22(f312(f312(f228(x78251),x78252),f2(x78251)))+P22(f312(f312(f228(x78251),f2(x78251)),x78252))+~P22(f312(f312(f227(x78251),x78254),f312(f312(f268(x78251),x78253),x78252)))+P22(f312(f312(f227(x78251),x78253),f312(f312(f90(x78251),x78254),x78252)))
% 155.94/155.63 [7966]~P103(x79661)+~P33(x79661,x79662)+~P22(f312(f312(f227(a853),x79663),x79664))+P22(f312(f312(f227(x79661),f312(f312(f161(x79661),x79662),x79663)),f312(f312(f161(x79661),x79662),x79664)))+~P22(f312(f312(f228(a853),x79664),f312(f190(f854(x79661)),x79662)))
% 155.94/155.63 [8020]~P117(x80201)+~P22(f312(f312(f228(x80201),x80202),f87(x80201)))+~P22(f312(f312(f228(x80201),f2(x80201)),x80202))+~P22(f312(f312(f228(a853),x80204),x80203))+P22(f312(f312(f228(x80201),f312(f312(f240(x80201),x80202),x80203)),f312(f312(f240(x80201),x80202),x80204)))
% 155.94/155.63 [8021]~P117(x80211)+~P22(f312(f312(f227(x80211),x80212),f87(x80211)))+~P22(f312(f312(f227(x80211),f2(x80211)),x80212))+~P22(f312(f312(f227(a853),x80214),x80213))+P22(f312(f312(f227(x80211),f312(f312(f240(x80211),x80212),x80213)),f312(f312(f240(x80211),x80212),x80214)))
% 155.94/155.63 [8022]~P117(x80221)+~P22(f312(f312(f227(x80221),f2(x80221)),x80222))+~P22(f312(f312(f228(a853),f2(a853)),x80223))+~P22(f312(f312(f228(x80221),x80222),x80224))+P22(f312(f312(f228(x80221),f312(f312(f240(x80221),x80222),x80223)),f312(f312(f240(x80221),x80224),x80223)))
% 155.94/155.63 [8042]~P103(x80421)+~P33(x80421,f312(f165(x80421),x80422))+~P22(f312(f312(f227(a853),x80424),x80423))+P22(f312(f312(f227(x80421),f312(f312(f161(x80421),x80422),x80423)),f312(f312(f161(x80421),x80422),x80424)))+~P22(f312(f312(f228(a853),x80423),f312(f190(f854(x80421)),x80422)))
% 155.94/155.63 [8292]~P67(x82921)+~P22(f312(f312(f228(x82921),x82922),f2(x82921)))+~P22(f312(f312(f228(x82921),x82923),x82924))+~P22(f312(f312(f228(x82921),f2(x82921)),f312(f312(f90(x82921),x82923),x82924)))+P22(f312(f312(f228(x82921),f312(f312(f268(x82921),x82922),x82923)),f312(f312(f268(x82921),x82922),x82924)))
% 155.94/155.63 [8293]~P66(x82931)+~P22(f312(f312(f227(x82931),x82932),f2(x82931)))+~P22(f312(f312(f227(x82931),x82933),x82934))+~P22(f312(f312(f228(x82931),f2(x82931)),f312(f312(f90(x82931),x82933),x82934)))+P22(f312(f312(f227(x82931),f312(f312(f268(x82931),x82932),x82933)),f312(f312(f268(x82931),x82932),x82934)))
% 155.94/155.63 [8304]~P67(x83041)+~P22(f312(f312(f228(x83041),x83044),x83043))+~P22(f312(f312(f228(x83041),f2(x83041)),x83042))+~P22(f312(f312(f228(x83041),f2(x83041)),f312(f312(f90(x83041),x83043),x83044)))+P22(f312(f312(f228(x83041),f312(f312(f268(x83041),x83042),x83043)),f312(f312(f268(x83041),x83042),x83044)))
% 155.94/155.63 [8305]~P67(x83051)+~P22(f312(f312(f227(x83051),x83054),x83053))+~P22(f312(f312(f227(x83051),f2(x83051)),x83052))+~P22(f312(f312(f228(x83051),f2(x83051)),f312(f312(f90(x83051),x83053),x83054)))+P22(f312(f312(f227(x83051),f312(f312(f268(x83051),x83052),x83053)),f312(f312(f268(x83051),x83052),x83054)))
% 155.94/155.63 [8417]P22(f312(x84171,x84172))+~P22(f312(f70(x84174),x84172))+P22(f312(x84171,f506(x84171,x84173,x84172,x84174)))+~P22(f312(x84171,f189(f861(x84174,a846))))+~P22(f312(f312(f227(f861(x84174,a846)),x84172),x84173))
% 155.94/155.63 [8425]P22(f312(x84251,x84252))+P22(f312(f70(x84253),f506(x84251,x84254,x84252,x84253)))+~P22(f312(f70(x84253),x84252))+~P22(f312(x84251,f189(f861(x84253,a846))))+~P22(f312(f312(f227(f861(x84253,a846)),x84252),x84254))
% 155.94/155.63 [8673]E(f312(f312(f89(a1),f467(x86731,x86732,x86733,x86734)),f461(x86731,x86732,x86733,x86734)),x86734)+~P22(f312(f312(f228(a1),f2(a1)),x86733))+~P22(f312(f312(f228(a1),x86732),x86734))+~P22(f312(f312(f314(a1),x86732),x86731))+P22(f312(f312(f228(a1),x86732),f312(f312(f21(a1),x86734),x86733)))
% 155.94/155.63 [8888]~P22(f312(f312(f228(a1),f2(a1)),x88883))+~P22(f312(f312(f228(a1),x88882),x88884))+~P22(f312(f312(f314(a1),x88882),x88881))+P22(f312(f312(f314(a1),f467(x88881,x88882,x88883,x88884)),x88881))+P22(f312(f312(f228(a1),x88882),f312(f312(f21(a1),x88884),x88883)))
% 155.94/155.63 [8902]P22(f312(x89021,x89022))+~P22(f312(f70(x89023),x89022))+P22(f312(f312(f314(x89023),f507(x89021,x89024,x89022,x89023)),x89024))+~P22(f312(x89021,f189(f861(x89023,a846))))+~P22(f312(f312(f227(f861(x89023,a846)),x89022),x89024))
% 155.94/155.63 [8919]E(f312(f312(f89(a1),f449(x89191,x89192,x89193,x89194)),f450(x89191,x89192,x89193,x89194)),x89194)+~P22(f312(f312(f228(a1),f2(a1)),x89193))+~P22(f312(f312(f227(a1),x89192),x89194))+P22(f312(f312(f227(a1),x89192),f312(f312(f21(a1),x89194),x89193)))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x89192),f87(a1))),x89191))
% 155.94/155.63 [8969]~P22(f312(f312(f228(a1),f2(a1)),x89693))+~P22(f312(f312(f228(a1),x89691),x89692))+~P22(f312(f312(f314(a1),x89691),x89694))+P22(f312(f312(f314(a1),f461(x89694,x89691,x89693,x89692)),f283(a1,f87(a1),x89693)))+P22(f312(f312(f228(a1),x89691),f312(f312(f21(a1),x89692),x89693)))
% 155.94/155.63 [9063]~P22(f312(f312(f228(a1),f2(a1)),x90633))+~P22(f312(f312(f227(a1),x90632),x90634))+P22(f312(f312(f314(a1),f449(x90631,x90632,x90633,x90634)),x90631))+P22(f312(f312(f227(a1),x90632),f312(f312(f21(a1),x90634),x90633)))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x90632),f87(a1))),x90631))
% 155.94/155.63 [9101]~P22(f312(f312(f228(a1),f2(a1)),x91013))+~P22(f312(f312(f227(a1),x91011),x91012))+P22(f312(f312(f314(a1),f450(x91014,x91011,x91013,x91012)),f283(a1,f87(a1),x91013)))+P22(f312(f312(f227(a1),x91011),f312(f312(f21(a1),x91012),x91013)))+~P22(f312(f312(f314(a1),f312(f312(f21(a1),x91011),f87(a1))),x91014))
% 155.94/155.63 [9336]P22(f312(x93361,x93362))+~P22(f312(f312(f314(x93363),f507(x93361,x93364,x93362,x93363)),f506(x93361,x93364,x93362,x93363)))+~P22(f312(f70(x93363),x93362))+~P22(f312(x93361,f189(f861(x93363,a846))))+~P22(f312(f312(f227(f861(x93363,a846)),x93362),x93364))
% 155.94/155.63 [9545]P22(f312(x95451,x95452))+~P22(f312(f70(x95453),x95452))+~P22(f312(x95451,f312(f312(f289(x95453),f507(x95451,x95454,x95452,x95453)),f506(x95451,x95454,x95452,x95453))))+~P22(f312(x95451,f189(f861(x95453,a846))))+~P22(f312(f312(f227(f861(x95453,a846)),x95452),x95454))
% 155.94/155.63 [7597]~P66(x75971)+P22(f312(f312(f228(x75971),x75972),f2(x75971)))+P22(f312(f312(f228(x75971),f2(x75971)),x75972))+~P22(f312(f312(f228(x75971),f2(x75971)),x75974))+P22(f312(f312(f228(x75971),f312(f312(f268(x75971),x75973),x75972)),x75974))
% 155.94/155.63 [7598]~P66(x75981)+P22(f312(f312(f228(x75981),x75982),f2(x75981)))+~P22(f312(f312(f227(x75981),f2(x75981)),x75984))+P22(f312(f312(f228(x75981),f2(x75981)),x75982))+P22(f312(f312(f227(x75981),f312(f312(f268(x75981),x75983),x75982)),x75984))
% 155.94/155.63 [7810]~P31(x78101)+~P49(x78101,x78101,x78104)+~E(x78103,f110(x78101,x78104))+P22(f312(f312(f227(x78101),x78102),x78103))+~P22(f312(f312(f227(x78101),x78102),f312(x78104,f312(f312(f124(x78101),x78102),x78103))))
% 155.94/155.63 [7872]~P22(f312(f312(f227(a1),x78724),f2(a1)))+~E(x78722,f312(f312(f89(a1),f312(f312(f90(a1),x78721),x78723)),x78724))+P22(f312(f312(f228(a1),f2(a1)),x78721))+~P22(f312(f312(f228(a1),x78721),x78724))+P22(f312(f57(x78722,x78721),f312(f312(f239(a1,a1),x78723),x78724)))
% 155.94/155.63 [7909]~P22(f312(x79091,x79094))+P22(f312(x79091,f838(x79092,x79091,x79093)))+~P22(f312(f312(f228(a1),f2(a1)),x79093))+~P22(f312(f312(f227(a1),f2(a1)),x79092))+P22(f312(x79091,f312(f312(f21(a1),x79094),f312(f312(f90(a1),x79092),x79093))))
% 155.94/155.63 [7910]~P22(f312(x79101,x79104))+P22(f312(x79101,f840(x79102,x79101,x79103)))+~P22(f312(f312(f228(a1),f2(a1)),x79103))+~P22(f312(f312(f227(a1),f2(a1)),x79102))+P22(f312(x79101,f312(f312(f89(a1),x79104),f312(f312(f90(a1),x79102),x79103))))
% 155.94/155.63 [7911]~P66(x79111)+P22(f312(f312(f228(x79111),x79112),f2(x79111)))+P22(f312(f312(f228(x79111),f2(x79111)),x79112))+P22(f312(f312(f228(x79111),f2(x79111)),x79113))+~P22(f312(f312(f228(x79111),f312(f312(f268(x79111),x79114),x79112)),x79113))
% 155.94/155.63 [7912]~P66(x79121)+P22(f312(f312(f228(x79121),x79122),f2(x79121)))+P22(f312(f312(f228(x79121),f2(x79121)),x79122))+P22(f312(f312(f227(x79121),f2(x79121)),x79123))+~P22(f312(f312(f227(x79121),f312(f312(f268(x79121),x79124),x79122)),x79123))
% 155.94/155.63 [7960]~E(x79601,f312(f312(f89(a1),f312(f312(f90(a1),x79602),x79603)),x79604))+~P22(f312(f312(f228(a1),f2(a1)),x79602))+~P22(f312(f312(f227(a1),f2(a1)),x79604))+~P22(f312(f312(f228(a1),x79604),x79602))+P22(f312(f57(x79601,x79602),f312(f312(f239(a1,a1),x79603),x79604)))
% 155.94/155.63 [8086]~P66(x80861)+P22(f312(f312(f228(x80861),x80862),f2(x80861)))+~P22(f312(f312(f228(x80861),f2(x80861)),x80864))+~P22(f312(f312(f228(x80861),x80863),f312(f312(f90(x80861),x80864),x80862)))+P22(f312(f312(f228(x80861),f312(f312(f268(x80861),x80863),x80862)),x80864))
% 155.94/155.63 [8087]~P66(x80871)+P22(f312(f312(f228(x80871),x80872),f2(x80871)))+~P22(f312(f312(f227(x80871),f2(x80871)),x80874))+~P22(f312(f312(f227(x80871),x80873),f312(f312(f90(x80871),x80874),x80872)))+P22(f312(f312(f227(x80871),f312(f312(f268(x80871),x80873),x80872)),x80874))
% 155.94/155.63 [8169]~P66(x81691)+P22(f312(f312(f228(x81691),x81692),f2(x81691)))+~P22(f312(f312(f228(x81691),x81693),f2(x81691)))+P22(f312(f312(f228(x81691),x81693),f312(f312(f268(x81691),x81694),x81692)))+~P22(f312(f312(f228(x81691),f312(f312(f90(x81691),x81693),x81692)),x81694))
% 155.94/155.63 [8170]~P66(x81701)+P22(f312(f312(f228(x81701),x81702),f2(x81701)))+~P22(f312(f312(f227(x81701),x81703),f2(x81701)))+P22(f312(f312(f227(x81701),x81703),f312(f312(f268(x81701),x81704),x81702)))+~P22(f312(f312(f227(x81701),f312(f312(f90(x81701),x81703),x81702)),x81704))
% 155.94/155.63 [8332]~P66(x83321)+~P22(f312(f312(f228(x83321),x83322),f2(x83321)))+P22(f312(f312(f228(x83321),f2(x83321)),x83322))+~P22(f312(f312(f228(x83321),f312(f312(f268(x83321),x83324),x83322)),x83323))+P22(f312(f312(f228(x83321),f312(f312(f90(x83321),x83323),x83322)),x83324))
% 155.94/155.63 [8333]~P66(x83331)+~P22(f312(f312(f228(x83331),x83332),f2(x83331)))+P22(f312(f312(f228(x83331),f2(x83331)),x83332))+~P22(f312(f312(f228(x83331),f312(f312(f90(x83331),x83334),x83332)),x83333))+P22(f312(f312(f228(x83331),f312(f312(f268(x83331),x83333),x83332)),x83334))
% 155.94/155.63 [8334]~P66(x83341)+~P22(f312(f312(f228(x83341),x83342),f2(x83341)))+P22(f312(f312(f228(x83341),f2(x83341)),x83342))+~P22(f312(f312(f227(x83341),f312(f312(f268(x83341),x83344),x83342)),x83343))+P22(f312(f312(f227(x83341),f312(f312(f90(x83341),x83343),x83342)),x83344))
% 155.94/155.63 [8335]~P66(x83351)+~P22(f312(f312(f228(x83351),x83352),f2(x83351)))+P22(f312(f312(f228(x83351),f2(x83351)),x83352))+~P22(f312(f312(f227(x83351),f312(f312(f90(x83351),x83354),x83352)),x83353))+P22(f312(f312(f227(x83351),f312(f312(f268(x83351),x83353),x83352)),x83354))
% 155.94/155.63 [8359]~P66(x83591)+~P22(f312(f312(f228(x83591),f2(x83591)),x83594))+P22(f312(f312(f228(x83591),f2(x83591)),x83592))+~P22(f312(f312(f228(x83591),f312(f312(f90(x83591),x83594),x83592)),x83593))+P22(f312(f312(f228(x83591),f312(f312(f268(x83591),x83593),x83592)),x83594))
% 155.94/155.63 [8360]~P66(x83601)+~P22(f312(f312(f227(x83601),f2(x83601)),x83604))+P22(f312(f312(f228(x83601),f2(x83601)),x83602))+~P22(f312(f312(f227(x83601),f312(f312(f90(x83601),x83604),x83602)),x83603))+P22(f312(f312(f227(x83601),f312(f312(f268(x83601),x83603),x83602)),x83604))
% 155.94/155.63 [8433]~P66(x84331)+~P22(f312(f312(f228(x84331),x84334),f2(x84331)))+~P22(f312(f312(f228(x84331),x84333),f312(f312(f90(x84331),x84332),x84334)))+P22(f312(f312(f228(x84331),x84332),f312(f312(f268(x84331),x84333),x84334)))+~P22(f312(f312(f228(x84331),f312(f312(f90(x84331),x84332),x84334)),x84333))
% 155.94/155.63 [8434]~P66(x84341)+~P22(f312(f312(f228(x84341),x84342),f2(x84341)))+~P22(f312(f312(f228(x84341),x84343),f312(f312(f90(x84341),x84342),x84344)))+P22(f312(f312(f228(x84341),x84342),f312(f312(f268(x84341),x84343),x84344)))+~P22(f312(f312(f228(x84341),f312(f312(f90(x84341),x84342),x84344)),x84343))
% 155.94/155.63 [8435]~P66(x84351)+~P22(f312(f312(f228(x84351),x84354),f2(x84351)))+~P22(f312(f312(f227(x84351),x84353),f312(f312(f90(x84351),x84352),x84354)))+P22(f312(f312(f227(x84351),x84352),f312(f312(f268(x84351),x84353),x84354)))+~P22(f312(f312(f227(x84351),f312(f312(f90(x84351),x84352),x84354)),x84353))
% 155.94/155.63 [8436]~P66(x84361)+~P22(f312(f312(f227(x84361),x84362),f2(x84361)))+~P22(f312(f312(f227(x84361),x84363),f312(f312(f90(x84361),x84362),x84364)))+P22(f312(f312(f227(x84361),x84362),f312(f312(f268(x84361),x84363),x84364)))+~P22(f312(f312(f227(x84361),f312(f312(f90(x84361),x84362),x84364)),x84363))
% 155.94/155.63 [8550]~P66(x85501)+~P22(f312(f312(f228(x85501),x85503),f2(x85501)))+~P22(f312(f312(f228(x85501),x85502),f312(f312(f90(x85501),x85504),x85503)))+~P22(f312(f312(f228(x85501),f312(f312(f90(x85501),x85504),x85503)),x85502))+P22(f312(f312(f228(x85501),f312(f312(f268(x85501),x85502),x85503)),x85504))
% 155.94/155.63 [8551]~P66(x85511)+~P22(f312(f312(f228(x85511),x85513),f2(x85511)))+~P22(f312(f312(f227(x85511),x85512),f312(f312(f90(x85511),x85514),x85513)))+~P22(f312(f312(f227(x85511),f312(f312(f90(x85511),x85514),x85513)),x85512))+P22(f312(f312(f227(x85511),f312(f312(f268(x85511),x85512),x85513)),x85514))
% 155.94/155.63 [8565]~P66(x85651)+~P22(f312(f312(f228(x85651),f2(x85651)),x85654))+~P22(f312(f312(f228(x85651),x85652),f312(f312(f90(x85651),x85654),x85653)))+~P22(f312(f312(f228(x85651),f312(f312(f90(x85651),x85654),x85653)),x85652))+P22(f312(f312(f228(x85651),f312(f312(f268(x85651),x85652),x85653)),x85654))
% 155.94/155.63 [8566]~P66(x85661)+~P22(f312(f312(f227(x85661),f2(x85661)),x85664))+~P22(f312(f312(f227(x85661),x85662),f312(f312(f90(x85661),x85664),x85663)))+~P22(f312(f312(f227(x85661),f312(f312(f90(x85661),x85664),x85663)),x85662))+P22(f312(f312(f227(x85661),f312(f312(f268(x85661),x85662),x85663)),x85664))
% 155.94/155.63 [8732]E(f312(f312(f21(a1),f468(x87321,x87322,x87323,x87324)),f469(x87321,x87322,x87323,x87324)),x87324)+~P22(f312(f312(f228(a1),f2(a1)),x87323))+~P22(f312(f312(f314(a1),x87322),x87321))+~P22(f312(f312(f228(a1),x87324),x87322))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x87324),x87323)),x87322))
% 155.94/155.63 [8807]~P22(f312(x88071,x88072))+~P22(f312(f312(f228(a1),f2(a1)),x88074))+~P22(f312(f312(f227(a1),f2(a1)),x88073))+~P22(f312(x88071,f312(f312(f89(a1),f840(x88073,x88071,x88074)),x88074)))+P22(f312(x88071,f312(f312(f89(a1),x88072),f312(f312(f90(a1),x88073),x88074))))
% 155.94/155.63 [8808]~P22(f312(x88081,x88082))+~P22(f312(f312(f228(a1),f2(a1)),x88084))+~P22(f312(f312(f227(a1),f2(a1)),x88083))+~P22(f312(x88081,f312(f312(f21(a1),f838(x88083,x88081,x88084)),x88084)))+P22(f312(x88081,f312(f312(f21(a1),x88082),f312(f312(f90(a1),x88083),x88084))))
% 155.94/155.63 [8964]~P22(f312(f312(f228(a1),f2(a1)),x89643))+~P22(f312(f312(f314(a1),x89642),x89641))+~P22(f312(f312(f228(a1),x89644),x89642))+P22(f312(f312(f314(a1),f468(x89641,x89642,x89643,x89644)),x89641))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x89644),x89643)),x89642))
% 155.94/155.63 [8982]E(f312(f312(f21(a1),f451(x89821,x89822,x89823,x89824)),f452(x89821,x89822,x89823,x89824)),x89824)+~P22(f312(f312(f228(a1),f2(a1)),x89823))+~P22(f312(f312(f227(a1),x89824),x89822))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x89822),f87(a1))),x89821))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x89824),x89823)),x89822))
% 155.94/155.63 [9007]~P22(f312(f312(f228(a1),f2(a1)),x90072))+~P22(f312(f312(f314(a1),x90073),x90074))+~P22(f312(f312(f228(a1),x90071),x90073))+P22(f312(f312(f314(a1),f469(x90074,x90073,x90072,x90071)),f283(a1,f87(a1),x90072)))+P22(f312(f312(f228(a1),f312(f312(f89(a1),x90071),x90072)),x90073))
% 155.94/155.63 [9096]~P22(f312(f312(f228(a1),f2(a1)),x90963))+~P22(f312(f312(f227(a1),x90964),x90962))+P22(f312(f312(f314(a1),f451(x90961,x90962,x90963,x90964)),x90961))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x90962),f87(a1))),x90961))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x90964),x90963)),x90962))
% 155.94/155.63 [9143]~P22(f312(f312(f228(a1),f2(a1)),x91432))+~P22(f312(f312(f227(a1),x91431),x91433))+P22(f312(f312(f314(a1),f452(x91434,x91433,x91432,x91431)),f283(a1,f87(a1),x91432)))+~P22(f312(f312(f314(a1),f312(f312(f89(a1),x91433),f87(a1))),x91434))+P22(f312(f312(f227(a1),f312(f312(f89(a1),x91431),x91432)),x91433))
% 155.94/155.63 [9426]~P41(x94261,x94263)+~P20(x94261,x94264)+P41(x94261,f312(f312(f124(f861(f860(x94261,x94261),a846)),x94262),x94263))+~P22(f312(f312(f227(f861(f860(x94261,x94261),a846)),x94262),f312(f246(f861(f860(x94261,x94261),a846),f861(f860(x94261,x94261),a846)),x94264)))+~P22(f312(f312(f227(f861(f860(x94261,x94261),a846)),x94263),f312(f248(f861(f860(x94261,x94261),a846),f861(f860(x94261,x94261),a846)),x94264)))
% 155.94/155.63 [9709]~E(f312(f351(x97091,x97094,x97093,x97092),f353(x97091,x97094,x97093,x97092)),f192(f854(a308)))+P22(f312(f312(f228(a1),f352(x97091,x97094,x97093,x97092)),f353(x97091,x97094,x97093,x97092)))+P22(f312(f312(f312(x97091,x97092),x97093),x97094))+P22(f312(f312(f312(x97091,f351(x97091,x97094,x97093,x97092)),f352(x97091,x97094,x97093,x97092)),f312(f312(f89(a1),f353(x97091,x97094,x97093,x97092)),f87(a1))))+~P22(f312(f300(f860(f861(a1,f857(f854(a308))),f860(a1,a1)),a297),f312(f312(f239(f861(a1,f857(f854(a308))),f860(a1,a1)),x97092),f312(f312(f239(a1,a1),x97093),x97094))))
% 155.94/155.63 [9816]~P13(x98162,x98164,x98163)+E(x98161,f189(f861(x98162,a846)))+~P22(f312(f70(x98162),x98161))+P22(f312(f312(f314(x98162),f312(x98163,x98161)),x98161))+~P22(f312(f312(f314(x98162),f312(f312(x98164,f383(x98161,x98163,x98164,x98162)),f384(x98161,x98163,x98164,x98162))),f312(f312(f289(x98162),f383(x98161,x98163,x98164,x98162)),f312(f312(f289(x98162),f384(x98161,x98163,x98164,x98162)),f189(f861(x98162,a846))))))
% 155.94/155.63 [8462]~P31(x84621)+~P49(x84621,x84621,x84624)+~E(x84622,f109(x84621,x84624))+P22(f312(f312(f227(x84621),x84622),x84623))+~P22(f312(f312(f227(x84621),f312(x84624,f312(f312(f115(x84621),x84622),x84623))),x84623))
% 155.94/155.63 [9744]~P105(x97442)+~P63(x97441)+~P22(f312(f312(f227(f861(x97441,x97442)),x97443),x97444))+P22(f312(f312(f228(f861(x97441,x97442)),x97443),x97444))+~P22(f312(f66(x97441),f312(f312(f8(a846,a846,x97441),a307),f312(f312(f18(x97441,x97442,a846),f312(f312(f8(x97442,f861(x97442,a846),x97441),a309),x97443)),x97444))))
% 155.94/155.63 [9343]~P54(x93431,x93431,x93434)+P22(f312(f312(f314(f860(x93431,x93431)),f312(f312(f239(x93431,x93431),x93432),x93433)),f287(x93431,x93434)))+P22(f312(f312(f314(f860(x93431,x93431)),f312(f312(f239(x93431,x93431),x93433),x93432)),f287(x93431,x93434)))+~P22(f312(f312(f314(f860(x93431,x93431)),f312(f312(f239(x93431,x93431),x93435),x93432)),f287(x93431,x93434)))+~P22(f312(f312(f314(f860(x93431,x93431)),f312(f312(f239(x93431,x93431),x93435),x93433)),f287(x93431,x93434)))
% 155.94/155.63 [5547]E(x55471,f2(a853))+~E(f312(f53(x55472),x55475),x55471)+E(f312(f53(x55472),x55473),f312(a126,x55471))+~E(x55473,f312(f312(f289(x55472),x55474),x55475))+P22(f312(f312(f314(x55472),x55474),x55475))
% 155.94/155.63 [5669]~P65(x56692)+E(x56691,f2(x56692))+E(x56693,f2(x56692))+~E(f312(f312(f268(x56692),x56694),x56693),f312(f312(f268(x56692),x56695),x56691))+E(f312(f312(f90(x56692),x56694),x56691),f312(f312(f90(x56692),x56695),x56693))
% 155.94/155.63 [5670]~P65(x56702)+E(x56701,f2(x56702))+E(x56703,f2(x56702))+~E(f312(f312(f90(x56702),x56704),x56703),f312(f312(f90(x56702),x56705),x56701))+E(f312(f312(f268(x56702),x56704),x56701),f312(f312(f268(x56702),x56705),x56703))
% 155.94/155.63 [5730]~E(f312(f53(x57301),x57305),x57303)+~E(x57305,f189(f861(x57301,a846)))+E(f312(f53(x57301),x57302),f312(a126,x57303))+~E(x57302,f312(f312(f289(x57301),x57304),x57305))+P22(f312(f312(f314(x57301),x57304),x57305))
% 155.94/155.63 [5955]~P107(x59552)+~E(f312(x59553,x59555),f2(x59552))+E(f312(f312(f9(x59551,x59552),x59553),x59554),f2(x59552))+~P22(f312(f70(x59551),x59554))+~P22(f312(f312(f314(x59551),x59555),x59554))
% 155.94/155.63 [6316]~P103(x63163)+E(x63161,x63162)+~E(f312(f282(x63163,x63164),x63161),f312(f282(x63163,x63165),x63162))+~P22(f312(f312(f228(x63163),x63165),x63162))+~P22(f312(f312(f228(x63163),x63164),x63161))
% 155.94/155.63 [6317]~P103(x63173)+E(x63171,x63172)+~E(f312(f282(x63173,x63171),x63174),f312(f282(x63173,x63172),x63175))+~P22(f312(f312(f228(x63173),x63172),x63175))+~P22(f312(f312(f228(x63173),x63171),x63174))
% 155.94/155.63 [6476]~P105(x64761)+~P49(x64765,x64761,x64762)+~P105(x64765)+P22(f312(f312(f227(x64761),f312(x64762,x64763)),f312(x64762,x64764)))+~P22(f312(f312(f227(x64765),x64763),x64764))
% 155.94/155.63 [7360]~P103(x73601)+~P33(x73601,f312(f312(f129(x73601),x73604),x73605))+~P22(f312(f312(f314(x73601),x73603),f312(f168(x73601),x73605)))+~P22(f312(f312(f314(x73601),x73602),f312(f168(x73601),x73604)))+P22(f312(f312(f227(x73601),x73602),x73603))
% 155.94/155.63 [8473]~P105(x84731)+~P22(f312(f312(f228(f861(x84731,a846)),f283(x84731,x84735,x84732)),f283(x84731,x84734,x84733)))+~P22(f312(f312(f227(x84731),x84735),x84732))+P22(f312(f312(f228(x84731),x84732),x84733))+P22(f312(f312(f228(x84731),x84734),x84735))
% 155.94/155.63 [9461]~P49(f861(x94614,a846),f861(x94614,a846),x94615)+P22(f312(x94611,x94612))+~E(x94613,f109(f861(x94614,a846),x94615))+~P22(f312(x94611,f559(x94611,x94612,x94615,x94614,x94613)))+~P22(f312(f312(f314(x94614),x94612),x94613))
% 155.94/155.63 [9859]~P12(x98592,x98595,x98593)+E(x98591,f189(f861(x98592,a846)))+~E(f312(f312(x98595,f312(x98594,f548(x98591,x98594,x98593,x98595,x98592))),f312(x98594,f549(x98591,x98594,x98593,x98595,x98592))),f312(x98594,f312(f312(x98595,f548(x98591,x98594,x98593,x98595,x98592)),f549(x98591,x98594,x98593,x98595,x98592))))+E(f312(x98593,f312(f290(x98592,x98592,x98594),x98591)),f312(x98594,f312(x98593,x98591)))+~P22(f312(f70(x98592),x98591))
% 155.94/155.63 [6311]~P13(x63112,x63115,x63113)+E(x63111,f189(f861(x63112,a846)))+~P22(f312(f70(x63112),x63111))+E(f312(x63113,f312(f312(f289(x63112),x63114),x63111)),f312(f312(x63115,x63114),f312(x63113,x63111)))+P22(f312(f312(f314(x63112),x63114),x63111))
% 155.94/155.63 [7130]~P12(x71302,x71303,x71304)+E(f312(f312(x71303,f312(x71304,x71301)),f312(x71304,x71305)),f312(x71304,x71305))+E(x71301,f189(f861(x71302,a846)))+~P22(f312(f70(x71302),x71305))+~P22(f312(f312(f227(f861(x71302,a846)),x71301),x71305))
% 155.94/155.63 [7495]~P13(x74954,x74955,x74951)+E(f312(x74951,x74952),x74953)+~P22(f312(f70(x74954),x74952))+~E(f312(f312(f21(f861(x74954,a846)),x74952),f312(f312(f289(x74954),x74953),f189(f861(x74954,a846)))),f189(f861(x74954,a846)))+~P22(f312(f312(f314(x74954),x74953),x74952))
% 155.94/155.63 [7580]E(x75801,x75802)+~E(f312(f190(f854(x75803)),x75802),f312(f190(f854(x75804)),x75805))+~E(f312(f190(f854(x75803)),x75801),f312(f190(f854(x75804)),x75805))+~E(f312(f173(x75804,x75803),f312(f312(f177(x75804,x75803),x75805),x75801)),f312(f173(x75804,x75803),f312(f312(f177(x75804,x75803),x75805),x75802)))+~P22(f312(f133(x75804),x75805))
% 155.94/155.63 [8441]E(x84411,x84412)+~P3(x84413,x84414,x84415)+E(f312(f312(f115(f861(x84413,a846)),x84411),x84412),f189(f861(x84413,a846)))+~P22(f312(f312(f314(f861(x84413,a846)),x84412),f312(f312(f69(x84413),x84414),x84415)))+~P22(f312(f312(f314(f861(x84413,a846)),x84411),f312(f312(f69(x84413),x84414),x84415)))
% 155.94/155.63 [9225]~P72(x92252)+~E(f312(x92253,f443(x92253,x92254,x92255,x92251,x92252)),f87(x92252))+E(f312(f312(f9(x92251,x92252),x92253),x92254),f312(f312(f9(x92251,x92252),x92253),x92255))+~P22(f312(f70(x92251),x92255))+~P22(f312(f312(f227(f861(x92251,a846)),x92254),x92255))
% 155.94/155.63 [9226]~P72(x92262)+~E(f312(x92263,f446(x92263,x92264,x92265,x92261,x92262)),f87(x92262))+E(f312(f312(f9(x92261,x92262),x92263),x92264),f312(f312(f9(x92261,x92262),x92263),x92265))+~P22(f312(f70(x92261),x92265))+~P22(f312(f312(f227(f861(x92261,a846)),x92264),x92265))
% 155.94/155.63 [9227]~P26(x92272)+~E(f312(x92273,f508(x92273,x92274,x92275,x92271,x92272)),f2(x92272))+E(f312(f312(f6(x92271,x92272),x92273),x92274),f312(f312(f6(x92271,x92272),x92273),x92275))+~P22(f312(f70(x92271),x92275))+~P22(f312(f312(f227(f861(x92271,a846)),x92274),x92275))
% 155.94/155.63 [9228]~P26(x92282)+~E(f312(x92283,f509(x92283,x92284,x92285,x92281,x92282)),f2(x92282))+E(f312(f312(f6(x92281,x92282),x92283),x92284),f312(f312(f6(x92281,x92282),x92283),x92285))+~P22(f312(f70(x92281),x92285))+~P22(f312(f312(f227(f861(x92281,a846)),x92284),x92285))
% 155.94/155.63 [9636]~P49(f861(x96361,a846),f861(x96361,a846),f312(f312(f8(f861(x96361,a846),f861(x96361,a846),f861(x96361,a846)),f233(x96361)),x96364))+~P22(f312(f312(x96364,f312(f312(f124(f861(x96361,a846)),x96365),x96363)),f563(x96365,x96362,x96364,x96361,x96363)))+~E(x96363,f110(f861(x96361,a846),f312(f312(f8(f861(x96361,a846),f861(x96361,a846),f861(x96361,a846)),f233(x96361)),x96364)))+P22(f312(f312(f314(x96361),x96362),x96363))+~P22(f312(f312(f314(x96361),x96362),x96365))
% 155.94/155.63 [9638]~P49(f861(x96381,a846),f861(x96381,a846),f312(f312(f8(f861(x96381,a846),f861(x96381,a846),f861(x96381,a846)),f233(x96381)),x96385))+~E(x96383,f110(f861(x96381,a846),f312(f312(f8(f861(x96381,a846),f861(x96381,a846),f861(x96381,a846)),f233(x96381)),x96385)))+~P22(f312(f312(f314(x96381),x96382),x96384))+P22(f312(f312(f314(x96381),f563(x96384,x96382,x96385,x96381,x96383)),x96384))+P22(f312(f312(f314(x96381),x96382),x96383))
% 155.94/155.63 [9691]~P84(x96911)+~P22(f312(f70(x96912),x96915))+~P22(f312(f312(f227(x96911),f2(x96911)),f312(x96913,f488(x96913,x96914,x96915,x96912,x96911))))+P22(f312(f312(f227(x96911),f312(f312(f6(x96912,x96911),x96913),x96914)),f312(f312(f6(x96912,x96911),x96913),x96915)))+~P22(f312(f312(f227(f861(x96912,a846)),x96914),x96915))
% 155.94/155.63 [7230]E(x72301,f2(a853))+P22(f312(x72302,x72303))+~E(x72304,f312(f312(f89(a853),f312(f312(f90(a853),x72301),x72303)),x72305))+~P22(f312(x72302,f312(f47(a853,x72304),x72301)))+~P22(f312(f312(f228(a853),x72305),x72301))
% 155.94/155.63 [7435]E(x74351,f2(a853))+P22(f312(x74352,x74353))+~P22(f312(x74352,f54(a853,x74354,x74351)))+~E(x74354,f312(f312(f89(a853),f312(f312(f90(a853),x74351),x74355)),x74353))+~P22(f312(f312(f228(a853),x74353),x74351))
% 155.94/155.63 [7729]~P65(x77293)+E(f312(x77291,x77292),f2(x77293))+~P22(f312(f70(x77294),x77295))+E(f312(f312(f9(x77294,x77293),x77291),f312(f312(f21(f861(x77294,a846)),x77295),f312(f312(f289(x77294),x77292),f189(f861(x77294,a846))))),f312(f312(f9(x77294,x77293),x77291),x77295))+P22(f312(f312(f314(x77294),x77292),x77295))
% 155.94/155.63 [8128]~P72(x81281)+~P22(f312(f70(x81282),x81285))+~P22(f312(f70(x81282),x81284))+~E(f312(f312(f115(f861(x81282,a846)),x81284),x81285),f189(f861(x81282,a846)))+E(f312(f312(f90(x81281),f312(f312(f9(x81282,x81281),x81283),x81284)),f312(f312(f9(x81282,x81281),x81283),x81285)),f312(f312(f9(x81282,x81281),x81283),f312(f312(f124(f861(x81282,a846)),x81284),x81285)))
% 155.94/155.63 [8129]~P26(x81291)+~P22(f312(f70(x81292),x81295))+~P22(f312(f70(x81292),x81294))+~E(f312(f312(f115(f861(x81292,a846)),x81294),x81295),f189(f861(x81292,a846)))+E(f312(f312(f89(x81291),f312(f312(f6(x81292,x81291),x81293),x81294)),f312(f312(f6(x81292,x81291),x81293),x81295)),f312(f312(f6(x81292,x81291),x81293),f312(f312(f124(f861(x81292,a846)),x81294),x81295)))
% 155.94/155.63 [8223]~P65(x82233)+E(f312(x82231,x82232),f2(x82233))+~P22(f312(f70(x82234),x82235))+E(f312(f312(f9(x82234,x82233),x82231),f312(f312(f21(f861(x82234,a846)),x82235),f312(f312(f289(x82234),x82232),f189(f861(x82234,a846))))),f312(f312(f268(x82233),f312(f312(f9(x82234,x82233),x82231),x82235)),f312(x82231,x82232)))+~P22(f312(f312(f314(x82234),x82232),x82235))
% 155.94/155.63 [8944]~P3(x89441,x89445,x89444)+~E(f312(f312(f69(x89441),f312(f312(f289(x89441),x89442),f189(f861(x89441,a846)))),x89444),f312(f312(f69(x89441),f312(f312(f289(x89441),x89443),f189(f861(x89441,a846)))),x89444))+~P22(f312(f312(f314(x89441),x89443),x89445))+~P22(f312(f312(f314(x89441),x89442),x89445))+P22(f312(f312(f314(f860(x89441,x89441)),f312(f312(f239(x89441,x89441),x89442),x89443)),x89444))
% 155.94/155.63 [8963]~P3(x89631,x89635,x89633)+E(f312(f312(f69(x89631),f312(f312(f289(x89631),x89632),f189(f861(x89631,a846)))),x89633),f312(f312(f69(x89631),f312(f312(f289(x89631),x89634),f189(f861(x89631,a846)))),x89633))+~P22(f312(f312(f314(x89631),x89634),x89635))+~P22(f312(f312(f314(x89631),x89632),x89635))+~P22(f312(f312(f314(f860(x89631,x89631)),f312(f312(f239(x89631,x89631),x89632),x89634)),x89633))
% 155.94/155.63 [9252]~P72(x92521)+~P22(f312(f70(x92522),x92525))+~P22(f312(f70(x92522),x92524))+~E(f312(f312(f115(f861(x92522,a846)),x92524),x92525),f189(f861(x92522,a846)))+E(f312(f312(f90(x92521),f312(f312(f312(f74(x92521,x92522,f90(x92521)),x92523),f87(x92521)),x92524)),f312(f312(f312(f74(x92521,x92522,f90(x92521)),x92523),f87(x92521)),x92525)),f312(f312(f312(f74(x92521,x92522,f90(x92521)),x92523),f87(x92521)),f312(f312(f124(f861(x92522,a846)),x92524),x92525)))
% 155.94/155.63 [9260]~P72(x92601)+~E(f312(x92603,f401(x92603,x92605,x92604,x92602,x92601)),f87(x92601))+~P22(f312(f70(x92602),x92604))+~P22(f312(f70(x92602),x92605))+E(f312(f312(f90(x92601),f312(f312(f9(x92602,x92601),x92603),x92604)),f312(f312(f9(x92602,x92601),x92603),x92605)),f312(f312(f9(x92602,x92601),x92603),f312(f312(f124(f861(x92602,a846)),x92604),x92605)))
% 155.94/155.63 [9261]~P72(x92611)+~E(f312(x92613,f402(x92613,x92615,x92614,x92612,x92611)),f87(x92611))+~P22(f312(f70(x92612),x92614))+~P22(f312(f70(x92612),x92615))+E(f312(f312(f90(x92611),f312(f312(f9(x92612,x92611),x92613),x92614)),f312(f312(f9(x92612,x92611),x92613),x92615)),f312(f312(f9(x92612,x92611),x92613),f312(f312(f124(f861(x92612,a846)),x92614),x92615)))
% 155.94/155.63 [9262]~P26(x92621)+~E(f312(x92623,f486(x92623,x92625,x92624,x92622,x92621)),f2(x92621))+~P22(f312(f70(x92622),x92624))+~P22(f312(f70(x92622),x92625))+E(f312(f312(f89(x92621),f312(f312(f6(x92622,x92621),x92623),x92624)),f312(f312(f6(x92622,x92621),x92623),x92625)),f312(f312(f6(x92622,x92621),x92623),f312(f312(f124(f861(x92622,a846)),x92624),x92625)))
% 155.94/155.63 [9263]~P26(x92631)+~E(f312(x92633,f498(x92633,x92635,x92634,x92632,x92631)),f2(x92631))+~P22(f312(f70(x92632),x92634))+~P22(f312(f70(x92632),x92635))+E(f312(f312(f89(x92631),f312(f312(f6(x92632,x92631),x92633),x92634)),f312(f312(f6(x92632,x92631),x92633),x92635)),f312(f312(f6(x92632,x92631),x92633),f312(f312(f124(f861(x92632,a846)),x92634),x92635)))
% 155.94/155.63 [9469]~P72(x94691)+~E(f312(x94693,f427(x94693,x94695,x94694,x94692,x94691)),f87(x94691))+~P22(f312(f70(x94692),x94694))+~P22(f312(f70(x94692),x94695))+E(f312(f312(f90(x94691),f312(f312(f312(f74(x94691,x94692,f90(x94691)),x94693),f87(x94691)),x94694)),f312(f312(f312(f74(x94691,x94692,f90(x94691)),x94693),f87(x94691)),x94695)),f312(f312(f312(f74(x94691,x94692,f90(x94691)),x94693),f87(x94691)),f312(f312(f124(f861(x94692,a846)),x94694),x94695)))
% 155.94/155.63 [9571]~P72(x95712)+E(f312(f312(f9(x95711,x95712),x95713),x95714),f312(f312(f9(x95711,x95712),x95713),x95715))+~P22(f312(f70(x95711),x95715))+~P22(f312(f312(f227(f861(x95711,a846)),x95714),x95715))+P22(f312(f312(f314(x95711),f443(x95713,x95714,x95715,x95711,x95712)),f312(f312(f21(f861(x95711,a846)),x95715),x95714)))
% 155.94/155.63 [9572]~P72(x95722)+E(f312(f312(f9(x95721,x95722),x95723),x95724),f312(f312(f9(x95721,x95722),x95723),x95725))+~P22(f312(f70(x95721),x95725))+~P22(f312(f312(f227(f861(x95721,a846)),x95724),x95725))+P22(f312(f312(f314(x95721),f446(x95723,x95724,x95725,x95721,x95722)),f312(f312(f21(f861(x95721,a846)),x95725),x95724)))
% 155.94/155.63 [9573]~P26(x95732)+E(f312(f312(f6(x95731,x95732),x95733),x95734),f312(f312(f6(x95731,x95732),x95733),x95735))+~P22(f312(f70(x95731),x95735))+~P22(f312(f312(f227(f861(x95731,a846)),x95734),x95735))+P22(f312(f312(f314(x95731),f508(x95733,x95734,x95735,x95731,x95732)),f312(f312(f21(f861(x95731,a846)),x95735),x95734)))
% 155.94/155.63 [9574]~P26(x95742)+E(f312(f312(f6(x95741,x95742),x95743),x95744),f312(f312(f6(x95741,x95742),x95743),x95745))+~P22(f312(f70(x95741),x95745))+~P22(f312(f312(f227(f861(x95741,a846)),x95744),x95745))+P22(f312(f312(f314(x95741),f509(x95743,x95744,x95745,x95741,x95742)),f312(f312(f21(f861(x95741,a846)),x95745),x95744)))
% 155.94/155.63 [9590]~P72(x95901)+~P22(f312(f70(x95902),x95904))+~P22(f312(f70(x95902),x95905))+E(f312(f312(f90(x95901),f312(f312(f9(x95902,x95901),x95903),x95904)),f312(f312(f9(x95902,x95901),x95903),x95905)),f312(f312(f9(x95902,x95901),x95903),f312(f312(f124(f861(x95902,a846)),x95904),x95905)))+P22(f312(f312(f314(x95902),f401(x95903,x95905,x95904,x95902,x95901)),f312(f312(f115(f861(x95902,a846)),x95904),x95905)))
% 155.94/155.63 [9591]~P72(x95911)+~P22(f312(f70(x95912),x95914))+~P22(f312(f70(x95912),x95915))+E(f312(f312(f90(x95911),f312(f312(f9(x95912,x95911),x95913),x95914)),f312(f312(f9(x95912,x95911),x95913),x95915)),f312(f312(f9(x95912,x95911),x95913),f312(f312(f124(f861(x95912,a846)),x95914),x95915)))+P22(f312(f312(f314(x95912),f402(x95913,x95915,x95914,x95912,x95911)),f312(f312(f115(f861(x95912,a846)),x95914),x95915)))
% 155.94/155.63 [9592]~P26(x95921)+~P22(f312(f70(x95922),x95924))+~P22(f312(f70(x95922),x95925))+E(f312(f312(f89(x95921),f312(f312(f6(x95922,x95921),x95923),x95924)),f312(f312(f6(x95922,x95921),x95923),x95925)),f312(f312(f6(x95922,x95921),x95923),f312(f312(f124(f861(x95922,a846)),x95924),x95925)))+P22(f312(f312(f314(x95922),f486(x95923,x95925,x95924,x95922,x95921)),f312(f312(f115(f861(x95922,a846)),x95924),x95925)))
% 155.94/155.63 [9593]~P26(x95931)+~P22(f312(f70(x95932),x95934))+~P22(f312(f70(x95932),x95935))+E(f312(f312(f89(x95931),f312(f312(f6(x95932,x95931),x95933),x95934)),f312(f312(f6(x95932,x95931),x95933),x95935)),f312(f312(f6(x95932,x95931),x95933),f312(f312(f124(f861(x95932,a846)),x95934),x95935)))+P22(f312(f312(f314(x95932),f498(x95933,x95935,x95934,x95932,x95931)),f312(f312(f115(f861(x95932,a846)),x95934),x95935)))
% 155.94/155.63 [9596]~P49(f861(x95963,a846),f861(x95963,a846),x95964)+P22(f312(x95961,x95962))+~E(x95965,f109(f861(x95963,a846),x95964))+~P22(f312(f312(f314(x95963),x95962),x95965))+P22(f312(f312(f314(x95963),f559(x95961,x95962,x95964,x95963,x95965)),f312(x95964,f312(f312(f115(f861(x95963,a846)),x95965),f312(f233(x95963),x95961)))))
% 155.94/155.63 [9601]~P84(x96015)+~P22(f312(f70(x96011),x96014))+P22(f312(f312(f227(x96015),f312(f312(f6(x96011,x96015),x96012),x96013)),f312(f312(f6(x96011,x96015),x96012),x96014)))+~P22(f312(f312(f227(f861(x96011,a846)),x96013),x96014))+P22(f312(f312(f314(x96011),f488(x96012,x96013,x96014,x96011,x96015)),f312(f312(f21(f861(x96011,a846)),x96014),x96013)))
% 155.94/155.63 [9655]~P72(x96551)+~P22(f312(f70(x96552),x96554))+~P22(f312(f70(x96552),x96555))+E(f312(f312(f90(x96551),f312(f312(f312(f74(x96551,x96552,f90(x96551)),x96553),f87(x96551)),x96554)),f312(f312(f312(f74(x96551,x96552,f90(x96551)),x96553),f87(x96551)),x96555)),f312(f312(f312(f74(x96551,x96552,f90(x96551)),x96553),f87(x96551)),f312(f312(f124(f861(x96552,a846)),x96554),x96555)))+P22(f312(f312(f314(x96552),f427(x96553,x96555,x96554,x96552,x96551)),f312(f312(f115(f861(x96552,a846)),x96554),x96555)))
% 155.94/155.63 [8632]~P13(x86321,x86324,x86325)+~P22(f312(f70(x86321),x86322))+E(f312(f312(f21(f861(x86321,a846)),x86322),f312(f312(f289(x86321),x86323),f189(f861(x86321,a846)))),f189(f861(x86321,a846)))+~P22(f312(f312(f314(x86321),x86323),x86322))+E(f312(f312(x86324,x86323),f312(x86325,f312(f312(f21(f861(x86321,a846)),x86322),f312(f312(f289(x86321),x86323),f189(f861(x86321,a846)))))),f312(x86325,x86322))
% 155.94/155.63 [8705]~P13(x87051,x87054,x87055)+~P22(f312(f70(x87051),x87053))+~P22(f312(f70(x87051),x87052))+E(f312(f312(f115(f861(x87051,a846)),x87052),x87053),f189(f861(x87051,a846)))+E(f312(f312(x87054,f312(x87055,f312(f312(f124(f861(x87051,a846)),x87052),x87053))),f312(x87055,f312(f312(f115(f861(x87051,a846)),x87052),x87053))),f312(f312(x87054,f312(x87055,x87052)),f312(x87055,x87053)))
% 155.94/155.63 [8891]~P49(f861(x88911,a846),f861(x88911,a846),x88914)+~E(x88913,f110(f861(x88911,a846),x88914))+P22(f312(f312(f314(x88911),x88912),x88913))+~P22(f312(f312(f314(x88911),x88912),x88915))+~P22(f312(f312(f227(f861(x88911,a846)),x88915),f312(x88914,f312(f312(f124(f861(x88911,a846)),x88915),x88913))))
% 155.94/155.63 [9265]~P22(f312(f312(f227(a1),x92654),f2(a1)))+~P22(f312(f312(f228(a1),x92653),x92655))+P22(f312(f312(f227(a1),x92651),x92652))+~P22(f312(f312(f228(a1),x92653),x92654))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),f312(f312(f90(a1),x92653),x92652)),x92655)),f312(f312(f89(a1),f312(f312(f90(a1),x92653),x92651)),x92654)))
% 155.94/155.63 [9267]~P22(f312(f312(f227(a1),f2(a1)),x92675))+P22(f312(f312(f227(a1),x92671),x92672))+~P22(f312(f312(f228(a1),x92673),x92674))+~P22(f312(f312(f228(a1),x92675),x92674))+~P22(f312(f312(f227(a1),f312(f312(f89(a1),f312(f312(f90(a1),x92674),x92671)),x92675)),f312(f312(f89(a1),f312(f312(f90(a1),x92674),x92672)),x92673)))
% 155.94/155.63 [9377]~P65(x93775)+E(f312(x93771,f421(x93771,x93772,x93773,x93774,x93775)),f2(x93775))+~P22(f312(f70(x93774),x93773))+~P22(f312(f70(x93774),x93772))+E(f312(f312(f268(x93775),f312(f312(f90(x93775),f312(f312(f9(x93774,x93775),x93771),x93773)),f312(f312(f9(x93774,x93775),x93771),x93772))),f312(f312(f9(x93774,x93775),x93771),f312(f312(f115(f861(x93774,a846)),x93773),x93772))),f312(f312(f9(x93774,x93775),x93771),f312(f312(f124(f861(x93774,a846)),x93773),x93772)))
% 155.94/155.63 [9650]~P65(x96501)+~P22(f312(f70(x96502),x96504))+~P22(f312(f70(x96502),x96505))+E(f312(f312(f268(x96501),f312(f312(f90(x96501),f312(f312(f9(x96502,x96501),x96503),x96504)),f312(f312(f9(x96502,x96501),x96503),x96505))),f312(f312(f9(x96502,x96501),x96503),f312(f312(f115(f861(x96502,a846)),x96504),x96505))),f312(f312(f9(x96502,x96501),x96503),f312(f312(f124(f861(x96502,a846)),x96504),x96505)))+P22(f312(f312(f314(x96502),f421(x96503,x96505,x96504,x96502,x96501)),f312(f312(f115(f861(x96502,a846)),x96504),x96505)))
% 155.94/155.63 [8981]E(f312(f312(f129(x89811),x89812),x89813),f312(f312(f129(x89811),x89814),x89815))+~E(f312(f312(f169(x89811),f312(f190(f854(x89811)),x89814)),x89812),x89814)+~E(f312(f312(f169(x89811),f312(f190(f854(x89811)),x89812)),x89814),x89812)+~E(x89815,f312(f312(f129(x89811),f312(f312(f134(x89811),f312(f190(f854(x89811)),x89814)),x89812)),x89813))+~E(f312(f312(f129(x89811),f312(f312(f134(x89811),f312(f190(f854(x89811)),x89812)),x89814)),x89815),x89813)
% 155.94/155.63 [9375]~P103(x93752)+E(f312(f312(f145(x93751,x93752,x93753),x93754),f166(x93751,x93754,x93755)),x93755)+~P33(x93752,f312(f312(f150(x93751,x93752),x93753),x93755))+~P22(f312(f312(f314(x93751),x93754),f312(f168(x93751),x93755)))+~E(f312(f137(x93751),f312(f132(x93751,f312(f312(f8(x93752,a846,x93751),f312(a309,f312(x93753,x93754))),x93753)),x93755)),x93754)
% 155.94/155.63 [9706]~P68(x97061)+~P22(f312(f75(x97061,x97061,f90(x97061),x97062,x97063),x97065))+~P22(f312(f312(f314(x97061),x97064),x97063))+P22(f312(f312(f314(x97061),x97062),x97063))+P22(f312(f75(x97061,x97061,f90(x97061),x97064,f312(f312(f289(x97061),x97062),f312(f312(f21(f861(x97061,a846)),x97063),f312(f312(f289(x97061),x97064),f189(f861(x97061,a846)))))),x97065))
% 155.94/155.63 [10052]~P49(f861(x100521,a846),f861(x100521,a846),x100524)+~E(x100523,f110(f861(x100521,a846),x100524))+P22(f312(f312(f314(x100521),x100522),x100523))+~P22(f312(f312(f314(x100521),x100522),x100525))+~P22(f312(f312(f227(f861(x100521,a846)),x100525),f312(x100524,f109(f861(x100521,a846),f312(f312(f7(f861(x100521,a846),f861(x100521,a846),f861(x100521,a846)),f312(f312(f8(f861(x100521,a846),f861(f861(x100521,a846),f861(x100521,a846)),f861(x100521,a846)),f124(f861(x100521,a846))),f312(f312(f7(f861(x100521,a846),f861(x100521,a846),f861(x100521,a846)),f312(f312(f8(f861(x100521,a846),f861(f861(x100521,a846),f861(x100521,a846)),f861(x100521,a846)),f124(f861(x100521,a846))),x100524)),x100525))),x100523)))))
% 155.94/155.63 [7135]E(x71351,x71352)+~P19(x71354,x71355,x71353,x71356)+~E(f312(x71353,x71351),f312(x71353,x71352))+~P22(f312(f312(f314(x71354),x71352),x71356))+~P22(f312(f312(f314(x71354),x71351),x71356))
% 155.94/155.63 [6405]~P136(x64054)+E(x64051,x64052)+~E(x64055,x64056)+E(x64053,f2(x64054))+~E(f312(f312(f89(x64054),x64055),f312(f312(f90(x64054),x64053),x64051)),f312(f312(f89(x64054),x64056),f312(f312(f90(x64054),x64053),x64052)))
% 155.94/155.63 [7416]~P103(x74161)+~P31(x74161)+~P22(f312(f312(f228(x74161),x74162),f312(x74165,x74166)))+~P22(f312(f312(f314(x74163),x74166),x74164))+P22(f312(f312(f228(x74161),x74162),f312(f312(f50(x74163,x74161),x74164),x74165)))
% 155.94/155.63 [8097]~P103(x80971)+~P31(x80971)+~P22(f312(f312(f228(x80971),f312(x80974,x80976)),x80975))+~P22(f312(f312(f314(x80972),x80976),x80973))+P22(f312(f312(f228(x80971),f312(f312(f51(x80972,x80971),x80973),x80974)),x80975))
% 155.94/155.63 [8365]~P14(x83652,x83655,x83656,x83651)+~P22(f312(f70(x83652),x83654))+~P22(f312(f70(x83652),x83653))+~E(f312(f312(f115(f861(x83652,a846)),x83653),x83654),f189(f861(x83652,a846)))+E(f312(x83651,f312(f312(f124(f861(x83652,a846)),x83653),x83654)),f312(f82(x83655,x83655,x83655,f312(x83651,x83653)),f312(x83651,x83654)))
% 155.94/155.63 [8676]E(x86761,x86762)+~P56(x86764,x86765,x86766,x86763,x86767)+~E(f312(x86763,x86761),f312(x86763,x86762))+~P22(f312(f312(f314(x86765),x86762),x86767))+~P22(f312(f312(f314(x86765),x86761),x86767))
% 155.94/155.63 [9963]~P22(f312(x99632,x99634))+~E(x99635,f312(f132(x99631,x99632),x99637))+E(f312(f132(x99631,x99632),x99633),f312(f312(f147(x99631),x99634),x99635))+~E(x99633,f312(f312(f129(x99631),x99636),f312(f312(f147(x99631),x99634),x99637)))+P22(f312(x99632,f732(x99635,x99634,x99633,x99632,x99631,x99636,x99637)))
% 155.94/155.63 [9964]~P22(f312(x99644,x99642))+~E(x99643,f312(f132(x99641,x99644),x99647))+E(f312(f312(f147(x99641),x99642),x99643),f312(f132(x99641,x99644),x99645))+~E(x99645,f312(f312(f129(x99641),x99646),f312(f312(f147(x99641),x99642),x99647)))+P22(f312(x99644,f734(x99645,x99644,x99643,x99642,x99641,x99646,x99647)))
% 155.94/155.63 [9997]~P22(f312(x99972,x99974))+~E(x99975,f312(f132(x99971,x99972),x99977))+E(f312(f132(x99971,x99972),x99973),f312(f312(f147(x99971),x99974),x99975))+~E(x99973,f312(f312(f129(x99971),x99976),f312(f312(f147(x99971),x99974),x99977)))+P22(f312(f312(f314(x99971),f732(x99975,x99974,x99973,x99972,x99971,x99976,x99977)),f312(f168(x99971),x99976)))
% 155.94/155.63 [9998]~P22(f312(x99984,x99982))+~E(x99983,f312(f132(x99981,x99984),x99987))+E(f312(f312(f147(x99981),x99982),x99983),f312(f132(x99981,x99984),x99985))+~E(x99985,f312(f312(f129(x99981),x99986),f312(f312(f147(x99981),x99982),x99987)))+P22(f312(f312(f314(x99981),f734(x99985,x99984,x99983,x99982,x99981,x99986,x99987)),f312(f168(x99981),x99986)))
% 155.94/155.63 [10001]~P3(x100011,x100017,x100016)+~P9(x100011,f861(x100015,a846),x100016,x100014)+P22(f312(f312(f314(x100011),f422(x100012,x100013,x100014,x100015,x100016,x100017,x100011)),x100017))+~P22(f312(f312(f314(f861(x100011,a846)),x100013),f312(f312(f69(x100011),x100017),x100016)))+P22(f312(f312(f314(f861(x100015,a846)),f312(f312(f50(x100011,f861(x100015,a846)),x100013),x100014)),x100012))
% 155.94/155.63 [10048]~P3(x100482,x100486,x100487)+~P9(x100482,f861(x100481,a846),x100487,x100484)+~P22(f312(f312(f314(f861(x100482,a846)),x100483),f312(f312(f69(x100482),x100486),x100487)))+~P22(f312(f312(f314(f861(x100481,a846)),f312(x100484,f422(x100485,x100483,x100484,x100481,x100487,x100486,x100482))),x100485))+P22(f312(f312(f314(f861(x100481,a846)),f312(f312(f50(x100482,f861(x100481,a846)),x100483),x100484)),x100485))
% 155.94/155.63 [8269]~P72(x82692)+~P19(x82691,x82695,x82698,x82694)+~E(x82693,f312(f82(x82695,x82692,x82691,x82696),x82698))+~E(x82697,f312(f290(x82691,x82695,x82698),x82694))+E(f312(f312(f9(x82691,x82692),x82693),x82694),f312(f312(f9(x82695,x82692),x82696),x82697))
% 155.94/155.63 [10051]~P72(x100512)+~P19(x100515,x100511,x100518,x100517)+~E(f312(x100516,f445(x100513,x100516,x100514,x100517,x100518,x100511,x100515,x100512)),f312(f312(f82(x100511,x100512,x100515,x100513),x100518),f445(x100513,x100516,x100514,x100517,x100518,x100511,x100515,x100512)))+~E(x100514,f312(f290(x100515,x100511,x100518),x100517))+E(f312(f312(f9(x100511,x100512),x100513),x100514),f312(f312(f9(x100515,x100512),x100516),x100517))
% 155.94/155.63 [10055]~P72(x100552)+~P19(x100551,x100555,x100558,x100554)+~E(x100557,f312(f290(x100551,x100555,x100558),x100554))+E(f312(f312(f9(x100551,x100552),x100553),x100554),f312(f312(f9(x100555,x100552),x100556),x100557))+P22(f312(f312(f314(x100551),f445(x100556,x100553,x100557,x100554,x100558,x100555,x100551,x100552)),x100554))
% 155.94/155.63 [10056]~P26(x100562)+~P19(x100561,x100565,x100568,x100564)+~E(x100567,f312(f290(x100561,x100565,x100568),x100564))+E(f312(f312(f6(x100561,x100562),x100563),x100564),f312(f312(f6(x100565,x100562),x100566),x100567))+P22(f312(f312(f314(x100561),f753(x100566,x100563,x100567,x100564,x100568,x100565,x100561,x100562)),x100564))
% 155.94/155.63 [10064]~P26(x100642)+~P19(x100645,x100641,x100648,x100647)+~E(x100644,f312(f290(x100645,x100641,x100648),x100647))+~E(f312(x100646,f753(x100643,x100646,x100644,x100647,x100648,x100641,x100645,x100642)),f312(x100643,f312(x100648,f753(x100643,x100646,x100644,x100647,x100648,x100641,x100645,x100642))))+E(f312(f312(f6(x100641,x100642),x100643),x100644),f312(f312(f6(x100645,x100642),x100646),x100647))
% 155.94/155.63 [9432]~E(f312(f190(f854(x94322)),x94325),f312(f190(f854(x94321)),x94323))+~E(f312(f190(f854(x94322)),x94324),f312(f190(f854(x94321)),x94323))+~E(f312(f312(f312(f81(x94321,f857(x94322)),f312(f173(x94321,x94322),f312(f312(f177(x94321,x94322),x94323),x94324))),x94326),f312(f219(x94322),x94327)),f312(f312(f312(f81(x94321,f857(x94322)),f312(f173(x94321,x94322),f312(f312(f177(x94321,x94322),x94323),x94325))),x94326),f312(f219(x94322),x94328)))+E(f312(f173(x94321,x94322),f312(f312(f177(x94321,x94322),x94323),x94324)),f312(f173(x94321,x94322),f312(f312(f177(x94321,x94322),x94323),x94325)))+P22(f312(f312(f314(x94321),x94326),f312(f168(x94321),x94323)))
% 155.94/155.63 [9540]~P17(x95406,x95402,x95405,x95407,x95408,x95401)+~P22(f312(f70(x95402),x95404))+~P22(f312(f70(x95402),x95403))+~E(f312(f312(f115(f861(x95402,a846)),x95403),x95404),f189(f861(x95402,a846)))+E(f312(x95401,f312(f312(f124(f861(x95402,a846)),x95403),x95404)),f312(f312(x95405,f312(x95401,x95403)),f312(x95401,x95404)))
% 155.94/155.63 [9949]~P17(x99498,x99492,x99495,x99497,x99496,x99491)+~E(f312(x99496,f552(x99494,x99493,x99491,x99496,x99497,x99495,x99492)),x99497)+~P22(f312(f70(x99492),x99493))+~P22(f312(f70(x99492),x99494))+E(f312(x99491,f312(f312(f124(f861(x99492,a846)),x99493),x99494)),f312(f312(x99495,f312(x99491,x99493)),f312(x99491,x99494)))
% 155.94/155.63 [10008]~P17(x100088,x100082,x100085,x100087,x100086,x100081)+~P22(f312(f70(x100082),x100083))+~P22(f312(f70(x100082),x100084))+E(f312(x100081,f312(f312(f124(f861(x100082,a846)),x100083),x100084)),f312(f312(x100085,f312(x100081,x100083)),f312(x100081,x100084)))+P22(f312(f312(f314(x100082),f552(x100084,x100083,x100081,x100086,x100087,x100085,x100082)),f312(f312(f115(f861(x100082,a846)),x100083),x100084)))
% 155.94/155.63 [9694]~P3(x96944,x96948,x96945)+~P3(x96941,x96949,x96943)+~P10(x96941,x96944,f861(x96942,a846),x96943,x96945,x96947)+P9(x96941,f861(x96942,a846),x96943,f312(f312(f8(f861(x96944,f861(x96942,a846)),f861(x96942,a846),x96941),f312(f50(x96944,f861(x96942,a846)),f312(f264(x96944,x96944,x96945),f312(f312(f289(x96944),x96946),f189(f861(x96944,a846)))))),x96947))+~P22(f312(f312(f314(x96944),x96946),x96948))
% 155.94/155.63 [5348]~P103(x53483)+~P33(x53483,x53481)+E(x53481,f688(x53482,x53483))+~E(f312(f168(x53483),x53481),x53482)+~P22(f312(f70(x53483),x53482))+~P22(f312(f133(x53483),x53481))
% 155.94/155.63 [4976]~P137(x49762)+~P126(x49762)+~P127(x49762)+~P109(x49762)+E(x49761,f2(x49762))+~E(f312(f312(f240(x49762),x49761),x49763),f2(x49762))
% 155.94/155.63 [4977]~P137(x49772)+~P126(x49772)+~P127(x49772)+~P109(x49772)+~E(x49771,f2(a853))+~E(f312(f312(f240(x49772),x49773),x49771),f2(x49772))
% 155.94/155.63 [6386]~P84(x63861)+~E(x63863,f2(x63861))+~E(x63862,f2(x63861))+E(f312(f312(f89(x63861),x63862),x63863),f2(x63861))+~P22(f312(f312(f227(x63861),f2(x63861)),x63863))+~P22(f312(f312(f227(x63861),f2(x63861)),x63862))
% 155.94/155.63 [8736]~E(f312(f246(a853,a853),x87363),f2(a853))+~E(x87361,f312(f312(f89(a853),f312(f312(f90(a853),f312(f246(a853,a853),x87363)),x87362)),f312(f248(a853,a853),x87363)))+P22(f312(f56(x87361,x87362),x87363))+~P22(f312(f312(f227(a853),f312(f248(a853,a853),x87363)),f2(a853)))+P22(f312(f312(f228(a853),f2(a853)),x87362))+~P22(f312(f312(f228(a853),x87362),f312(f248(a853,a853),x87363)))
% 155.94/155.63 [8744]E(x87441,f2(a853))+~E(x87442,f312(f312(f89(a853),f312(f312(f90(a853),f312(f246(a853,a853),x87443)),x87441)),f312(f248(a853,a853),x87443)))+P22(f312(f56(x87442,x87441),x87443))+~P22(f312(f312(f228(a853),f2(a853)),x87441))+~P22(f312(f312(f227(a853),f2(a853)),f312(f248(a853,a853),x87443)))+~P22(f312(f312(f228(a853),f312(f248(a853,a853),x87443)),x87441))
% 155.94/155.63 [8761]~E(f312(f246(a853,a853),x87613),f2(a853))+~E(x87611,f312(f312(f89(a853),f312(f312(f90(a853),f312(f246(a853,a853),x87613)),x87612)),f312(f248(a853,a853),x87613)))+P22(f312(f56(x87611,x87612),x87613))+~P22(f312(f312(f228(a853),f2(a853)),x87612))+~P22(f312(f312(f227(a853),f2(a853)),f312(f248(a853,a853),x87613)))+~P22(f312(f312(f228(a853),f312(f248(a853,a853),x87613)),x87612))
% 155.94/155.63 [6757]~P87(x67572)+E(x67571,f189(f861(x67572,a846)))+E(x67573,f189(f861(x67572,a846)))+~P22(f312(f70(x67572),x67571))+~P22(f312(f70(x67572),x67573))+E(f11(x67572,f312(f312(f124(f861(x67572,a846)),x67573),x67571)),f312(f312(f115(x67572),f11(x67572,x67573)),f11(x67572,x67571)))
% 155.94/155.63 [6758]~P87(x67582)+E(x67581,f189(f861(x67582,a846)))+E(x67583,f189(f861(x67582,a846)))+~P22(f312(f70(x67582),x67581))+~P22(f312(f70(x67582),x67583))+E(f10(x67582,f312(f312(f124(f861(x67582,a846)),x67583),x67581)),f312(f312(f124(x67582),f10(x67582,x67583)),f10(x67582,x67581)))
% 155.94/155.63 [6759]~P103(x67592)+E(x67591,f189(f861(x67592,a846)))+E(x67593,f189(f861(x67592,a846)))+~P22(f312(f70(x67592),x67591))+~P22(f312(f70(x67592),x67593))+E(f14(x67592,f312(f312(f124(f861(x67592,a846)),x67593),x67591)),f312(f312(f226(x67592),f14(x67592,x67593)),f14(x67592,x67591)))
% 155.94/155.63 [6760]~P103(x67602)+E(x67601,f189(f861(x67602,a846)))+E(x67603,f189(f861(x67602,a846)))+~P22(f312(f70(x67602),x67601))+~P22(f312(f70(x67602),x67603))+E(f15(x67602,f312(f312(f124(f861(x67602,a846)),x67603),x67601)),f312(f312(f225(x67602),f15(x67602,x67603)),f15(x67602,x67601)))
% 155.94/155.63 [7391]~P93(x73912)+E(x73911,f189(f861(x73912,a846)))+E(x73913,f189(f861(x73912,a846)))+~P22(f312(f70(x73912),x73911))+~P22(f312(f70(x73912),x73913))+E(f312(f312(f90(x73912),f312(f72(x73912,f90(x73912)),x73913)),f312(f72(x73912,f90(x73912)),x73911)),f312(f72(x73912,f90(x73912)),f312(f312(f124(f861(x73912,a846)),x73913),x73911)))
% 155.94/155.63 [7548]~P103(x75482)+E(x75481,f189(f861(x75482,a846)))+E(x75483,f189(f861(x75482,a846)))+~P22(f312(f70(x75482),x75481))+~P22(f312(f70(x75482),x75483))+E(f312(f312(f226(x75482),f12(x75482,f226(x75482),x75483)),f12(x75482,f226(x75482),x75481)),f12(x75482,f226(x75482),f312(f312(f124(f861(x75482,a846)),x75483),x75481)))
% 155.94/155.63 [7549]~P103(x75492)+E(x75491,f189(f861(x75492,a846)))+E(x75493,f189(f861(x75492,a846)))+~P22(f312(f70(x75492),x75491))+~P22(f312(f70(x75492),x75493))+E(f312(f312(f225(x75492),f13(x75492,f225(x75492),x75493)),f13(x75492,f225(x75492),x75491)),f13(x75492,f225(x75492),f312(f312(f124(f861(x75492,a846)),x75493),x75491)))
% 155.94/155.63 [8585]~P22(f312(x85851,x85853))+P22(f312(x85851,f478(x85851,x85852)))+P22(f312(x85851,f470(x85851,x85852)))+~P22(f312(f312(f228(a1),f2(a1)),x85852))+~P22(f312(f312(f314(a1),x85853),f283(a1,f87(a1),x85852)))+P22(f312(x85851,f312(f312(f21(a1),f470(x85851,x85852)),f312(f312(f90(a1),f476(x85851,x85852)),x85852))))
% 155.94/155.63 [8881]~P22(f312(x88811,x88813))+~P22(f312(x88811,f470(x88811,x88812)))+P22(f312(x88811,f478(x88811,x88812)))+~P22(f312(f312(f228(a1),f2(a1)),x88812))+~P22(f312(f312(f314(a1),x88813),f283(a1,f87(a1),x88812)))+~P22(f312(x88811,f312(f312(f21(a1),f470(x88811,x88812)),f312(f312(f90(a1),f476(x88811,x88812)),x88812))))
% 155.94/155.63 [10088]~P96(x100882)+E(x100881,f189(f861(x100882,a846)))+E(x100883,f189(f861(x100882,a846)))+~P22(f312(f70(x100882),x100881))+~P22(f312(f70(x100882),x100883))+E(f11(x100882,f312(f233(x100882),f312(f312(f8(f861(x100882,a846),a846,x100882),f96(x100882)),f312(f312(f8(f861(x100882,f861(x100882,a846)),f861(x100882,a846),x100882),f312(f8(f861(x100882,a846),a846,x100882),f96(x100882))),f312(f312(f7(x100882,f861(x100882,f861(x100882,a846)),f861(x100882,f861(x100882,a846))),f312(f312(f8(f861(x100882,f861(f861(x100882,a846),f861(x100882,a846))),f861(f861(x100882,f861(x100882,a846)),f861(x100882,f861(x100882,a846))),x100882),f18(x100882,f861(x100882,a846),f861(x100882,a846))),f312(f312(f8(f861(x100882,f861(x100882,f861(a846,a846))),f861(x100882,f861(f861(x100882,a846),f861(x100882,a846))),x100882),f312(f8(f861(x100882,f861(a846,a846)),f861(f861(x100882,a846),f861(x100882,a846)),x100882),f18(x100882,a846,a846))),f312(f312(f8(f861(x100882,f861(x100882,a846)),f861(x100882,f861(x100882,f861(a846,a846))),x100882),f312(f8(f861(x100882,a846),f861(x100882,f861(a846,a846)),x100882),f312(f8(a846,f861(a846,a846),x100882),a310))),f312(f312(f7(x100882,f861(x100882,f861(x100882,x100882)),f861(x100882,f861(x100882,a846))),f312(f312(f8(f861(f861(x100882,x100882),f861(x100882,a846)),f861(f861(x100882,f861(x100882,x100882)),f861(x100882,f861(x100882,a846))),x100882),f8(f861(x100882,x100882),f861(x100882,a846),x100882)),f312(f312(f8(f861(x100882,a846),f861(f861(x100882,x100882),f861(x100882,a846)),x100882),f8(x100882,a846,x100882)),a309))),f124(x100882)))))),f312(f312(f7(x100882,f861(x100882,a846),f861(x100882,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x100882,a846),f861(x100882,a846)),x100882),f8(a846,a846,x100882)),f312(f312(f8(a846,f861(a846,a846),x100882),a310),f312(f312(f7(x100882,f861(x100882,a846),a846),f314(x100882)),x100883)))),f312(f312(f7(x100882,f861(x100882,a846),a846),f314(x100882)),x100881))))))),f312(f312(f124(x100882),f11(x100882,x100883)),f11(x100882,x100881)))
% 155.94/155.63 [10089]~P96(x100892)+E(x100891,f189(f861(x100892,a846)))+E(x100893,f189(f861(x100892,a846)))+~P22(f312(f70(x100892),x100891))+~P22(f312(f70(x100892),x100893))+E(f10(x100892,f312(f233(x100892),f312(f312(f8(f861(x100892,a846),a846,x100892),f96(x100892)),f312(f312(f8(f861(x100892,f861(x100892,a846)),f861(x100892,a846),x100892),f312(f8(f861(x100892,a846),a846,x100892),f96(x100892))),f312(f312(f7(x100892,f861(x100892,f861(x100892,a846)),f861(x100892,f861(x100892,a846))),f312(f312(f8(f861(x100892,f861(f861(x100892,a846),f861(x100892,a846))),f861(f861(x100892,f861(x100892,a846)),f861(x100892,f861(x100892,a846))),x100892),f18(x100892,f861(x100892,a846),f861(x100892,a846))),f312(f312(f8(f861(x100892,f861(x100892,f861(a846,a846))),f861(x100892,f861(f861(x100892,a846),f861(x100892,a846))),x100892),f312(f8(f861(x100892,f861(a846,a846)),f861(f861(x100892,a846),f861(x100892,a846)),x100892),f18(x100892,a846,a846))),f312(f312(f8(f861(x100892,f861(x100892,a846)),f861(x100892,f861(x100892,f861(a846,a846))),x100892),f312(f8(f861(x100892,a846),f861(x100892,f861(a846,a846)),x100892),f312(f8(a846,f861(a846,a846),x100892),a310))),f312(f312(f7(x100892,f861(x100892,f861(x100892,x100892)),f861(x100892,f861(x100892,a846))),f312(f312(f8(f861(f861(x100892,x100892),f861(x100892,a846)),f861(f861(x100892,f861(x100892,x100892)),f861(x100892,f861(x100892,a846))),x100892),f8(f861(x100892,x100892),f861(x100892,a846),x100892)),f312(f312(f8(f861(x100892,a846),f861(f861(x100892,x100892),f861(x100892,a846)),x100892),f8(x100892,a846,x100892)),a309))),f115(x100892)))))),f312(f312(f7(x100892,f861(x100892,a846),f861(x100892,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x100892,a846),f861(x100892,a846)),x100892),f8(a846,a846,x100892)),f312(f312(f8(a846,f861(a846,a846),x100892),a310),f312(f312(f7(x100892,f861(x100892,a846),a846),f314(x100892)),x100893)))),f312(f312(f7(x100892,f861(x100892,a846),a846),f314(x100892)),x100891))))))),f312(f312(f115(x100892),f10(x100892,x100893)),f10(x100892,x100891)))
% 155.94/155.63 [10090]~P103(x100902)+E(x100901,f189(f861(x100902,a846)))+E(x100903,f189(f861(x100902,a846)))+~P22(f312(f70(x100902),x100901))+~P22(f312(f70(x100902),x100903))+E(f12(x100902,f226(x100902),f312(f233(x100902),f312(f312(f8(f861(x100902,a846),a846,x100902),f96(x100902)),f312(f312(f8(f861(x100902,f861(x100902,a846)),f861(x100902,a846),x100902),f312(f8(f861(x100902,a846),a846,x100902),f96(x100902))),f312(f312(f7(x100902,f861(x100902,f861(x100902,a846)),f861(x100902,f861(x100902,a846))),f312(f312(f8(f861(x100902,f861(f861(x100902,a846),f861(x100902,a846))),f861(f861(x100902,f861(x100902,a846)),f861(x100902,f861(x100902,a846))),x100902),f18(x100902,f861(x100902,a846),f861(x100902,a846))),f312(f312(f8(f861(x100902,f861(x100902,f861(a846,a846))),f861(x100902,f861(f861(x100902,a846),f861(x100902,a846))),x100902),f312(f8(f861(x100902,f861(a846,a846)),f861(f861(x100902,a846),f861(x100902,a846)),x100902),f18(x100902,a846,a846))),f312(f312(f8(f861(x100902,f861(x100902,a846)),f861(x100902,f861(x100902,f861(a846,a846))),x100902),f312(f8(f861(x100902,a846),f861(x100902,f861(a846,a846)),x100902),f312(f8(a846,f861(a846,a846),x100902),a310))),f312(f312(f7(x100902,f861(x100902,f861(x100902,x100902)),f861(x100902,f861(x100902,a846))),f312(f312(f8(f861(f861(x100902,x100902),f861(x100902,a846)),f861(f861(x100902,f861(x100902,x100902)),f861(x100902,f861(x100902,a846))),x100902),f8(f861(x100902,x100902),f861(x100902,a846),x100902)),f312(f312(f8(f861(x100902,a846),f861(f861(x100902,x100902),f861(x100902,a846)),x100902),f8(x100902,a846,x100902)),a309))),f225(x100902)))))),f312(f312(f7(x100902,f861(x100902,a846),f861(x100902,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x100902,a846),f861(x100902,a846)),x100902),f8(a846,a846,x100902)),f312(f312(f8(a846,f861(a846,a846),x100902),a310),f312(f312(f7(x100902,f861(x100902,a846),a846),f314(x100902)),x100903)))),f312(f312(f7(x100902,f861(x100902,a846),a846),f314(x100902)),x100901))))))),f312(f312(f225(x100902),f12(x100902,f226(x100902),x100903)),f12(x100902,f226(x100902),x100901)))
% 155.94/155.63 [10091]~P103(x100912)+E(x100911,f189(f861(x100912,a846)))+E(x100913,f189(f861(x100912,a846)))+~P22(f312(f70(x100912),x100911))+~P22(f312(f70(x100912),x100913))+E(f13(x100912,f225(x100912),f312(f233(x100912),f312(f312(f8(f861(x100912,a846),a846,x100912),f96(x100912)),f312(f312(f8(f861(x100912,f861(x100912,a846)),f861(x100912,a846),x100912),f312(f8(f861(x100912,a846),a846,x100912),f96(x100912))),f312(f312(f7(x100912,f861(x100912,f861(x100912,a846)),f861(x100912,f861(x100912,a846))),f312(f312(f8(f861(x100912,f861(f861(x100912,a846),f861(x100912,a846))),f861(f861(x100912,f861(x100912,a846)),f861(x100912,f861(x100912,a846))),x100912),f18(x100912,f861(x100912,a846),f861(x100912,a846))),f312(f312(f8(f861(x100912,f861(x100912,f861(a846,a846))),f861(x100912,f861(f861(x100912,a846),f861(x100912,a846))),x100912),f312(f8(f861(x100912,f861(a846,a846)),f861(f861(x100912,a846),f861(x100912,a846)),x100912),f18(x100912,a846,a846))),f312(f312(f8(f861(x100912,f861(x100912,a846)),f861(x100912,f861(x100912,f861(a846,a846))),x100912),f312(f8(f861(x100912,a846),f861(x100912,f861(a846,a846)),x100912),f312(f8(a846,f861(a846,a846),x100912),a310))),f312(f312(f7(x100912,f861(x100912,f861(x100912,x100912)),f861(x100912,f861(x100912,a846))),f312(f312(f8(f861(f861(x100912,x100912),f861(x100912,a846)),f861(f861(x100912,f861(x100912,x100912)),f861(x100912,f861(x100912,a846))),x100912),f8(f861(x100912,x100912),f861(x100912,a846),x100912)),f312(f312(f8(f861(x100912,a846),f861(f861(x100912,x100912),f861(x100912,a846)),x100912),f8(x100912,a846,x100912)),a309))),f226(x100912)))))),f312(f312(f7(x100912,f861(x100912,a846),f861(x100912,a846)),f312(f312(f8(f861(a846,a846),f861(f861(x100912,a846),f861(x100912,a846)),x100912),f8(a846,a846,x100912)),f312(f312(f8(a846,f861(a846,a846),x100912),a310),f312(f312(f7(x100912,f861(x100912,a846),a846),f314(x100912)),x100913)))),f312(f312(f7(x100912,f861(x100912,a846),a846),f314(x100912)),x100911))))))),f312(f312(f226(x100912),f13(x100912,f225(x100912),x100913)),f13(x100912,f225(x100912),x100911)))
% 155.94/155.63 [7090]~P117(x70903)+E(x70901,x70902)+~E(f312(f312(f240(x70903),x70901),x70904),f312(f312(f240(x70903),x70902),x70904))+~P22(f312(f312(f227(x70903),f2(x70903)),x70902))+~P22(f312(f312(f227(x70903),f2(x70903)),x70901))+~P22(f312(f312(f228(a853),f2(a853)),x70904))
% 155.94/155.63 [9015]~P22(f312(x90152,x90153))+~P22(f312(x90151,x90154))+E(f231(a853,x90151),f312(a126,f231(a853,x90152)))+P22(f312(x90152,f751(x90153,x90152,x90154,x90151)))+P22(f312(x90151,f2(a853)))+P22(f312(x90151,f312(a126,f751(x90153,x90152,x90154,x90151))))
% 155.94/155.63 [9269]~P22(f312(x92692,x92693))+~P22(f312(x92691,x92694))+E(f231(a853,x92691),f312(a126,f231(a853,x92692)))+~P22(f312(x92692,f751(x92693,x92692,x92694,x92691)))+P22(f312(x92691,f2(a853)))+~P22(f312(x92691,f312(a126,f751(x92693,x92692,x92694,x92691))))
% 155.94/155.63 [7350]~P103(x73502)+E(x73501,f189(f861(x73502,a846)))+~P22(f312(f70(x73502),x73501))+~P22(f312(f312(f314(x73502),x73504),x73501))+P22(f312(f312(f228(x73502),x73503),x73504))+~P22(f312(f312(f228(x73502),x73503),f312(f72(x73502,f225(x73502)),x73501)))
% 155.94/155.63 [7351]~P99(x73512)+E(x73511,f189(f861(x73512,a846)))+~P22(f312(f70(x73512),x73511))+~P22(f312(f312(f314(x73512),x73514),x73511))+P22(f312(f312(f227(x73512),x73513),x73514))+~P22(f312(f312(f227(x73512),x73513),f312(f72(x73512,f115(x73512)),x73511)))
% 155.94/155.63 [7352]~P103(x73522)+E(x73521,f189(f861(x73522,a846)))+~P22(f312(f70(x73522),x73521))+~P22(f312(f312(f314(x73522),x73524),x73521))+P22(f312(f312(f227(x73522),x73523),x73524))+~P22(f312(f312(f227(x73522),x73523),f312(f72(x73522,f225(x73522)),x73521)))
% 155.94/155.63 [7229]E(x72291,f2(a1))+E(f312(f47(a1,x72292),x72291),x72293)+~P22(f312(f312(f227(a1),x72294),f2(a1)))+~E(x72292,f312(f312(f89(a1),f312(f312(f90(a1),x72291),x72293)),x72294))+P22(f312(f312(f228(a1),f2(a1)),x72291))+~P22(f312(f312(f228(a1),x72291),x72294))
% 155.94/155.63 [7268]E(f54(a1,x72682,x72681),x72683)+E(x72681,f2(a1))+~P22(f312(f312(f227(a1),x72683),f2(a1)))+~E(x72682,f312(f312(f89(a1),f312(f312(f90(a1),x72681),x72684)),x72683))+P22(f312(f312(f228(a1),f2(a1)),x72681))+~P22(f312(f312(f228(a1),x72681),x72683))
% 155.94/155.63 [7378]E(x73781,f2(a1))+E(f312(f47(a1,x73782),x73781),x73783)+~E(x73782,f312(f312(f89(a1),f312(f312(f90(a1),x73781),x73783)),x73784))+~P22(f312(f312(f228(a1),f2(a1)),x73781))+~P22(f312(f312(f227(a1),f2(a1)),x73784))+~P22(f312(f312(f228(a1),x73784),x73781))
% 155.94/155.63 [7412]E(f54(a1,x74122,x74121),x74123)+E(x74121,f2(a1))+~E(x74122,f312(f312(f89(a1),f312(f312(f90(a1),x74121),x74124)),x74123))+~P22(f312(f312(f228(a1),f2(a1)),x74121))+~P22(f312(f312(f227(a1),f2(a1)),x74123))+~P22(f312(f312(f228(a1),x74123),x74121))
% 155.94/155.63 [7551]~P103(x75512)+E(x75511,f189(f861(x75512,a846)))+~P22(f312(f70(x75512),x75511))+~P22(f312(f312(f228(x75512),x75514),x75513))+~P22(f312(f312(f314(x75512),x75514),x75511))+P22(f312(f312(f228(x75512),f312(f72(x75512,f225(x75512)),x75511)),x75513))
% 155.94/155.63 [7552]~P103(x75522)+E(x75521,f189(f861(x75522,a846)))+~P22(f312(f70(x75522),x75521))+~P22(f312(f312(f227(x75522),x75524),x75523))+~P22(f312(f312(f314(x75522),x75524),x75521))+P22(f312(f312(f227(x75522),f312(f72(x75522,f225(x75522)),x75521)),x75523))
% 155.94/155.63 [8122]~P22(f312(f312(f227(a1),x81224),f2(a1)))+~E(x81221,f312(f312(f89(a1),f312(f312(f90(a1),x81222),x81223)),x81224))+~P22(f312(f312(f227(a1),f2(a1)),x81224))+~P22(f312(f312(f228(a1),x81224),x81222))+~P22(f312(f312(f228(a1),x81222),x81224))+P22(f312(f57(x81221,x81222),f312(f312(f239(a1,a1),x81223),x81224)))
% 155.94/155.63 [9071]~P63(x90713)+~P63(x90714)+E(x90711,x90712)+~E(f312(f190(f854(x90713)),x90712),f312(f190(f854(x90714)),f64(x90714)))+~E(f312(f190(f854(x90713)),x90711),f312(f190(f854(x90714)),f64(x90714)))+~E(f312(f82(f857(x90713),x90713,x90714,f223(x90713)),f312(f173(x90714,x90713),f312(f312(f177(x90714,x90713),f64(x90714)),x90711))),f312(f82(f857(x90713),x90713,x90714,f223(x90713)),f312(f173(x90714,x90713),f312(f312(f177(x90714,x90713),f64(x90714)),x90712))))
% 155.94/155.63 [8290]~P105(x82901)+P22(f312(f312(f228(f861(x82901,a846)),f283(x82901,x82902,x82903)),f283(x82901,x82904,x82905)))+~P22(f312(f312(f228(x82901),x82903),x82905))+~P22(f312(f312(f227(x82901),x82904),x82902))+~P22(f312(f312(f227(x82901),x82904),x82905))+~P22(f312(f312(f227(x82901),x82903),x82905))
% 155.94/155.63 [8291]~P105(x82911)+P22(f312(f312(f228(f861(x82911,a846)),f283(x82911,x82912,x82913)),f283(x82911,x82914,x82915)))+~P22(f312(f312(f228(x82911),x82914),x82912))+~P22(f312(f312(f227(x82911),x82913),x82915))+~P22(f312(f312(f227(x82911),x82914),x82915))+~P22(f312(f312(f227(x82911),x82914),x82912))
% 155.94/155.63 [9137]P58(x91372,x91373,x91374,x91371)+E(x91371,f189(f861(x91372,a846)))+~P22(f312(f70(x91372),x91374))+~P22(f312(f70(x91372),x91371))+~P22(f312(f312(x91373,f511(x91371,x91374,x91373,x91372)),x91375))+~P22(f312(f312(f314(x91372),x91375),x91371))
% 155.94/155.63 [9284]~E(x92843,x92845)+~P26(x92841)+~P72(x92841)+~P43(x92843)+E(f312(f312(f9(a1,x92841),x92842),x92843),f312(f312(f9(a1,x92841),x92844),x92845))+P22(f312(f312(f227(a1),f2(a1)),f512(x92842,x92844,x92843,x92845,x92841)))
% 155.94/155.63 [9285]~E(x92853,x92855)+~P26(x92851)+~P72(x92851)+~P43(x92853)+E(f312(f312(f6(a1,x92851),x92852),x92853),f312(f312(f6(a1,x92851),x92854),x92855))+P22(f312(f312(f227(a1),f2(a1)),f513(x92852,x92854,x92853,x92855,x92851)))
% 155.94/155.63 [9452]~E(x94525,x94523)+~P26(x94521)+~P72(x94521)+~P43(x94525)+~E(f312(x94522,f512(x94524,x94522,x94525,x94523,x94521)),f312(x94524,f512(x94524,x94522,x94525,x94523,x94521)))+E(f312(f312(f9(a1,x94521),x94522),x94523),f312(f312(f9(a1,x94521),x94524),x94525))
% 155.94/155.63 [9453]~E(x94535,x94533)+~P26(x94531)+~P72(x94531)+~P43(x94535)+~E(f312(x94532,f513(x94534,x94532,x94535,x94533,x94531)),f312(x94534,f513(x94534,x94532,x94535,x94533,x94531)))+E(f312(f312(f6(a1,x94531),x94532),x94533),f312(f312(f6(a1,x94531),x94534),x94535))
% 155.94/155.63 [9537]~P76(x95373)+E(f312(x95371,x95372),f2(x95373))+~E(f312(f312(f6(x95374,x95373),x95371),x95375),f2(x95373))+~P22(f312(f70(x95374),x95375))+P22(f312(f312(f314(x95374),f500(x95372,x95371,x95375,x95374,x95373)),x95375))+~P22(f312(f312(f314(x95374),x95372),x95375))
% 155.94/155.63 [9671]~P76(x96713)+E(f312(x96711,x96712),f2(x96713))+~E(f312(f312(f6(x96714,x96713),x96711),x96715),f2(x96713))+~P22(f312(f70(x96714),x96715))+~P22(f312(f312(f314(x96714),x96712),x96715))+~P22(f312(f312(f227(x96713),f2(x96713)),f312(x96711,f500(x96712,x96711,x96715,x96714,x96713))))
% 155.94/155.63 [8205]~P122(x82051)+~P22(f312(f312(f227(x82051),f2(x82051)),x82053))+~P22(f312(f312(f228(x82051),x82053),x82055))+~P22(f312(f312(f228(x82051),x82052),x82054))+~P22(f312(f312(f228(x82051),f2(x82051)),x82054))+P22(f312(f312(f228(x82051),f312(f312(f90(x82051),x82052),x82053)),f312(f312(f90(x82051),x82054),x82055)))
% 155.94/155.63 [8206]~P122(x82061)+~P22(f312(f312(f227(x82061),f2(x82061)),x82063))+~P22(f312(f312(f227(x82061),f2(x82061)),x82062))+~P22(f312(f312(f228(x82061),x82063),x82065))+~P22(f312(f312(f228(x82061),x82062),x82064))+P22(f312(f312(f228(x82061),f312(f312(f90(x82061),x82062),x82063)),f312(f312(f90(x82061),x82064),x82065)))
% 155.94/155.63 [8207]~P122(x82071)+~P22(f312(f312(f227(x82071),x82072),x82074))+~P22(f312(f312(f227(x82071),f2(x82071)),x82073))+~P22(f312(f312(f228(x82071),x82073),x82075))+~P22(f312(f312(f228(x82071),f2(x82071)),x82072))+P22(f312(f312(f228(x82071),f312(f312(f90(x82071),x82072),x82073)),f312(f312(f90(x82071),x82074),x82075)))
% 155.94/155.63 [8208]~P122(x82081)+~P22(f312(f312(f227(x82081),x82083),x82085))+~P22(f312(f312(f227(x82081),f2(x82081)),x82082))+~P22(f312(f312(f228(x82081),x82082),x82084))+~P22(f312(f312(f228(x82081),f2(x82081)),x82083))+P22(f312(f312(f228(x82081),f312(f312(f90(x82081),x82082),x82083)),f312(f312(f90(x82081),x82084),x82085)))
% 155.94/155.63 [8209]~P67(x82091)+~P22(f312(f312(f227(x82091),x82092),x82094))+~P22(f312(f312(f228(x82091),x82095),x82093))+~P22(f312(f312(f228(x82091),f2(x82091)),x82095))+~P22(f312(f312(f228(x82091),f2(x82091)),x82092))+P22(f312(f312(f228(x82091),f312(f312(f268(x82091),x82092),x82093)),f312(f312(f268(x82091),x82094),x82095)))
% 155.94/155.63 [8210]~P67(x82101)+~P22(f312(f312(f227(x82101),x82105),x82103))+~P22(f312(f312(f227(x82101),f2(x82101)),x82102))+~P22(f312(f312(f228(x82101),x82102),x82104))+~P22(f312(f312(f228(x82101),f2(x82101)),x82105))+P22(f312(f312(f228(x82101),f312(f312(f268(x82101),x82102),x82103)),f312(f312(f268(x82101),x82104),x82105)))
% 155.94/155.63 [8211]~P130(x82111)+~P22(f312(f312(f227(x82111),x82113),x82115))+~P22(f312(f312(f227(x82111),x82112),x82114))+~P22(f312(f312(f227(x82111),f2(x82111)),x82113))+~P22(f312(f312(f227(x82111),f2(x82111)),x82114))+P22(f312(f312(f227(x82111),f312(f312(f90(x82111),x82112),x82113)),f312(f312(f90(x82111),x82114),x82115)))
% 155.94/155.63 [8212]~P130(x82121)+~P22(f312(f312(f227(x82121),x82123),x82125))+~P22(f312(f312(f227(x82121),x82122),x82124))+~P22(f312(f312(f227(x82121),f2(x82121)),x82123))+~P22(f312(f312(f227(x82121),f2(x82121)),x82122))+P22(f312(f312(f227(x82121),f312(f312(f90(x82121),x82122),x82123)),f312(f312(f90(x82121),x82124),x82125)))
% 155.94/155.63 [8213]~P67(x82131)+~P22(f312(f312(f228(x82131),f2(x82131)),x82135))+~P22(f312(f312(f227(x82131),x82135),x82133))+~P22(f312(f312(f227(x82131),x82132),x82134))+~P22(f312(f312(f227(x82131),f2(x82131)),x82132))+P22(f312(f312(f227(x82131),f312(f312(f268(x82131),x82132),x82133)),f312(f312(f268(x82131),x82134),x82135)))
% 155.94/155.63 [9575]~P26(x95755)+~P80(x95755)+E(x95751,f189(f861(x95752,a846)))+~P22(f312(f70(x95752),x95751))+P22(f312(f312(f314(x95752),f510(x95753,x95754,x95751,x95752,x95755)),x95751))+P22(f312(f312(f228(x95755),f312(f312(f6(x95752,x95755),x95754),x95751)),f312(f312(f6(x95752,x95755),x95753),x95751)))
% 155.94/155.63 [9692]~P26(x96921)+~P82(x96921)+~P22(f312(f70(x96922),x96925))+~P22(f312(f312(f227(x96921),f2(x96921)),f312(x96923,f501(x96923,x96924,x96925,x96922,x96921))))+P22(f312(f312(f227(x96921),f312(f312(f6(x96922,x96921),x96923),x96924)),f312(f312(f6(x96922,x96921),x96923),x96925)))+~P22(f312(f312(f227(f861(x96922,a846)),x96924),x96925))
% 155.94/155.63 [9864]~P26(x98643)+~P80(x98643)+E(x98641,f189(f861(x98642,a846)))+~P22(f312(f70(x98642),x98641))+~P22(f312(f312(f228(x98643),f312(x98644,f510(x98645,x98644,x98641,x98642,x98643))),f312(x98645,f510(x98645,x98644,x98641,x98642,x98643))))+P22(f312(f312(f228(x98643),f312(f312(f6(x98642,x98643),x98644),x98641)),f312(f312(f6(x98642,x98643),x98645),x98641)))
% 155.94/155.63 [6947]~P12(x69472,x69475,x69474)+E(x69471,f189(f861(x69472,a846)))+E(x69473,f189(f861(x69472,a846)))+~P22(f312(f70(x69472),x69471))+~P22(f312(f70(x69472),x69473))+E(f312(x69474,f312(f312(f124(f861(x69472,a846)),x69473),x69471)),f312(f312(x69475,f312(x69474,x69473)),f312(x69474,x69471)))
% 155.94/155.63 [7520]~P140(x75201,x75204,x75203)+P22(f312(x75201,x75202))+~P22(f312(f312(f228(a1),x75204),f2(a1)))+~P22(f312(f312(f227(a1),x75205),f2(a1)))+~E(x75203,f312(f312(f89(a1),f312(f312(f90(a1),x75204),x75202)),x75205))+~P22(f312(f312(f228(a1),x75204),x75205))
% 155.94/155.63 [7521]~P139(x75211,x75214,x75213)+P22(f312(x75211,x75212))+~P22(f312(f312(f228(a1),x75214),f2(a1)))+~P22(f312(f312(f227(a1),x75212),f2(a1)))+~E(x75213,f312(f312(f89(a1),f312(f312(f90(a1),x75214),x75215)),x75212))+~P22(f312(f312(f228(a1),x75214),x75212))
% 155.94/155.63 [7561]~P140(x75611,x75614,x75613)+P22(f312(x75611,x75612))+~E(x75613,f312(f312(f89(a1),f312(f312(f90(a1),x75614),x75612)),x75615))+~P22(f312(f312(f228(a1),f2(a1)),x75614))+~P22(f312(f312(f227(a1),f2(a1)),x75615))+~P22(f312(f312(f228(a1),x75615),x75614))
% 155.94/155.63 [7562]~P139(x75621,x75624,x75623)+P22(f312(x75621,x75622))+~E(x75623,f312(f312(f89(a1),f312(f312(f90(a1),x75624),x75625)),x75622))+~P22(f312(f312(f228(a1),f2(a1)),x75624))+~P22(f312(f312(f227(a1),f2(a1)),x75622))+~P22(f312(f312(f228(a1),x75622),x75624))
% 155.94/155.63 [8439]P22(f312(f312(x84391,x84392),x84393))+~P22(f312(f312(x84391,f312(f47(a1,x84394),x84395)),f54(a1,x84394,x84395)))+~P22(f312(f312(f228(a1),x84395),f2(a1)))+~P22(f312(f312(f227(a1),x84393),f2(a1)))+~E(x84394,f312(f312(f89(a1),f312(f312(f90(a1),x84395),x84392)),x84393))+~P22(f312(f312(f228(a1),x84395),x84393))
% 155.94/155.63 [8459]P22(f312(f312(x84591,x84592),x84593))+~P22(f312(f312(x84591,f312(f47(a1,x84594),x84595)),f54(a1,x84594,x84595)))+~E(x84594,f312(f312(f89(a1),f312(f312(f90(a1),x84595),x84592)),x84593))+~P22(f312(f312(f228(a1),f2(a1)),x84595))+~P22(f312(f312(f227(a1),f2(a1)),x84593))+~P22(f312(f312(f228(a1),x84593),x84595))
% 155.94/155.63 [8751]E(x87511,x87512)+~P55(x87513,x87515,x87514)+~P22(f312(f312(f314(x87513),x87512),x87515))+~P22(f312(f312(f314(x87513),x87511),x87515))+P22(f312(f312(f314(f860(x87513,x87513)),f312(f312(f239(x87513,x87513),x87511),x87512)),x87514))+P22(f312(f312(f314(f860(x87513,x87513)),f312(f312(f239(x87513,x87513),x87512),x87511)),x87514))
% 155.94/155.63 [9555]~P105(x95551)+~P105(x95552)+~P49(x95552,x95551,x95553)+~P22(f312(f312(f227(x95552),x95555),f831(x95554,x95553,x95552,x95551,x95555)))+E(f231(x95551,f312(f312(f7(x95551,f861(x95551,a846),a846),f314(x95551)),f312(f290(x95552,x95551,x95553),x95554))),f312(x95553,f231(x95552,f312(f312(f7(x95552,f861(x95552,a846),a846),f314(x95552)),x95554))))+~P22(f312(f312(f314(x95552),x95555),x95554))
% 155.94/155.63 [9602]~P26(x96025)+~P82(x96025)+~P22(f312(f70(x96021),x96024))+P22(f312(f312(f227(x96025),f312(f312(f6(x96021,x96025),x96022),x96023)),f312(f312(f6(x96021,x96025),x96022),x96024)))+~P22(f312(f312(f227(f861(x96021,a846)),x96023),x96024))+P22(f312(f312(f314(x96021),f501(x96022,x96023,x96024,x96021,x96025)),f312(f312(f21(f861(x96021,a846)),x96024),x96023)))
% 155.94/155.63 [9619]~P105(x96191)+~P105(x96192)+~P49(x96192,x96191,x96193)+E(f231(x96191,f312(f312(f7(x96191,f861(x96191,a846),a846),f314(x96191)),f312(f290(x96192,x96191,x96193),x96194))),f312(x96193,f231(x96192,f312(f312(f7(x96192,f861(x96192,a846),a846),f314(x96192)),x96194))))+~P22(f312(f312(f314(x96192),x96195),x96194))+P22(f312(f312(f314(x96192),f831(x96194,x96193,x96192,x96191,x96195)),x96194))
% 155.94/155.63 [9698]E(x96981,f189(f861(x96982,a846)))+~P22(f312(f70(x96982),x96983))+~P22(f312(f70(x96982),x96981))+P22(f312(f312(f314(f860(f861(x96982,a846),f861(x96982,a846))),f312(f312(f239(f861(x96982,a846),f861(x96982,a846)),x96983),x96981)),f303(x96982,x96984)))+~P22(f312(f312(f314(x96982),x96985),x96981))+~P22(f312(f312(f314(f860(x96982,x96982)),f312(f312(f239(x96982,x96982),f516(x96984,x96981,x96983,x96982)),x96985)),x96984))
% 155.94/155.63 [9699]E(x96991,f189(f861(x96992,a846)))+~P22(f312(f70(x96992),x96993))+~P22(f312(f70(x96992),x96991))+P22(f312(f312(f314(f860(f861(x96992,a846),f861(x96992,a846))),f312(f312(f239(f861(x96992,a846),f861(x96992,a846)),x96993),x96991)),f303(x96992,x96994)))+~P22(f312(f312(f314(x96992),x96995),x96991))+~P22(f312(f312(f314(f860(x96992,x96992)),f312(f312(f239(x96992,x96992),f741(x96994,x96991,x96993,x96992)),x96995)),x96994))
% 155.94/155.63 [9869]~P76(x98691)+~E(f312(f312(f6(x98695,x98691),x98692),x98696),x98694)+~P22(f312(f70(x98695),x98696))+P22(f312(f312(f314(x98695),f504(x98693,x98694,x98692,x98696,x98695,x98691)),x98696))+P22(f312(f312(f227(x98691),f312(x98692,x98693)),x98694))+~P22(f312(f312(f314(x98695),x98693),x98696))
% 155.94/155.63 [9920]~P76(x99201)+~E(f312(f312(f6(x99205,x99201),x99202),x99206),x99204)+~P22(f312(f70(x99205),x99206))+~P22(f312(f312(f314(x99205),x99203),x99206))+~P22(f312(f312(f227(x99201),f2(x99201)),f312(x99202,f504(x99203,x99204,x99202,x99206,x99205,x99201))))+P22(f312(f312(f227(x99201),f312(x99202,x99203)),x99204))
% 155.94/155.63 [10034]~E(x100345,x100348)+~E(x100344,x100347)+~P26(x100342)+~P104(x100341)+E(f312(f312(f6(x100341,x100342),x100343),f312(f282(x100341,x100344),x100345)),f312(f312(f6(x100341,x100342),x100346),f312(f282(x100341,x100347),x100348)))+P22(f312(f312(f227(x100341),x100344),f752(x100343,x100346,x100345,x100348,x100344,x100347,x100341,x100342)))
% 155.94/155.63 [10050]~E(x100507,x100504)+~E(x100508,x100505)+~P26(x100502)+~P104(x100501)+~E(f312(x100503,f752(x100506,x100503,x100508,x100505,x100507,x100504,x100501,x100502)),f312(x100506,f752(x100506,x100503,x100508,x100505,x100507,x100504,x100501,x100502)))+E(f312(f312(f6(x100501,x100502),x100503),f312(f282(x100501,x100504),x100505)),f312(f312(f6(x100501,x100502),x100506),f312(f282(x100501,x100507),x100508)))
% 155.94/155.63 [10054]~E(x100544,x100547)+~E(x100545,x100548)+~P26(x100542)+~P104(x100541)+E(f312(f312(f6(x100541,x100542),x100543),f312(f282(x100541,x100544),x100545)),f312(f312(f6(x100541,x100542),x100546),f312(f282(x100541,x100547),x100548)))+P22(f312(f312(f228(x100541),f752(x100543,x100546,x100545,x100548,x100544,x100547,x100541,x100542)),x100545))
% 155.94/155.63 [9704]~P3(x97045,x97049,x97046)+~P3(x97041,x970410,x97043)+~P10(x97041,x97045,f861(x97042,a846),x97043,x97046,x97048)+~P22(f312(f312(f314(x97045),x97047),x97049))+~P22(f312(f312(f314(x97041),x97044),x970410))+E(f312(f312(f50(x97041,f861(x97042,a846)),f312(f264(x97041,x97041,x97043),f312(f312(f289(x97041),x97044),f189(f861(x97041,a846))))),f312(f312(f8(f861(x97045,f861(x97042,a846)),f861(x97042,a846),x97041),f312(f50(x97045,f861(x97042,a846)),f312(f264(x97045,x97045,x97046),f312(f312(f289(x97045),x97047),f189(f861(x97045,a846)))))),x97048)),f312(f312(x97048,x97044),x97047))
% 155.94/155.63 [5516]~P103(x55163)+~P33(x55163,x55162)+~P33(x55163,x55161)+E(x55161,x55162)+~E(f312(f168(x55163),x55161),f312(f168(x55163),x55162))+~P22(f312(f133(x55163),x55162))+~P22(f312(f133(x55163),x55161))
% 155.94/155.63 [4864]~P137(x48642)+~P126(x48642)+~P127(x48642)+~P109(x48642)+~E(x48643,f2(x48642))+E(x48641,f2(a853))+E(f312(f312(f240(x48642),x48643),x48641),f2(x48642))
% 155.94/155.63 [9014]E(x90141,f2(a853))+~E(x90142,f312(f312(f89(a853),f312(f312(f90(a853),f312(f246(a853,a853),x90143)),x90141)),f312(f248(a853,a853),x90143)))+P22(f312(f56(x90142,x90141),x90143))+~P22(f312(f312(f227(a853),f312(f248(a853,a853),x90143)),f2(a853)))+~P22(f312(f312(f227(a853),f2(a853)),f312(f248(a853,a853),x90143)))+~P22(f312(f312(f228(a853),x90141),f312(f248(a853,a853),x90143)))+~P22(f312(f312(f228(a853),f312(f248(a853,a853),x90143)),x90141))
% 155.94/155.63 [9024]~E(f312(f246(a853,a853),x90243),f2(a853))+~E(x90241,f312(f312(f89(a853),f312(f312(f90(a853),f312(f246(a853,a853),x90243)),x90242)),f312(f248(a853,a853),x90243)))+P22(f312(f56(x90241,x90242),x90243))+~P22(f312(f312(f227(a853),f312(f248(a853,a853),x90243)),f2(a853)))+~P22(f312(f312(f227(a853),f2(a853)),f312(f248(a853,a853),x90243)))+~P22(f312(f312(f228(a853),x90242),f312(f248(a853,a853),x90243)))+~P22(f312(f312(f228(a853),f312(f248(a853,a853),x90243)),x90242))
% 155.94/155.63 [7868]~P68(x78682)+E(x78681,f189(f861(x78682,a846)))+E(x78683,f189(f861(x78682,a846)))+~P22(f312(f70(x78682),x78681))+~P22(f312(f70(x78682),x78683))+~E(f312(f312(f115(f861(x78682,a846)),x78683),x78681),f189(f861(x78682,a846)))+E(f312(f312(f90(x78682),f312(f72(x78682,f90(x78682)),x78683)),f312(f72(x78682,f90(x78682)),x78681)),f312(f72(x78682,f90(x78682)),f312(f312(f124(f861(x78682,a846)),x78683),x78681)))
% 155.94/155.63 [7647]E(x76471,f2(a1))+E(f312(f47(a1,x76472),x76471),x76473)+~P22(f312(f312(f227(a1),x76474),f2(a1)))+~E(x76472,f312(f312(f89(a1),f312(f312(f90(a1),x76471),x76473)),x76474))+~P22(f312(f312(f227(a1),f2(a1)),x76474))+~P22(f312(f312(f228(a1),x76474),x76471))+~P22(f312(f312(f228(a1),x76471),x76474))
% 155.94/155.63 [7665]E(f54(a1,x76652,x76651),x76653)+E(x76651,f2(a1))+~P22(f312(f312(f227(a1),x76653),f2(a1)))+~E(x76652,f312(f312(f89(a1),f312(f312(f90(a1),x76651),x76654)),x76653))+~P22(f312(f312(f227(a1),f2(a1)),x76653))+~P22(f312(f312(f228(a1),x76653),x76651))+~P22(f312(f312(f228(a1),x76651),x76653))
% 155.94/155.63 [7569]~P13(x75692,x75695,x75694)+E(x75691,f189(f861(x75692,a846)))+E(x75693,f189(f861(x75692,a846)))+~P22(f312(f70(x75692),x75691))+~P22(f312(f70(x75692),x75693))+~E(f312(f312(f115(f861(x75692,a846)),x75693),x75691),f189(f861(x75692,a846)))+E(f312(x75694,f312(f312(f124(f861(x75692,a846)),x75693),x75691)),f312(f312(x75695,f312(x75694,x75693)),f312(x75694,x75691)))
% 155.94/155.63 [9256]~P19(x92563,x92561,x92565,x92564)+~P19(x92561,x92563,x92566,x92562)+E(f312(f53(x92561),x92562),f312(f53(x92563),x92564))+~P22(f312(f70(x92563),x92564))+~P22(f312(f70(x92561),x92562))+~P22(f312(f312(f227(f861(x92563,a846)),f312(f290(x92561,x92563,x92566),x92562)),x92564))+~P22(f312(f312(f227(f861(x92561,a846)),f312(f290(x92563,x92561,x92565),x92564)),x92562))
% 155.94/155.63 [9204]~P22(f312(f312(f228(a1),f312(f312(f89(a1),f312(f312(f90(a1),x92045),x92041)),x92046)),f2(a1)))+~E(f312(f312(f89(a1),f312(f312(f90(a1),x92043),x92042)),x92044),f312(f312(f89(a1),f312(f312(f90(a1),x92045),x92041)),x92046))+~P22(f312(f312(f228(a1),f2(a1)),x92045))+~P22(f312(f312(f227(a1),f2(a1)),x92046))+~P22(f312(f312(f228(a1),x92044),x92043))+~P22(f312(f312(f227(a1),x92045),x92043))+P22(f312(f312(f227(a1),x92041),x92042))
% 155.94/155.63 [8968]~E(f312(f312(f89(a1),f312(f312(f90(a1),x89683),x89681)),x89684),f312(f312(f89(a1),f312(f312(f90(a1),x89685),x89682)),x89686))+~P22(f312(f312(f228(a1),f2(a1)),x89685))+~P22(f312(f312(f227(a1),f2(a1)),x89684))+~P22(f312(f312(f228(a1),x89686),x89685))+~P22(f312(f312(f227(a1),x89685),x89683))+P22(f312(f312(f227(a1),x89681),x89682))+~P22(f312(f312(f227(a1),f2(a1)),f312(f312(f89(a1),f312(f312(f90(a1),x89685),x89682)),x89686)))
% 155.94/155.63 [9144]~P124(x91441)+~E(f312(f312(f89(x91441),x91442),x91444),f87(x91441))+~P22(f312(f312(f227(x91441),f2(x91441)),x91444))+~P22(f312(f312(f227(x91441),f2(x91441)),x91442))+~P22(f312(f312(f228(x91441),x91445),x91446))+~P22(f312(f312(f228(x91441),x91443),x91446))+P22(f312(f312(f228(x91441),f312(f312(f89(x91441),f312(f312(f90(x91441),x91442),x91443)),f312(f312(f90(x91441),x91444),x91445))),x91446))
% 155.94/155.63 [9145]~P125(x91451)+~E(f312(f312(f89(x91451),x91452),x91454),f87(x91451))+~P22(f312(f312(f227(x91451),x91455),x91456))+~P22(f312(f312(f227(x91451),x91453),x91456))+~P22(f312(f312(f227(x91451),f2(x91451)),x91454))+~P22(f312(f312(f227(x91451),f2(x91451)),x91452))+P22(f312(f312(f227(x91451),f312(f312(f89(x91451),f312(f312(f90(x91451),x91452),x91453)),f312(f312(f90(x91451),x91454),x91455))),x91456))
% 155.94/155.63 [9966]~P3(x99667,x99666,x99665)+E(x99661,x99662)+~P9(x99667,f861(x99664,a846),x99665,x99663)+E(f312(x99663,f415(x99661,x99662,x99663,x99664,x99665,x99666,x99667)),f312(x99663,f416(x99661,x99662,x99663,x99664,x99665,x99666,x99667)))+~E(f312(f312(f50(x99667,f861(x99664,a846)),x99661),x99663),f312(f312(f50(x99667,f861(x99664,a846)),x99662),x99663))+~P22(f312(f312(f314(f861(x99667,a846)),x99662),f312(f312(f69(x99667),x99666),x99665)))+~P22(f312(f312(f314(f861(x99667,a846)),x99661),f312(f312(f69(x99667),x99666),x99665)))
% 155.94/155.63 [9999]~P3(x99993,x99997,x99996)+E(x99991,x99992)+~P9(x99993,f861(x99995,a846),x99996,x99994)+~E(f312(f312(f50(x99993,f861(x99995,a846)),x99991),x99994),f312(f312(f50(x99993,f861(x99995,a846)),x99992),x99994))+P22(f312(f312(f314(x99993),f416(x99991,x99992,x99994,x99995,x99996,x99997,x99993)),x99997))+~P22(f312(f312(f314(f861(x99993,a846)),x99992),f312(f312(f69(x99993),x99997),x99996)))+~P22(f312(f312(f314(f861(x99993,a846)),x99991),f312(f312(f69(x99993),x99997),x99996)))
% 155.94/155.63 [10000]~P3(x100003,x100007,x100006)+E(x100001,x100002)+~P9(x100003,f861(x100005,a846),x100006,x100004)+~E(f312(f312(f50(x100003,f861(x100005,a846)),x100001),x100004),f312(f312(f50(x100003,f861(x100005,a846)),x100002),x100004))+P22(f312(f312(f314(x100003),f415(x100001,x100002,x100004,x100005,x100006,x100007,x100003)),x100007))+~P22(f312(f312(f314(f861(x100003,a846)),x100002),f312(f312(f69(x100003),x100007),x100006)))+~P22(f312(f312(f314(f861(x100003,a846)),x100001),f312(f312(f69(x100003),x100007),x100006)))
% 155.94/155.63 [10072]E(x100721,x100722)+~P3(x100723,x100726,x100727)+~P9(x100723,f861(x100724,a846),x100727,x100725)+~E(f312(f312(f50(x100723,f861(x100724,a846)),x100721),x100725),f312(f312(f50(x100723,f861(x100724,a846)),x100722),x100725))+~P22(f312(f312(f314(f860(x100723,x100723)),f312(f312(f239(x100723,x100723),f416(x100721,x100722,x100725,x100724,x100727,x100726,x100723)),f415(x100721,x100722,x100725,x100724,x100727,x100726,x100723))),x100727))+~P22(f312(f312(f314(f861(x100723,a846)),x100722),f312(f312(f69(x100723),x100726),x100727)))+~P22(f312(f312(f314(f861(x100723,a846)),x100721),f312(f312(f69(x100723),x100726),x100727)))
% 155.94/155.63 [8967]~P3(x89671,x89677,x89674)+~E(x89675,x89676)+~P22(f312(f312(f314(x89671),x89673),x89676))+~P22(f312(f312(f314(x89671),x89672),x89675))+~P22(f312(f312(f314(f861(x89671,a846)),x89676),f312(f312(f69(x89671),x89677),x89674)))+~P22(f312(f312(f314(f861(x89671,a846)),x89675),f312(f312(f69(x89671),x89677),x89674)))+P22(f312(f312(f314(f860(x89671,x89671)),f312(f312(f239(x89671,x89671),x89672),x89673)),x89674))
% 155.94/155.63 [9099]E(x90991,x90992)+~P3(x90993,x90994,x90995)+~P22(f312(f312(f314(x90993),x90996),x90992))+~P22(f312(f312(f314(x90993),x90997),x90991))+~P22(f312(f312(f314(f861(x90993,a846)),x90992),f312(f312(f69(x90993),x90994),x90995)))+~P22(f312(f312(f314(f861(x90993,a846)),x90991),f312(f312(f69(x90993),x90994),x90995)))+~P22(f312(f312(f314(f860(x90993,x90993)),f312(f312(f239(x90993,x90993),x90997),x90996)),x90995))
% 155.94/155.63 [10095]~P3(x100959,x100958,x100957)+~P3(x100951,x1009511,x1009510)+~P10(x100951,x100959,f861(x100956,a846),x1009510,x100957,x100955)+P22(f312(f312(f314(x100951),f417(x100952,x100953,x100954,x100955,x100956,x100957,x100958,x100959,x1009510,x1009511,x100951)),x1009511))+~P22(f312(f312(f314(f861(x100959,a846)),x100953),f312(f312(f69(x100959),x100958),x100957)))+~P22(f312(f312(f314(f861(x100951,a846)),x100954),f312(f312(f69(x100951),x1009511),x1009510)))+P22(f312(f312(f314(f861(x100956,a846)),f312(f312(f50(x100951,f861(x100956,a846)),x100954),f312(f312(f8(f861(x100959,f861(x100956,a846)),f861(x100956,a846),x100951),f312(f50(x100959,f861(x100956,a846)),x100953)),x100955))),x100952))
% 155.94/155.63 [10096]~P3(x1009611,x1009610,x100969)+~P3(x100961,x100968,x100967)+~P10(x1009611,x100961,f861(x100966,a846),x100969,x100967,x100965)+P22(f312(f312(f314(x100961),f423(x100962,x100963,x100964,x100965,x100966,x100967,x100968,x100961,x100969,x1009610,x1009611)),x100968))+~P22(f312(f312(f314(f861(x1009611,a846)),x100964),f312(f312(f69(x1009611),x1009610),x100969)))+~P22(f312(f312(f314(f861(x100961,a846)),x100963),f312(f312(f69(x100961),x100968),x100967)))+P22(f312(f312(f314(f861(x100966,a846)),f312(f312(f50(x1009611,f861(x100966,a846)),x100964),f312(f312(f8(f861(x100961,f861(x100966,a846)),f861(x100966,a846),x1009611),f312(f50(x100961,f861(x100966,a846)),x100963)),x100965))),x100962))
% 155.94/155.63 [10099]~P3(x100992,x100998,x100999)+~P3(x100994,x1009910,x1009911)+~P10(x100992,x100994,f861(x100991,a846),x100999,x1009911,x100996)+~P22(f312(f312(f314(f861(x100992,a846)),x100993),f312(f312(f69(x100992),x100998),x100999)))+~P22(f312(f312(f314(f861(x100994,a846)),x100995),f312(f312(f69(x100994),x1009910),x1009911)))+~P22(f312(f312(f314(f861(x100991,a846)),f312(f312(x100996,f417(x100997,x100995,x100993,x100996,x100991,x1009911,x1009910,x100994,x100999,x100998,x100992)),f423(x100997,x100995,x100993,x100996,x100991,x1009911,x1009910,x100994,x100999,x100998,x100992))),x100997))+P22(f312(f312(f314(f861(x100991,a846)),f312(f312(f50(x100992,f861(x100991,a846)),x100993),f312(f312(f8(f861(x100994,f861(x100991,a846)),f861(x100991,a846),x100992),f312(f50(x100994,f861(x100991,a846)),x100995)),x100996))),x100997))
% 155.94/155.63 [9001]E(x90011,x90012)+~P103(x90014)+~P19(x90013,x90014,x90015,f312(f312(f124(f861(x90013,a846)),f312(f168(x90013),x90011)),f312(f168(x90013),x90012)))+~E(f312(f168(x90013),x90011),f312(f168(x90013),x90012))+~P33(x90014,f312(f312(f150(x90013,x90014),x90015),x90012))+~P33(x90014,f312(f312(f150(x90013,x90014),x90015),x90011))+~P22(f312(f133(x90014),f312(f312(f150(x90013,x90014),x90015),x90012)))+~P22(f312(f133(x90014),f312(f312(f150(x90013,x90014),x90015),x90011)))
% 155.94/155.63 %EqnAxiom
% 155.94/155.63 [1]E(x11,x11)
% 155.94/155.63 [2]E(x22,x21)+~E(x21,x22)
% 155.94/155.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 155.94/155.63 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 155.94/155.63 [5]~E(x51,x52)+E(f114(x51),f114(x52))
% 155.94/155.63 [6]~E(x61,x62)+E(f21(x61),f21(x62))
% 155.94/155.63 [7]~E(x71,x72)+E(f189(x71),f189(x72))
% 155.94/155.63 [8]~E(x81,x82)+E(f312(x81,x83),f312(x82,x83))
% 155.94/155.63 [9]~E(x91,x92)+E(f312(x93,x91),f312(x93,x92))
% 155.94/155.63 [10]~E(x101,x102)+E(f34(x101),f34(x102))
% 155.94/155.63 [11]~E(x111,x112)+E(f8(x111,x113,x114),f8(x112,x113,x114))
% 155.94/155.63 [12]~E(x121,x122)+E(f8(x123,x121,x124),f8(x123,x122,x124))
% 155.94/155.63 [13]~E(x131,x132)+E(f8(x133,x134,x131),f8(x133,x134,x132))
% 155.94/155.63 [14]~E(x141,x142)+E(f93(x141),f93(x142))
% 155.94/155.63 [15]~E(x151,x152)+E(f861(x151,x153),f861(x152,x153))
% 155.94/155.63 [16]~E(x161,x162)+E(f861(x163,x161),f861(x163,x162))
% 155.94/155.63 [17]~E(x171,x172)+E(f228(x171),f228(x172))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [29]~E(x291,x292)+E(f115(x291),f115(x292))
% 155.94/155.63 [30]~E(x301,x302)+E(f225(x301),f225(x302))
% 155.94/155.63 [31]~E(x311,x312)+E(f124(x311),f124(x312))
% 155.94/155.63 [32]~E(x321,x322)+E(f226(x321),f226(x322))
% 155.94/155.63 [33]~E(x331,x332)+E(f116(x331),f116(x332))
% 155.94/155.63 [34]~E(x341,x342)+E(f39(x341),f39(x342))
% 155.94/155.63 [35]~E(x351,x352)+E(f227(x351),f227(x352))
% 155.94/155.63 [36]~E(x361,x362)+E(f87(x361),f87(x362))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [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))
% 155.94/155.63 [48]~E(x481,x482)+E(f125(x481),f125(x482))
% 155.94/155.63 [49]~E(x491,x492)+E(f314(x491),f314(x492))
% 155.94/155.63 [50]~E(x501,x502)+E(f857(x501),f857(x502))
% 155.94/155.63 [51]~E(x511,x512)+E(f4(x511),f4(x512))
% 155.94/155.63 [52]~E(x521,x522)+E(f13(x521,x523,x524),f13(x522,x523,x524))
% 155.94/155.63 [53]~E(x531,x532)+E(f13(x533,x531,x534),f13(x533,x532,x534))
% 155.94/155.63 [54]~E(x541,x542)+E(f13(x543,x544,x541),f13(x543,x544,x542))
% 155.94/155.63 [55]~E(x551,x552)+E(f852(x551),f852(x552))
% 155.94/155.63 [56]~E(x561,x562)+E(f291(x561,x563,x564),f291(x562,x563,x564))
% 155.94/155.63 [57]~E(x571,x572)+E(f291(x573,x571,x574),f291(x573,x572,x574))
% 155.94/155.63 [58]~E(x581,x582)+E(f291(x583,x584,x581),f291(x583,x584,x582))
% 155.94/155.63 [59]~E(x591,x592)+E(f854(x591),f854(x592))
% 155.94/155.63 [60]~E(x601,x602)+E(f855(x601),f855(x602))
% 155.94/155.63 [61]~E(x611,x612)+E(f40(x611),f40(x612))
% 155.94/155.63 [62]~E(x621,x622)+E(f42(x621),f42(x622))
% 155.94/155.63 [63]~E(x631,x632)+E(f860(x631,x633),f860(x632,x633))
% 155.94/155.63 [64]~E(x641,x642)+E(f860(x643,x641),f860(x643,x642))
% 155.94/155.63 [65]~E(x651,x652)+E(f41(x651),f41(x652))
% 155.94/155.63 [66]~E(x661,x662)+E(f239(x661,x663),f239(x662,x663))
% 155.94/155.63 [67]~E(x671,x672)+E(f239(x673,x671),f239(x673,x672))
% 155.94/155.63 [68]~E(x681,x682)+E(f18(x681,x683,x684),f18(x682,x683,x684))
% 155.94/155.63 [69]~E(x691,x692)+E(f18(x693,x691,x694),f18(x693,x692,x694))
% 155.94/155.63 [70]~E(x701,x702)+E(f18(x703,x704,x701),f18(x703,x704,x702))
% 155.94/155.63 [71]~E(x711,x712)+E(f88(x711),f88(x712))
% 155.94/155.63 [72]~E(x721,x722)+E(f145(x721,x723,x724),f145(x722,x723,x724))
% 155.94/155.63 [73]~E(x731,x732)+E(f145(x733,x731,x734),f145(x733,x732,x734))
% 155.94/155.63 [74]~E(x741,x742)+E(f145(x743,x744,x741),f145(x743,x744,x742))
% 155.94/155.63 [75]~E(x751,x752)+E(f190(x751),f190(x752))
% 155.94/155.63 [76]~E(x761,x762)+E(f7(x761,x763,x764),f7(x762,x763,x764))
% 155.94/155.63 [77]~E(x771,x772)+E(f7(x773,x771,x774),f7(x773,x772,x774))
% 155.94/155.63 [78]~E(x781,x782)+E(f7(x783,x784,x781),f7(x783,x784,x782))
% 155.94/155.63 [79]~E(x791,x792)+E(f117(x791),f117(x792))
% 155.94/155.63 [80]~E(x801,x802)+E(f90(x801),f90(x802))
% 155.94/155.63 [81]~E(x811,x812)+E(f69(x811),f69(x812))
% 155.94/155.63 [82]~E(x821,x822)+E(f89(x821),f89(x822))
% 155.94/155.63 [83]~E(x831,x832)+E(f47(x831,x833),f47(x832,x833))
% 155.94/155.63 [84]~E(x841,x842)+E(f47(x843,x841),f47(x843,x842))
% 155.94/155.63 [85]~E(x851,x852)+E(f35(x851,x853),f35(x852,x853))
% 155.94/155.63 [86]~E(x861,x862)+E(f35(x863,x861),f35(x863,x862))
% 155.94/155.63 [87]~E(x871,x872)+E(f54(x871,x873,x874),f54(x872,x873,x874))
% 155.94/155.63 [88]~E(x881,x882)+E(f54(x883,x881,x884),f54(x883,x882,x884))
% 155.94/155.63 [89]~E(x891,x892)+E(f54(x893,x894,x891),f54(x893,x894,x892))
% 155.94/155.63 [90]~E(x901,x902)+E(f219(x901),f219(x902))
% 155.94/155.63 [91]~E(x911,x912)+E(f168(x911),f168(x912))
% 155.94/155.63 [92]~E(x921,x922)+E(f246(x921,x923),f246(x922,x923))
% 155.94/155.63 [93]~E(x931,x932)+E(f246(x933,x931),f246(x933,x932))
% 155.94/155.63 [94]~E(x941,x942)+E(f172(x941,x943,x944),f172(x942,x943,x944))
% 155.94/155.63 [95]~E(x951,x952)+E(f172(x953,x951,x954),f172(x953,x952,x954))
% 155.94/155.63 [96]~E(x961,x962)+E(f172(x963,x964,x961),f172(x963,x964,x962))
% 155.94/155.63 [97]~E(x971,x972)+E(f33(x971,x973,x974),f33(x972,x973,x974))
% 155.94/155.63 [98]~E(x981,x982)+E(f33(x983,x981,x984),f33(x983,x982,x984))
% 155.94/155.63 [99]~E(x991,x992)+E(f33(x993,x994,x991),f33(x993,x994,x992))
% 155.94/155.63 [100]~E(x1001,x1002)+E(f129(x1001),f129(x1002))
% 155.94/155.63 [101]~E(x1011,x1012)+E(f169(x1011),f169(x1012))
% 155.94/155.63 [102]~E(x1021,x1022)+E(f161(x1021),f161(x1022))
% 155.94/155.63 [103]~E(x1031,x1032)+E(f67(x1031),f67(x1032))
% 155.94/155.63 [104]~E(x1041,x1042)+E(f32(x1041,x1043,x1044),f32(x1042,x1043,x1044))
% 155.94/155.63 [105]~E(x1051,x1052)+E(f32(x1053,x1051,x1054),f32(x1053,x1052,x1054))
% 155.94/155.63 [106]~E(x1061,x1062)+E(f32(x1063,x1064,x1061),f32(x1063,x1064,x1062))
% 155.94/155.63 [107]~E(x1071,x1072)+E(f70(x1071),f70(x1072))
% 155.94/155.63 [108]~E(x1081,x1082)+E(f162(x1081),f162(x1082))
% 155.94/155.63 [109]~E(x1091,x1092)+E(f730(x1091,x1093,x1094,x1095,x1096),f730(x1092,x1093,x1094,x1095,x1096))
% 155.94/155.63 [110]~E(x1101,x1102)+E(f730(x1103,x1101,x1104,x1105,x1106),f730(x1103,x1102,x1104,x1105,x1106))
% 155.94/155.63 [111]~E(x1111,x1112)+E(f730(x1113,x1114,x1111,x1115,x1116),f730(x1113,x1114,x1112,x1115,x1116))
% 155.94/155.63 [112]~E(x1121,x1122)+E(f730(x1123,x1124,x1125,x1121,x1126),f730(x1123,x1124,x1125,x1122,x1126))
% 155.94/155.63 [113]~E(x1131,x1132)+E(f730(x1133,x1134,x1135,x1136,x1131),f730(x1133,x1134,x1135,x1136,x1132))
% 155.94/155.63 [114]~E(x1141,x1142)+E(f179(x1141,x1143,x1144),f179(x1142,x1143,x1144))
% 155.94/155.63 [115]~E(x1151,x1152)+E(f179(x1153,x1151,x1154),f179(x1153,x1152,x1154))
% 155.94/155.63 [116]~E(x1161,x1162)+E(f179(x1163,x1164,x1161),f179(x1163,x1164,x1162))
% 155.94/155.63 [117]~E(x1171,x1172)+E(f177(x1171,x1173),f177(x1172,x1173))
% 155.94/155.63 [118]~E(x1181,x1182)+E(f177(x1183,x1181),f177(x1183,x1182))
% 155.94/155.63 [119]~E(x1191,x1192)+E(f127(x1191),f127(x1192))
% 155.94/155.63 [120]~E(x1201,x1202)+E(f153(x1201,x1203),f153(x1202,x1203))
% 155.94/155.63 [121]~E(x1211,x1212)+E(f153(x1213,x1211),f153(x1213,x1212))
% 155.94/155.63 [122]~E(x1221,x1222)+E(f157(x1221,x1223),f157(x1222,x1223))
% 155.94/155.63 [123]~E(x1231,x1232)+E(f157(x1233,x1231),f157(x1233,x1232))
% 155.94/155.63 [124]~E(x1241,x1242)+E(f789(x1241,x1243,x1244),f789(x1242,x1243,x1244))
% 155.94/155.63 [125]~E(x1251,x1252)+E(f789(x1253,x1251,x1254),f789(x1253,x1252,x1254))
% 155.94/155.63 [126]~E(x1261,x1262)+E(f789(x1263,x1264,x1261),f789(x1263,x1264,x1262))
% 155.94/155.63 [127]~E(x1271,x1272)+E(f264(x1271,x1273,x1274),f264(x1272,x1273,x1274))
% 155.94/155.63 [128]~E(x1281,x1282)+E(f264(x1283,x1281,x1284),f264(x1283,x1282,x1284))
% 155.94/155.63 [129]~E(x1291,x1292)+E(f264(x1293,x1294,x1291),f264(x1293,x1294,x1292))
% 155.94/155.63 [130]~E(x1301,x1302)+E(f9(x1301,x1303),f9(x1302,x1303))
% 155.94/155.63 [131]~E(x1311,x1312)+E(f9(x1313,x1311),f9(x1313,x1312))
% 155.94/155.63 [132]~E(x1321,x1322)+E(f166(x1321,x1323,x1324),f166(x1322,x1323,x1324))
% 155.94/155.63 [133]~E(x1331,x1332)+E(f166(x1333,x1331,x1334),f166(x1333,x1332,x1334))
% 155.94/155.63 [134]~E(x1341,x1342)+E(f166(x1343,x1344,x1341),f166(x1343,x1344,x1342))
% 155.94/155.63 [135]~E(x1351,x1352)+E(f36(x1351,x1353),f36(x1352,x1353))
% 155.94/155.63 [136]~E(x1361,x1362)+E(f36(x1363,x1361),f36(x1363,x1362))
% 155.94/155.63 [137]~E(x1371,x1372)+E(f249(x1371,x1373,x1374),f249(x1372,x1373,x1374))
% 155.94/155.63 [138]~E(x1381,x1382)+E(f249(x1383,x1381,x1384),f249(x1383,x1382,x1384))
% 155.94/155.63 [139]~E(x1391,x1392)+E(f249(x1393,x1394,x1391),f249(x1393,x1394,x1392))
% 155.94/155.63 [140]~E(x1401,x1402)+E(f147(x1401),f147(x1402))
% 155.94/155.63 [141]~E(x1411,x1412)+E(f593(x1411,x1413,x1414,x1415,x1416),f593(x1412,x1413,x1414,x1415,x1416))
% 155.94/155.63 [142]~E(x1421,x1422)+E(f593(x1423,x1421,x1424,x1425,x1426),f593(x1423,x1422,x1424,x1425,x1426))
% 155.94/155.63 [143]~E(x1431,x1432)+E(f593(x1433,x1434,x1431,x1435,x1436),f593(x1433,x1434,x1432,x1435,x1436))
% 155.94/155.63 [144]~E(x1441,x1442)+E(f593(x1443,x1444,x1445,x1441,x1446),f593(x1443,x1444,x1445,x1442,x1446))
% 155.94/155.63 [145]~E(x1451,x1452)+E(f593(x1453,x1454,x1455,x1456,x1451),f593(x1453,x1454,x1455,x1456,x1452))
% 155.94/155.63 [146]~E(x1461,x1462)+E(f238(x1461,x1463),f238(x1462,x1463))
% 155.94/155.63 [147]~E(x1471,x1472)+E(f238(x1473,x1471),f238(x1473,x1472))
% 155.94/155.63 [148]~E(x1481,x1482)+E(f260(x1481,x1483,x1484),f260(x1482,x1483,x1484))
% 155.94/155.63 [149]~E(x1491,x1492)+E(f260(x1493,x1491,x1494),f260(x1493,x1492,x1494))
% 155.94/155.63 [150]~E(x1501,x1502)+E(f260(x1503,x1504,x1501),f260(x1503,x1504,x1502))
% 155.94/155.63 [151]~E(x1511,x1512)+E(f233(x1511),f233(x1512))
% 155.94/155.63 [152]~E(x1521,x1522)+E(f290(x1521,x1523,x1524),f290(x1522,x1523,x1524))
% 155.94/155.63 [153]~E(x1531,x1532)+E(f290(x1533,x1531,x1534),f290(x1533,x1532,x1534))
% 155.94/155.63 [154]~E(x1541,x1542)+E(f290(x1543,x1544,x1541),f290(x1543,x1544,x1542))
% 155.94/155.63 [155]~E(x1551,x1552)+E(f244(x1551,x1553,x1554),f244(x1552,x1553,x1554))
% 155.94/155.63 [156]~E(x1561,x1562)+E(f244(x1563,x1561,x1564),f244(x1563,x1562,x1564))
% 155.94/155.63 [157]~E(x1571,x1572)+E(f244(x1573,x1574,x1571),f244(x1573,x1574,x1572))
% 155.94/155.63 [158]~E(x1581,x1582)+E(f16(x1581,x1583),f16(x1582,x1583))
% 155.94/155.63 [159]~E(x1591,x1592)+E(f16(x1593,x1591),f16(x1593,x1592))
% 155.94/155.63 [160]~E(x1601,x1602)+E(f66(x1601),f66(x1602))
% 155.94/155.63 [161]~E(x1611,x1612)+E(f173(x1611,x1613),f173(x1612,x1613))
% 155.94/155.63 [162]~E(x1621,x1622)+E(f173(x1623,x1621),f173(x1623,x1622))
% 155.94/155.63 [163]~E(x1631,x1632)+E(f119(x1631),f119(x1632))
% 155.94/155.63 [164]~E(x1641,x1642)+E(f120(x1641),f120(x1642))
% 155.94/155.63 [165]~E(x1651,x1652)+E(f313(x1651),f313(x1652))
% 155.94/155.63 [166]~E(x1661,x1662)+E(f53(x1661),f53(x1662))
% 155.94/155.63 [167]~E(x1671,x1672)+E(f192(x1671),f192(x1672))
% 155.94/155.63 [168]~E(x1681,x1682)+E(f305(x1681,x1683),f305(x1682,x1683))
% 155.94/155.63 [169]~E(x1691,x1692)+E(f305(x1693,x1691),f305(x1693,x1692))
% 155.94/155.63 [170]~E(x1701,x1702)+E(f683(x1701,x1703,x1704,x1705),f683(x1702,x1703,x1704,x1705))
% 155.94/155.63 [171]~E(x1711,x1712)+E(f683(x1713,x1711,x1714,x1715),f683(x1713,x1712,x1714,x1715))
% 155.94/155.63 [172]~E(x1721,x1722)+E(f683(x1723,x1724,x1721,x1725),f683(x1723,x1724,x1722,x1725))
% 155.94/155.63 [173]~E(x1731,x1732)+E(f683(x1733,x1734,x1735,x1731),f683(x1733,x1734,x1735,x1732))
% 155.94/155.63 [174]~E(x1741,x1742)+E(f268(x1741),f268(x1742))
% 155.94/155.63 [175]~E(x1751,x1752)+E(f5(x1751),f5(x1752))
% 155.94/155.63 [176]~E(x1761,x1762)+E(f155(x1761,x1763),f155(x1762,x1763))
% 155.94/155.63 [177]~E(x1771,x1772)+E(f155(x1773,x1771),f155(x1773,x1772))
% 155.94/155.63 [178]~E(x1781,x1782)+E(f250(x1781,x1783,x1784,x1785,x1786,x1787),f250(x1782,x1783,x1784,x1785,x1786,x1787))
% 155.94/155.63 [179]~E(x1791,x1792)+E(f250(x1793,x1791,x1794,x1795,x1796,x1797),f250(x1793,x1792,x1794,x1795,x1796,x1797))
% 155.94/155.63 [180]~E(x1801,x1802)+E(f250(x1803,x1804,x1801,x1805,x1806,x1807),f250(x1803,x1804,x1802,x1805,x1806,x1807))
% 155.94/155.63 [181]~E(x1811,x1812)+E(f250(x1813,x1814,x1815,x1811,x1816,x1817),f250(x1813,x1814,x1815,x1812,x1816,x1817))
% 155.94/155.63 [182]~E(x1821,x1822)+E(f250(x1823,x1824,x1825,x1826,x1821,x1827),f250(x1823,x1824,x1825,x1826,x1822,x1827))
% 155.94/155.63 [183]~E(x1831,x1832)+E(f250(x1833,x1834,x1835,x1836,x1837,x1831),f250(x1833,x1834,x1835,x1836,x1837,x1832))
% 155.94/155.63 [184]~E(x1841,x1842)+E(f630(x1841,x1843,x1844),f630(x1842,x1843,x1844))
% 155.94/155.63 [185]~E(x1851,x1852)+E(f630(x1853,x1851,x1854),f630(x1853,x1852,x1854))
% 155.94/155.63 [186]~E(x1861,x1862)+E(f630(x1863,x1864,x1861),f630(x1863,x1864,x1862))
% 155.94/155.63 [187]~E(x1871,x1872)+E(f247(x1871,x1873),f247(x1872,x1873))
% 155.94/155.63 [188]~E(x1881,x1882)+E(f247(x1883,x1881),f247(x1883,x1882))
% 155.94/155.63 [189]~E(x1891,x1892)+E(f91(x1891,x1893),f91(x1892,x1893))
% 155.94/155.63 [190]~E(x1901,x1902)+E(f91(x1903,x1901),f91(x1903,x1902))
% 155.94/155.63 [191]~E(x1911,x1912)+E(f282(x1911,x1913),f282(x1912,x1913))
% 155.94/155.63 [192]~E(x1921,x1922)+E(f282(x1923,x1921),f282(x1923,x1922))
% 155.94/155.63 [193]~E(x1931,x1932)+E(f266(x1931,x1933),f266(x1932,x1933))
% 155.94/155.63 [194]~E(x1941,x1942)+E(f266(x1943,x1941),f266(x1943,x1942))
% 155.94/155.63 [195]~E(x1951,x1952)+E(f150(x1951,x1953),f150(x1952,x1953))
% 155.94/155.63 [196]~E(x1961,x1962)+E(f150(x1963,x1961),f150(x1963,x1962))
% 155.94/155.63 [197]~E(x1971,x1972)+E(f662(x1971,x1973,x1974),f662(x1972,x1973,x1974))
% 155.94/155.63 [198]~E(x1981,x1982)+E(f662(x1983,x1981,x1984),f662(x1983,x1982,x1984))
% 155.94/155.63 [199]~E(x1991,x1992)+E(f662(x1993,x1994,x1991),f662(x1993,x1994,x1992))
% 155.94/155.63 [200]~E(x2001,x2002)+E(f82(x2001,x2003,x2004,x2005),f82(x2002,x2003,x2004,x2005))
% 155.94/155.63 [201]~E(x2011,x2012)+E(f82(x2013,x2011,x2014,x2015),f82(x2013,x2012,x2014,x2015))
% 155.94/155.63 [202]~E(x2021,x2022)+E(f82(x2023,x2024,x2021,x2025),f82(x2023,x2024,x2022,x2025))
% 155.94/155.63 [203]~E(x2031,x2032)+E(f82(x2033,x2034,x2035,x2031),f82(x2033,x2034,x2035,x2032))
% 155.94/155.63 [204]~E(x2041,x2042)+E(f56(x2041,x2043),f56(x2042,x2043))
% 155.94/155.63 [205]~E(x2051,x2052)+E(f56(x2053,x2051),f56(x2053,x2052))
% 155.94/155.63 [206]~E(x2061,x2062)+E(f235(x2061),f235(x2062))
% 155.94/155.63 [207]~E(x2071,x2072)+E(f845(x2071,x2073,x2074,x2075),f845(x2072,x2073,x2074,x2075))
% 155.94/155.63 [208]~E(x2081,x2082)+E(f845(x2083,x2081,x2084,x2085),f845(x2083,x2082,x2084,x2085))
% 155.94/155.63 [209]~E(x2091,x2092)+E(f845(x2093,x2094,x2091,x2095),f845(x2093,x2094,x2092,x2095))
% 155.94/155.63 [210]~E(x2101,x2102)+E(f845(x2103,x2104,x2105,x2101),f845(x2103,x2104,x2105,x2102))
% 155.94/155.63 [211]~E(x2111,x2112)+E(f144(x2111,x2113,x2114,x2115),f144(x2112,x2113,x2114,x2115))
% 155.94/155.63 [212]~E(x2121,x2122)+E(f144(x2123,x2121,x2124,x2125),f144(x2123,x2122,x2124,x2125))
% 155.94/155.63 [213]~E(x2131,x2132)+E(f144(x2133,x2134,x2131,x2135),f144(x2133,x2134,x2132,x2135))
% 155.94/155.63 [214]~E(x2141,x2142)+E(f144(x2143,x2144,x2145,x2141),f144(x2143,x2144,x2145,x2142))
% 155.94/155.63 [215]~E(x2151,x2152)+E(f790(x2151,x2153,x2154),f790(x2152,x2153,x2154))
% 155.94/155.63 [216]~E(x2161,x2162)+E(f790(x2163,x2161,x2164),f790(x2163,x2162,x2164))
% 155.94/155.63 [217]~E(x2171,x2172)+E(f790(x2173,x2174,x2171),f790(x2173,x2174,x2172))
% 155.94/155.63 [218]~E(x2181,x2182)+E(f287(x2181,x2183),f287(x2182,x2183))
% 155.94/155.63 [219]~E(x2191,x2192)+E(f287(x2193,x2191),f287(x2193,x2192))
% 155.94/155.63 [220]~E(x2201,x2202)+E(f279(x2201),f279(x2202))
% 155.94/155.63 [221]~E(x2211,x2212)+E(f132(x2211,x2213),f132(x2212,x2213))
% 155.94/155.63 [222]~E(x2221,x2222)+E(f132(x2223,x2221),f132(x2223,x2222))
% 155.94/155.63 [223]~E(x2231,x2232)+E(f240(x2231),f240(x2232))
% 155.94/155.63 [224]~E(x2241,x2242)+E(f281(x2241),f281(x2242))
% 155.94/155.63 [225]~E(x2251,x2252)+E(f50(x2251,x2253),f50(x2252,x2253))
% 155.94/155.63 [226]~E(x2261,x2262)+E(f50(x2263,x2261),f50(x2263,x2262))
% 155.94/155.63 [227]~E(x2271,x2272)+E(f109(x2271,x2273),f109(x2272,x2273))
% 155.94/155.63 [228]~E(x2281,x2282)+E(f109(x2283,x2281),f109(x2283,x2282))
% 155.94/155.63 [229]~E(x2291,x2292)+E(f6(x2291,x2293),f6(x2292,x2293))
% 155.94/155.63 [230]~E(x2301,x2302)+E(f6(x2303,x2301),f6(x2303,x2302))
% 155.94/155.63 [231]~E(x2311,x2312)+E(f248(x2311,x2313),f248(x2312,x2313))
% 155.94/155.63 [232]~E(x2321,x2322)+E(f248(x2323,x2321),f248(x2323,x2322))
% 155.94/155.63 [233]~E(x2331,x2332)+E(f289(x2331),f289(x2332))
% 155.94/155.63 [234]~E(x2341,x2342)+E(f236(x2341,x2343),f236(x2342,x2343))
% 155.94/155.63 [235]~E(x2351,x2352)+E(f236(x2353,x2351),f236(x2353,x2352))
% 155.94/155.63 [236]~E(x2361,x2362)+E(f81(x2361,x2363),f81(x2362,x2363))
% 155.94/155.63 [237]~E(x2371,x2372)+E(f81(x2373,x2371),f81(x2373,x2372))
% 155.94/155.63 [238]~E(x2381,x2382)+E(f283(x2381,x2383,x2384),f283(x2382,x2383,x2384))
% 155.94/155.63 [239]~E(x2391,x2392)+E(f283(x2393,x2391,x2394),f283(x2393,x2392,x2394))
% 155.94/155.63 [240]~E(x2401,x2402)+E(f283(x2403,x2404,x2401),f283(x2403,x2404,x2402))
% 155.94/155.63 [241]~E(x2411,x2412)+E(f288(x2411),f288(x2412))
% 155.94/155.63 [242]~E(x2421,x2422)+E(f154(x2421,x2423),f154(x2422,x2423))
% 155.94/155.63 [243]~E(x2431,x2432)+E(f154(x2433,x2431),f154(x2433,x2432))
% 155.94/155.63 [244]~E(x2441,x2442)+E(f133(x2441),f133(x2442))
% 155.94/155.63 [245]~E(x2451,x2452)+E(f181(x2451,x2453,x2454),f181(x2452,x2453,x2454))
% 155.94/155.63 [246]~E(x2461,x2462)+E(f181(x2463,x2461,x2464),f181(x2463,x2462,x2464))
% 155.94/155.63 [247]~E(x2471,x2472)+E(f181(x2473,x2474,x2471),f181(x2473,x2474,x2472))
% 155.94/155.63 [248]~E(x2481,x2482)+E(f75(x2481,x2483,x2484,x2485,x2486),f75(x2482,x2483,x2484,x2485,x2486))
% 155.94/155.63 [249]~E(x2491,x2492)+E(f75(x2493,x2491,x2494,x2495,x2496),f75(x2493,x2492,x2494,x2495,x2496))
% 155.94/155.63 [250]~E(x2501,x2502)+E(f75(x2503,x2504,x2501,x2505,x2506),f75(x2503,x2504,x2502,x2505,x2506))
% 155.94/155.63 [251]~E(x2511,x2512)+E(f75(x2513,x2514,x2515,x2511,x2516),f75(x2513,x2514,x2515,x2512,x2516))
% 155.94/155.63 [252]~E(x2521,x2522)+E(f75(x2523,x2524,x2525,x2526,x2521),f75(x2523,x2524,x2525,x2526,x2522))
% 155.94/155.63 [253]~E(x2531,x2532)+E(f267(x2531,x2533,x2534),f267(x2532,x2533,x2534))
% 155.94/155.63 [254]~E(x2541,x2542)+E(f267(x2543,x2541,x2544),f267(x2543,x2542,x2544))
% 155.94/155.63 [255]~E(x2551,x2552)+E(f267(x2553,x2554,x2551),f267(x2553,x2554,x2552))
% 155.94/155.63 [256]~E(x2561,x2562)+E(f796(x2561,x2563,x2564),f796(x2562,x2563,x2564))
% 155.94/155.63 [257]~E(x2571,x2572)+E(f796(x2573,x2571,x2574),f796(x2573,x2572,x2574))
% 155.94/155.63 [258]~E(x2581,x2582)+E(f796(x2583,x2584,x2581),f796(x2583,x2584,x2582))
% 155.94/155.63 [259]~E(x2591,x2592)+E(f811(x2591,x2593,x2594,x2595),f811(x2592,x2593,x2594,x2595))
% 155.94/155.63 [260]~E(x2601,x2602)+E(f811(x2603,x2601,x2604,x2605),f811(x2603,x2602,x2604,x2605))
% 155.94/155.63 [261]~E(x2611,x2612)+E(f811(x2613,x2614,x2611,x2615),f811(x2613,x2614,x2612,x2615))
% 155.94/155.63 [262]~E(x2621,x2622)+E(f811(x2623,x2624,x2625,x2621),f811(x2623,x2624,x2625,x2622))
% 155.94/155.63 [263]~E(x2631,x2632)+E(f128(x2631,x2633),f128(x2632,x2633))
% 155.94/155.63 [264]~E(x2641,x2642)+E(f128(x2643,x2641),f128(x2643,x2642))
% 155.94/155.63 [265]~E(x2651,x2652)+E(f251(x2651,x2653,x2654,x2655),f251(x2652,x2653,x2654,x2655))
% 155.94/155.63 [266]~E(x2661,x2662)+E(f251(x2663,x2661,x2664,x2665),f251(x2663,x2662,x2664,x2665))
% 155.94/155.63 [267]~E(x2671,x2672)+E(f251(x2673,x2674,x2671,x2675),f251(x2673,x2674,x2672,x2675))
% 155.94/155.63 [268]~E(x2681,x2682)+E(f251(x2683,x2684,x2685,x2681),f251(x2683,x2684,x2685,x2682))
% 155.94/155.63 [269]~E(x2691,x2692)+E(f94(x2691,x2693),f94(x2692,x2693))
% 155.94/155.63 [270]~E(x2701,x2702)+E(f94(x2703,x2701),f94(x2703,x2702))
% 155.94/155.63 [271]~E(x2711,x2712)+E(f148(x2711,x2713),f148(x2712,x2713))
% 155.94/155.63 [272]~E(x2721,x2722)+E(f148(x2723,x2721),f148(x2723,x2722))
% 155.94/155.63 [273]~E(x2731,x2732)+E(f498(x2731,x2733,x2734,x2735,x2736),f498(x2732,x2733,x2734,x2735,x2736))
% 155.94/155.63 [274]~E(x2741,x2742)+E(f498(x2743,x2741,x2744,x2745,x2746),f498(x2743,x2742,x2744,x2745,x2746))
% 155.94/155.63 [275]~E(x2751,x2752)+E(f498(x2753,x2754,x2751,x2755,x2756),f498(x2753,x2754,x2752,x2755,x2756))
% 155.94/155.63 [276]~E(x2761,x2762)+E(f498(x2763,x2764,x2765,x2761,x2766),f498(x2763,x2764,x2765,x2762,x2766))
% 155.94/155.63 [277]~E(x2771,x2772)+E(f498(x2773,x2774,x2775,x2776,x2771),f498(x2773,x2774,x2775,x2776,x2772))
% 155.94/155.63 [278]~E(x2781,x2782)+E(f58(x2781,x2783),f58(x2782,x2783))
% 155.94/155.63 [279]~E(x2791,x2792)+E(f58(x2793,x2791),f58(x2793,x2792))
% 155.94/155.63 [280]~E(x2801,x2802)+E(f351(x2801,x2803,x2804,x2805),f351(x2802,x2803,x2804,x2805))
% 155.94/155.63 [281]~E(x2811,x2812)+E(f351(x2813,x2811,x2814,x2815),f351(x2813,x2812,x2814,x2815))
% 155.94/155.63 [282]~E(x2821,x2822)+E(f351(x2823,x2824,x2821,x2825),f351(x2823,x2824,x2822,x2825))
% 155.94/155.63 [283]~E(x2831,x2832)+E(f351(x2833,x2834,x2835,x2831),f351(x2833,x2834,x2835,x2832))
% 155.94/155.63 [284]~E(x2841,x2842)+E(f676(x2841,x2843,x2844),f676(x2842,x2843,x2844))
% 155.94/155.63 [285]~E(x2851,x2852)+E(f676(x2853,x2851,x2854),f676(x2853,x2852,x2854))
% 155.94/155.63 [286]~E(x2861,x2862)+E(f676(x2863,x2864,x2861),f676(x2863,x2864,x2862))
% 155.94/155.63 [287]~E(x2871,x2872)+E(f805(x2871,x2873,x2874,x2875),f805(x2872,x2873,x2874,x2875))
% 155.94/155.63 [288]~E(x2881,x2882)+E(f805(x2883,x2881,x2884,x2885),f805(x2883,x2882,x2884,x2885))
% 155.94/155.63 [289]~E(x2891,x2892)+E(f805(x2893,x2894,x2891,x2895),f805(x2893,x2894,x2892,x2895))
% 155.94/155.63 [290]~E(x2901,x2902)+E(f805(x2903,x2904,x2905,x2901),f805(x2903,x2904,x2905,x2902))
% 155.94/155.63 [291]~E(x2911,x2912)+E(f48(x2911,x2913),f48(x2912,x2913))
% 155.94/155.63 [292]~E(x2921,x2922)+E(f48(x2923,x2921),f48(x2923,x2922))
% 155.94/155.63 [293]~E(x2931,x2932)+E(f367(x2931,x2933),f367(x2932,x2933))
% 155.94/155.63 [294]~E(x2941,x2942)+E(f367(x2943,x2941),f367(x2943,x2942))
% 155.94/155.63 [295]~E(x2951,x2952)+E(f14(x2951,x2953),f14(x2952,x2953))
% 155.94/155.63 [296]~E(x2961,x2962)+E(f14(x2963,x2961),f14(x2963,x2962))
% 155.94/155.63 [297]~E(x2971,x2972)+E(f563(x2971,x2973,x2974,x2975,x2976),f563(x2972,x2973,x2974,x2975,x2976))
% 155.94/155.63 [298]~E(x2981,x2982)+E(f563(x2983,x2981,x2984,x2985,x2986),f563(x2983,x2982,x2984,x2985,x2986))
% 155.94/155.63 [299]~E(x2991,x2992)+E(f563(x2993,x2994,x2991,x2995,x2996),f563(x2993,x2994,x2992,x2995,x2996))
% 155.94/155.63 [300]~E(x3001,x3002)+E(f563(x3003,x3004,x3005,x3001,x3006),f563(x3003,x3004,x3005,x3002,x3006))
% 155.94/155.63 [301]~E(x3011,x3012)+E(f563(x3013,x3014,x3015,x3016,x3011),f563(x3013,x3014,x3015,x3016,x3012))
% 155.94/155.63 [302]~E(x3021,x3022)+E(f100(x3021),f100(x3022))
% 155.94/155.63 [303]~E(x3031,x3032)+E(f222(x3031,x3033,x3034,x3035,x3036),f222(x3032,x3033,x3034,x3035,x3036))
% 155.94/155.63 [304]~E(x3041,x3042)+E(f222(x3043,x3041,x3044,x3045,x3046),f222(x3043,x3042,x3044,x3045,x3046))
% 155.94/155.63 [305]~E(x3051,x3052)+E(f222(x3053,x3054,x3051,x3055,x3056),f222(x3053,x3054,x3052,x3055,x3056))
% 155.94/155.63 [306]~E(x3061,x3062)+E(f222(x3063,x3064,x3065,x3061,x3066),f222(x3063,x3064,x3065,x3062,x3066))
% 155.94/155.63 [307]~E(x3071,x3072)+E(f222(x3073,x3074,x3075,x3076,x3071),f222(x3073,x3074,x3075,x3076,x3072))
% 155.94/155.63 [308]~E(x3081,x3082)+E(f300(x3081,x3083),f300(x3082,x3083))
% 155.94/155.63 [309]~E(x3091,x3092)+E(f300(x3093,x3091),f300(x3093,x3092))
% 155.94/155.63 [310]~E(x3101,x3102)+E(f669(x3101,x3103),f669(x3102,x3103))
% 155.94/155.63 [311]~E(x3111,x3112)+E(f669(x3113,x3111),f669(x3113,x3112))
% 155.94/155.63 [312]~E(x3121,x3122)+E(f31(x3121,x3123,x3124),f31(x3122,x3123,x3124))
% 155.94/155.63 [313]~E(x3131,x3132)+E(f31(x3133,x3131,x3134),f31(x3133,x3132,x3134))
% 155.94/155.63 [314]~E(x3141,x3142)+E(f31(x3143,x3144,x3141),f31(x3143,x3144,x3142))
% 155.94/155.63 [315]~E(x3151,x3152)+E(f859(x3151,x3153),f859(x3152,x3153))
% 155.94/155.63 [316]~E(x3161,x3162)+E(f859(x3163,x3161),f859(x3163,x3162))
% 155.94/155.63 [317]~E(x3171,x3172)+E(f858(x3171,x3173),f858(x3172,x3173))
% 155.94/155.63 [318]~E(x3181,x3182)+E(f858(x3183,x3181),f858(x3183,x3182))
% 155.94/155.63 [319]~E(x3191,x3192)+E(f99(x3191,x3193),f99(x3192,x3193))
% 155.94/155.63 [320]~E(x3201,x3202)+E(f99(x3203,x3201),f99(x3203,x3202))
% 155.94/155.63 [321]~E(x3211,x3212)+E(f164(x3211),f164(x3212))
% 155.94/155.63 [322]~E(x3221,x3222)+E(f761(x3221,x3223),f761(x3222,x3223))
% 155.94/155.63 [323]~E(x3231,x3232)+E(f761(x3233,x3231),f761(x3233,x3232))
% 155.94/155.63 [324]~E(x3241,x3242)+E(f703(x3241,x3243),f703(x3242,x3243))
% 155.94/155.63 [325]~E(x3251,x3252)+E(f703(x3253,x3251),f703(x3253,x3252))
% 155.94/155.63 [326]~E(x3261,x3262)+E(f319(x3261),f319(x3262))
% 155.94/155.63 [327]~E(x3271,x3272)+E(f167(x3271),f167(x3272))
% 155.94/155.63 [328]~E(x3281,x3282)+E(f138(x3281,x3283,x3284,x3285),f138(x3282,x3283,x3284,x3285))
% 155.94/155.63 [329]~E(x3291,x3292)+E(f138(x3293,x3291,x3294,x3295),f138(x3293,x3292,x3294,x3295))
% 155.94/155.63 [330]~E(x3301,x3302)+E(f138(x3303,x3304,x3301,x3305),f138(x3303,x3304,x3302,x3305))
% 155.94/155.63 [331]~E(x3311,x3312)+E(f138(x3313,x3314,x3315,x3311),f138(x3313,x3314,x3315,x3312))
% 155.94/155.63 [332]~E(x3321,x3322)+E(f183(x3321,x3323,x3324,x3325),f183(x3322,x3323,x3324,x3325))
% 155.94/155.63 [333]~E(x3331,x3332)+E(f183(x3333,x3331,x3334,x3335),f183(x3333,x3332,x3334,x3335))
% 155.94/155.63 [334]~E(x3341,x3342)+E(f183(x3343,x3344,x3341,x3345),f183(x3343,x3344,x3342,x3345))
% 155.94/155.63 [335]~E(x3351,x3352)+E(f183(x3353,x3354,x3355,x3351),f183(x3353,x3354,x3355,x3352))
% 155.94/155.63 [336]~E(x3361,x3362)+E(f673(x3361,x3363,x3364,x3365,x3366),f673(x3362,x3363,x3364,x3365,x3366))
% 155.94/155.63 [337]~E(x3371,x3372)+E(f673(x3373,x3371,x3374,x3375,x3376),f673(x3373,x3372,x3374,x3375,x3376))
% 155.94/155.63 [338]~E(x3381,x3382)+E(f673(x3383,x3384,x3381,x3385,x3386),f673(x3383,x3384,x3382,x3385,x3386))
% 155.94/155.63 [339]~E(x3391,x3392)+E(f673(x3393,x3394,x3395,x3391,x3396),f673(x3393,x3394,x3395,x3392,x3396))
% 155.94/155.63 [340]~E(x3401,x3402)+E(f673(x3403,x3404,x3405,x3406,x3401),f673(x3403,x3404,x3405,x3406,x3402))
% 155.94/155.63 [341]~E(x3411,x3412)+E(f165(x3411),f165(x3412))
% 155.94/155.63 [342]~E(x3421,x3422)+E(f685(x3421,x3423,x3424,x3425,x3426),f685(x3422,x3423,x3424,x3425,x3426))
% 155.94/155.63 [343]~E(x3431,x3432)+E(f685(x3433,x3431,x3434,x3435,x3436),f685(x3433,x3432,x3434,x3435,x3436))
% 155.94/155.63 [344]~E(x3441,x3442)+E(f685(x3443,x3444,x3441,x3445,x3446),f685(x3443,x3444,x3442,x3445,x3446))
% 155.94/155.63 [345]~E(x3451,x3452)+E(f685(x3453,x3454,x3455,x3451,x3456),f685(x3453,x3454,x3455,x3452,x3456))
% 155.94/155.63 [346]~E(x3461,x3462)+E(f685(x3463,x3464,x3465,x3466,x3461),f685(x3463,x3464,x3465,x3466,x3462))
% 155.94/155.63 [347]~E(x3471,x3472)+E(f140(x3471,x3473),f140(x3472,x3473))
% 155.94/155.63 [348]~E(x3481,x3482)+E(f140(x3483,x3481),f140(x3483,x3482))
% 155.94/155.63 [349]~E(x3491,x3492)+E(f265(x3491,x3493),f265(x3492,x3493))
% 155.94/155.63 [350]~E(x3501,x3502)+E(f265(x3503,x3501),f265(x3503,x3502))
% 155.94/155.63 [351]~E(x3511,x3512)+E(f72(x3511,x3513),f72(x3512,x3513))
% 155.94/155.63 [352]~E(x3521,x3522)+E(f72(x3523,x3521),f72(x3523,x3522))
% 155.94/155.63 [353]~E(x3531,x3532)+E(f170(x3531,x3533,x3534),f170(x3532,x3533,x3534))
% 155.94/155.63 [354]~E(x3541,x3542)+E(f170(x3543,x3541,x3544),f170(x3543,x3542,x3544))
% 155.94/155.63 [355]~E(x3551,x3552)+E(f170(x3553,x3554,x3551),f170(x3553,x3554,x3552))
% 155.94/155.63 [356]~E(x3561,x3562)+E(f543(x3561,x3563,x3564),f543(x3562,x3563,x3564))
% 155.94/155.63 [357]~E(x3571,x3572)+E(f543(x3573,x3571,x3574),f543(x3573,x3572,x3574))
% 155.94/155.63 [358]~E(x3581,x3582)+E(f543(x3583,x3584,x3581),f543(x3583,x3584,x3582))
% 155.94/155.63 [359]~E(x3591,x3592)+E(f174(x3591,x3593),f174(x3592,x3593))
% 155.94/155.63 [360]~E(x3601,x3602)+E(f174(x3603,x3601),f174(x3603,x3602))
% 155.94/155.63 [361]~E(x3611,x3612)+E(f28(x3611,x3613),f28(x3612,x3613))
% 155.94/155.63 [362]~E(x3621,x3622)+E(f28(x3623,x3621),f28(x3623,x3622))
% 155.94/155.63 [363]~E(x3631,x3632)+E(f788(x3631,x3633,x3634),f788(x3632,x3633,x3634))
% 155.94/155.63 [364]~E(x3641,x3642)+E(f788(x3643,x3641,x3644),f788(x3643,x3642,x3644))
% 155.94/155.63 [365]~E(x3651,x3652)+E(f788(x3653,x3654,x3651),f788(x3653,x3654,x3652))
% 155.94/155.63 [366]~E(x3661,x3662)+E(f474(x3661,x3663,x3664,x3665),f474(x3662,x3663,x3664,x3665))
% 155.94/155.63 [367]~E(x3671,x3672)+E(f474(x3673,x3671,x3674,x3675),f474(x3673,x3672,x3674,x3675))
% 155.94/155.63 [368]~E(x3681,x3682)+E(f474(x3683,x3684,x3681,x3685),f474(x3683,x3684,x3682,x3685))
% 155.94/155.63 [369]~E(x3691,x3692)+E(f474(x3693,x3694,x3695,x3691),f474(x3693,x3694,x3695,x3692))
% 155.94/155.63 [370]~E(x3701,x3702)+E(f171(x3701,x3703,x3704),f171(x3702,x3703,x3704))
% 155.94/155.63 [371]~E(x3711,x3712)+E(f171(x3713,x3711,x3714),f171(x3713,x3712,x3714))
% 155.94/155.63 [372]~E(x3721,x3722)+E(f171(x3723,x3724,x3721),f171(x3723,x3724,x3722))
% 155.94/155.63 [373]~E(x3731,x3732)+E(f704(x3731,x3733,x3734),f704(x3732,x3733,x3734))
% 155.94/155.63 [374]~E(x3741,x3742)+E(f704(x3743,x3741,x3744),f704(x3743,x3742,x3744))
% 155.94/155.63 [375]~E(x3751,x3752)+E(f704(x3753,x3754,x3751),f704(x3753,x3754,x3752))
% 155.94/155.63 [376]~E(x3761,x3762)+E(f63(x3761,x3763,x3764),f63(x3762,x3763,x3764))
% 155.94/155.63 [377]~E(x3771,x3772)+E(f63(x3773,x3771,x3774),f63(x3773,x3772,x3774))
% 155.94/155.63 [378]~E(x3781,x3782)+E(f63(x3783,x3784,x3781),f63(x3783,x3784,x3782))
% 155.94/155.63 [379]~E(x3791,x3792)+E(f303(x3791,x3793),f303(x3792,x3793))
% 155.94/155.63 [380]~E(x3801,x3802)+E(f303(x3803,x3801),f303(x3803,x3802))
% 155.94/155.63 [381]~E(x3811,x3812)+E(f254(x3811,x3813),f254(x3812,x3813))
% 155.94/155.63 [382]~E(x3821,x3822)+E(f254(x3823,x3821),f254(x3823,x3822))
% 155.94/155.63 [383]~E(x3831,x3832)+E(f195(x3831),f195(x3832))
% 155.94/155.63 [384]~E(x3841,x3842)+E(f408(x3841,x3843,x3844,x3845,x3846),f408(x3842,x3843,x3844,x3845,x3846))
% 155.94/155.63 [385]~E(x3851,x3852)+E(f408(x3853,x3851,x3854,x3855,x3856),f408(x3853,x3852,x3854,x3855,x3856))
% 155.94/155.63 [386]~E(x3861,x3862)+E(f408(x3863,x3864,x3861,x3865,x3866),f408(x3863,x3864,x3862,x3865,x3866))
% 155.94/155.63 [387]~E(x3871,x3872)+E(f408(x3873,x3874,x3875,x3871,x3876),f408(x3873,x3874,x3875,x3872,x3876))
% 155.94/155.63 [388]~E(x3881,x3882)+E(f408(x3883,x3884,x3885,x3886,x3881),f408(x3883,x3884,x3885,x3886,x3882))
% 155.94/155.63 [389]~E(x3891,x3892)+E(f10(x3891,x3893),f10(x3892,x3893))
% 155.94/155.63 [390]~E(x3901,x3902)+E(f10(x3903,x3901),f10(x3903,x3902))
% 155.94/155.63 [391]~E(x3911,x3912)+E(f51(x3911,x3913),f51(x3912,x3913))
% 155.94/155.63 [392]~E(x3921,x3922)+E(f51(x3923,x3921),f51(x3923,x3922))
% 155.94/155.63 [393]~E(x3931,x3932)+E(f237(x3931,x3933),f237(x3932,x3933))
% 155.94/155.63 [394]~E(x3941,x3942)+E(f237(x3943,x3941),f237(x3943,x3942))
% 155.94/155.63 [395]~E(x3951,x3952)+E(f263(x3951),f263(x3952))
% 155.94/155.63 [396]~E(x3961,x3962)+E(f245(x3961,x3963,x3964),f245(x3962,x3963,x3964))
% 155.94/155.63 [397]~E(x3971,x3972)+E(f245(x3973,x3971,x3974),f245(x3973,x3972,x3974))
% 155.94/155.63 [398]~E(x3981,x3982)+E(f245(x3983,x3984,x3981),f245(x3983,x3984,x3982))
% 155.94/155.63 [399]~E(x3991,x3992)+E(f76(x3991,x3993,x3994),f76(x3992,x3993,x3994))
% 155.94/155.63 [400]~E(x4001,x4002)+E(f76(x4003,x4001,x4004),f76(x4003,x4002,x4004))
% 155.94/155.63 [401]~E(x4011,x4012)+E(f76(x4013,x4014,x4011),f76(x4013,x4014,x4012))
% 155.94/155.63 [402]~E(x4021,x4022)+E(f187(x4021),f187(x4022))
% 155.94/155.63 [403]~E(x4031,x4032)+E(f11(x4031,x4033),f11(x4032,x4033))
% 155.94/155.63 [404]~E(x4041,x4042)+E(f11(x4043,x4041),f11(x4043,x4042))
% 155.94/155.63 [405]~E(x4051,x4052)+E(f84(x4051),f84(x4052))
% 155.94/155.63 [406]~E(x4061,x4062)+E(f86(x4061,x4063,x4064,x4065),f86(x4062,x4063,x4064,x4065))
% 155.94/155.63 [407]~E(x4071,x4072)+E(f86(x4073,x4071,x4074,x4075),f86(x4073,x4072,x4074,x4075))
% 155.94/155.63 [408]~E(x4081,x4082)+E(f86(x4083,x4084,x4081,x4085),f86(x4083,x4084,x4082,x4085))
% 155.94/155.63 [409]~E(x4091,x4092)+E(f86(x4093,x4094,x4095,x4091),f86(x4093,x4094,x4095,x4092))
% 155.94/155.63 [410]~E(x4101,x4102)+E(f600(x4101,x4103,x4104),f600(x4102,x4103,x4104))
% 155.94/155.63 [411]~E(x4111,x4112)+E(f600(x4113,x4111,x4114),f600(x4113,x4112,x4114))
% 155.94/155.63 [412]~E(x4121,x4122)+E(f600(x4123,x4124,x4121),f600(x4123,x4124,x4122))
% 155.94/155.63 [413]~E(x4131,x4132)+E(f547(x4131,x4133,x4134),f547(x4132,x4133,x4134))
% 155.94/155.63 [414]~E(x4141,x4142)+E(f547(x4143,x4141,x4144),f547(x4143,x4142,x4144))
% 155.94/155.63 [415]~E(x4151,x4152)+E(f547(x4153,x4154,x4151),f547(x4153,x4154,x4152))
% 155.94/155.63 [416]~E(x4161,x4162)+E(f184(x4161,x4163),f184(x4162,x4163))
% 155.94/155.63 [417]~E(x4171,x4172)+E(f184(x4173,x4171),f184(x4173,x4172))
% 155.94/155.63 [418]~E(x4181,x4182)+E(f470(x4181,x4183),f470(x4182,x4183))
% 155.94/155.63 [419]~E(x4191,x4192)+E(f470(x4193,x4191),f470(x4193,x4192))
% 155.94/155.63 [420]~E(x4201,x4202)+E(f575(x4201,x4203,x4204,x4205),f575(x4202,x4203,x4204,x4205))
% 155.94/155.63 [421]~E(x4211,x4212)+E(f575(x4213,x4211,x4214,x4215),f575(x4213,x4212,x4214,x4215))
% 155.94/155.63 [422]~E(x4221,x4222)+E(f575(x4223,x4224,x4221,x4225),f575(x4223,x4224,x4222,x4225))
% 155.94/155.63 [423]~E(x4231,x4232)+E(f575(x4233,x4234,x4235,x4231),f575(x4233,x4234,x4235,x4232))
% 155.94/155.63 [424]~E(x4241,x4242)+E(f793(x4241,x4243,x4244),f793(x4242,x4243,x4244))
% 155.94/155.63 [425]~E(x4251,x4252)+E(f793(x4253,x4251,x4254),f793(x4253,x4252,x4254))
% 155.94/155.63 [426]~E(x4261,x4262)+E(f793(x4263,x4264,x4261),f793(x4263,x4264,x4262))
% 155.94/155.63 [427]~E(x4271,x4272)+E(f12(x4271,x4273,x4274),f12(x4272,x4273,x4274))
% 155.94/155.63 [428]~E(x4281,x4282)+E(f12(x4283,x4281,x4284),f12(x4283,x4282,x4284))
% 155.94/155.63 [429]~E(x4291,x4292)+E(f12(x4293,x4294,x4291),f12(x4293,x4294,x4292))
% 155.94/155.63 [430]~E(x4301,x4302)+E(f671(x4301,x4303,x4304),f671(x4302,x4303,x4304))
% 155.94/155.63 [431]~E(x4311,x4312)+E(f671(x4313,x4311,x4314),f671(x4313,x4312,x4314))
% 155.94/155.63 [432]~E(x4321,x4322)+E(f671(x4323,x4324,x4321),f671(x4323,x4324,x4322))
% 155.94/155.63 [433]~E(x4331,x4332)+E(f135(x4331,x4333),f135(x4332,x4333))
% 155.94/155.63 [434]~E(x4341,x4342)+E(f135(x4343,x4341),f135(x4343,x4342))
% 155.94/155.63 [435]~E(x4351,x4352)+E(f149(x4351,x4353),f149(x4352,x4353))
% 155.94/155.63 [436]~E(x4361,x4362)+E(f149(x4363,x4361),f149(x4363,x4362))
% 155.94/155.63 [437]~E(x4371,x4372)+E(f110(x4371,x4373),f110(x4372,x4373))
% 155.94/155.63 [438]~E(x4381,x4382)+E(f110(x4383,x4381),f110(x4383,x4382))
% 155.94/155.63 [439]~E(x4391,x4392)+E(f587(x4391,x4393,x4394),f587(x4392,x4393,x4394))
% 155.94/155.63 [440]~E(x4401,x4402)+E(f587(x4403,x4401,x4404),f587(x4403,x4402,x4404))
% 155.94/155.63 [441]~E(x4411,x4412)+E(f587(x4413,x4414,x4411),f587(x4413,x4414,x4412))
% 155.94/155.63 [442]~E(x4421,x4422)+E(f608(x4421,x4423,x4424),f608(x4422,x4423,x4424))
% 155.94/155.63 [443]~E(x4431,x4432)+E(f608(x4433,x4431,x4434),f608(x4433,x4432,x4434))
% 155.94/155.63 [444]~E(x4441,x4442)+E(f608(x4443,x4444,x4441),f608(x4443,x4444,x4442))
% 155.94/155.63 [445]~E(x4451,x4452)+E(f180(x4451,x4453,x4454,x4455),f180(x4452,x4453,x4454,x4455))
% 155.94/155.63 [446]~E(x4461,x4462)+E(f180(x4463,x4461,x4464,x4465),f180(x4463,x4462,x4464,x4465))
% 155.94/155.63 [447]~E(x4471,x4472)+E(f180(x4473,x4474,x4471,x4475),f180(x4473,x4474,x4472,x4475))
% 155.94/155.63 [448]~E(x4481,x4482)+E(f180(x4483,x4484,x4485,x4481),f180(x4483,x4484,x4485,x4482))
% 155.94/155.63 [449]~E(x4491,x4492)+E(f583(x4491,x4493),f583(x4492,x4493))
% 155.94/155.63 [450]~E(x4501,x4502)+E(f583(x4503,x4501),f583(x4503,x4502))
% 155.94/155.63 [451]~E(x4511,x4512)+E(f146(x4511,x4513,x4514,x4515,x4516),f146(x4512,x4513,x4514,x4515,x4516))
% 155.94/155.63 [452]~E(x4521,x4522)+E(f146(x4523,x4521,x4524,x4525,x4526),f146(x4523,x4522,x4524,x4525,x4526))
% 155.94/155.63 [453]~E(x4531,x4532)+E(f146(x4533,x4534,x4531,x4535,x4536),f146(x4533,x4534,x4532,x4535,x4536))
% 155.94/155.63 [454]~E(x4541,x4542)+E(f146(x4543,x4544,x4545,x4541,x4546),f146(x4543,x4544,x4545,x4542,x4546))
% 155.94/155.63 [455]~E(x4551,x4552)+E(f146(x4553,x4554,x4555,x4556,x4551),f146(x4553,x4554,x4555,x4556,x4552))
% 155.94/155.63 [456]~E(x4561,x4562)+E(f389(x4561,x4563),f389(x4562,x4563))
% 155.94/155.63 [457]~E(x4571,x4572)+E(f389(x4573,x4571),f389(x4573,x4572))
% 155.94/155.63 [458]~E(x4581,x4582)+E(f348(x4581,x4583,x4584),f348(x4582,x4583,x4584))
% 155.94/155.63 [459]~E(x4591,x4592)+E(f348(x4593,x4591,x4594),f348(x4593,x4592,x4594))
% 155.94/155.63 [460]~E(x4601,x4602)+E(f348(x4603,x4604,x4601),f348(x4603,x4604,x4602))
% 155.94/155.63 [461]~E(x4611,x4612)+E(f306(x4611,x4613,x4614),f306(x4612,x4613,x4614))
% 155.94/155.63 [462]~E(x4621,x4622)+E(f306(x4623,x4621,x4624),f306(x4623,x4622,x4624))
% 155.94/155.63 [463]~E(x4631,x4632)+E(f306(x4633,x4634,x4631),f306(x4633,x4634,x4632))
% 155.94/155.63 [464]~E(x4641,x4642)+E(f510(x4641,x4643,x4644,x4645,x4646),f510(x4642,x4643,x4644,x4645,x4646))
% 155.94/155.63 [465]~E(x4651,x4652)+E(f510(x4653,x4651,x4654,x4655,x4656),f510(x4653,x4652,x4654,x4655,x4656))
% 155.94/155.63 [466]~E(x4661,x4662)+E(f510(x4663,x4664,x4661,x4665,x4666),f510(x4663,x4664,x4662,x4665,x4666))
% 155.94/155.63 [467]~E(x4671,x4672)+E(f510(x4673,x4674,x4675,x4671,x4676),f510(x4673,x4674,x4675,x4672,x4676))
% 155.94/155.63 [468]~E(x4681,x4682)+E(f510(x4683,x4684,x4685,x4686,x4681),f510(x4683,x4684,x4685,x4686,x4682))
% 155.94/155.63 [469]~E(x4691,x4692)+E(f96(x4691),f96(x4692))
% 155.94/155.63 [470]~E(x4701,x4702)+E(f451(x4701,x4703,x4704,x4705),f451(x4702,x4703,x4704,x4705))
% 155.94/155.63 [471]~E(x4711,x4712)+E(f451(x4713,x4711,x4714,x4715),f451(x4713,x4712,x4714,x4715))
% 155.94/155.63 [472]~E(x4721,x4722)+E(f451(x4723,x4724,x4721,x4725),f451(x4723,x4724,x4722,x4725))
% 155.94/155.63 [473]~E(x4731,x4732)+E(f451(x4733,x4734,x4735,x4731),f451(x4733,x4734,x4735,x4732))
% 155.94/155.63 [474]~E(x4741,x4742)+E(f71(x4741,x4743,x4744),f71(x4742,x4743,x4744))
% 155.94/155.63 [475]~E(x4751,x4752)+E(f71(x4753,x4751,x4754),f71(x4753,x4752,x4754))
% 155.94/155.63 [476]~E(x4761,x4762)+E(f71(x4763,x4764,x4761),f71(x4763,x4764,x4762))
% 155.94/155.63 [477]~E(x4771,x4772)+E(f158(x4771,x4773),f158(x4772,x4773))
% 155.94/155.63 [478]~E(x4781,x4782)+E(f158(x4783,x4781),f158(x4783,x4782))
% 155.94/155.63 [479]~E(x4791,x4792)+E(f701(x4791,x4793),f701(x4792,x4793))
% 155.94/155.63 [480]~E(x4801,x4802)+E(f701(x4803,x4801),f701(x4803,x4802))
% 155.94/155.63 [481]~E(x4811,x4812)+E(f337(x4811,x4813,x4814),f337(x4812,x4813,x4814))
% 155.94/155.63 [482]~E(x4821,x4822)+E(f337(x4823,x4821,x4824),f337(x4823,x4822,x4824))
% 155.94/155.63 [483]~E(x4831,x4832)+E(f337(x4833,x4834,x4831),f337(x4833,x4834,x4832))
% 155.94/155.63 [484]~E(x4841,x4842)+E(f182(x4841,x4843,x4844,x4845,x4846),f182(x4842,x4843,x4844,x4845,x4846))
% 155.94/155.63 [485]~E(x4851,x4852)+E(f182(x4853,x4851,x4854,x4855,x4856),f182(x4853,x4852,x4854,x4855,x4856))
% 155.94/155.63 [486]~E(x4861,x4862)+E(f182(x4863,x4864,x4861,x4865,x4866),f182(x4863,x4864,x4862,x4865,x4866))
% 155.94/155.63 [487]~E(x4871,x4872)+E(f182(x4873,x4874,x4875,x4871,x4876),f182(x4873,x4874,x4875,x4872,x4876))
% 155.94/155.63 [488]~E(x4881,x4882)+E(f182(x4883,x4884,x4885,x4886,x4881),f182(x4883,x4884,x4885,x4886,x4882))
% 155.94/155.63 [489]~E(x4891,x4892)+E(f691(x4891,x4893,x4894),f691(x4892,x4893,x4894))
% 155.94/155.63 [490]~E(x4901,x4902)+E(f691(x4903,x4901,x4904),f691(x4903,x4902,x4904))
% 155.94/155.63 [491]~E(x4911,x4912)+E(f691(x4913,x4914,x4911),f691(x4913,x4914,x4912))
% 155.94/155.63 [492]~E(x4921,x4922)+E(f143(x4921,x4923),f143(x4922,x4923))
% 155.94/155.63 [493]~E(x4931,x4932)+E(f143(x4933,x4931),f143(x4933,x4932))
% 155.94/155.63 [494]~E(x4941,x4942)+E(f646(x4941,x4943,x4944),f646(x4942,x4943,x4944))
% 155.94/155.63 [495]~E(x4951,x4952)+E(f646(x4953,x4951,x4954),f646(x4953,x4952,x4954))
% 155.94/155.63 [496]~E(x4961,x4962)+E(f646(x4963,x4964,x4961),f646(x4963,x4964,x4962))
% 155.94/155.63 [497]~E(x4971,x4972)+E(f316(x4971,x4973,x4974,x4975),f316(x4972,x4973,x4974,x4975))
% 155.94/155.63 [498]~E(x4981,x4982)+E(f316(x4983,x4981,x4984,x4985),f316(x4983,x4982,x4984,x4985))
% 155.94/155.63 [499]~E(x4991,x4992)+E(f316(x4993,x4994,x4991,x4995),f316(x4993,x4994,x4992,x4995))
% 155.94/155.63 [500]~E(x5001,x5002)+E(f316(x5003,x5004,x5005,x5001),f316(x5003,x5004,x5005,x5002))
% 155.94/155.63 [501]~E(x5011,x5012)+E(f175(x5011,x5013),f175(x5012,x5013))
% 155.94/155.63 [502]~E(x5021,x5022)+E(f175(x5023,x5021),f175(x5023,x5022))
% 155.94/155.63 [503]~E(x5031,x5032)+E(f284(x5031,x5033,x5034),f284(x5032,x5033,x5034))
% 155.94/155.63 [504]~E(x5041,x5042)+E(f284(x5043,x5041,x5044),f284(x5043,x5042,x5044))
% 155.94/155.63 [505]~E(x5051,x5052)+E(f284(x5053,x5054,x5051),f284(x5053,x5054,x5052))
% 155.94/155.63 [506]~E(x5061,x5062)+E(f273(x5061,x5063,x5064),f273(x5062,x5063,x5064))
% 155.94/155.63 [507]~E(x5071,x5072)+E(f273(x5073,x5071,x5074),f273(x5073,x5072,x5074))
% 155.94/155.63 [508]~E(x5081,x5082)+E(f273(x5083,x5084,x5081),f273(x5083,x5084,x5082))
% 155.94/155.63 [509]~E(x5091,x5092)+E(f686(x5091,x5093,x5094,x5095,x5096),f686(x5092,x5093,x5094,x5095,x5096))
% 155.94/155.63 [510]~E(x5101,x5102)+E(f686(x5103,x5101,x5104,x5105,x5106),f686(x5103,x5102,x5104,x5105,x5106))
% 155.94/155.63 [511]~E(x5111,x5112)+E(f686(x5113,x5114,x5111,x5115,x5116),f686(x5113,x5114,x5112,x5115,x5116))
% 155.94/155.63 [512]~E(x5121,x5122)+E(f686(x5123,x5124,x5125,x5121,x5126),f686(x5123,x5124,x5125,x5122,x5126))
% 155.94/155.63 [513]~E(x5131,x5132)+E(f686(x5133,x5134,x5135,x5136,x5131),f686(x5133,x5134,x5135,x5136,x5132))
% 155.94/155.63 [514]~E(x5141,x5142)+E(f837(x5141,x5143,x5144,x5145),f837(x5142,x5143,x5144,x5145))
% 155.94/155.63 [515]~E(x5151,x5152)+E(f837(x5153,x5151,x5154,x5155),f837(x5153,x5152,x5154,x5155))
% 155.94/155.63 [516]~E(x5161,x5162)+E(f837(x5163,x5164,x5161,x5165),f837(x5163,x5164,x5162,x5165))
% 155.94/155.63 [517]~E(x5171,x5172)+E(f837(x5173,x5174,x5175,x5171),f837(x5173,x5174,x5175,x5172))
% 155.94/155.63 [518]~E(x5181,x5182)+E(f199(x5181,x5183),f199(x5182,x5183))
% 155.94/155.63 [519]~E(x5191,x5192)+E(f199(x5193,x5191),f199(x5193,x5192))
% 155.94/155.63 [520]~E(x5201,x5202)+E(f520(x5201,x5203,x5204,x5205,x5206),f520(x5202,x5203,x5204,x5205,x5206))
% 155.94/155.63 [521]~E(x5211,x5212)+E(f520(x5213,x5211,x5214,x5215,x5216),f520(x5213,x5212,x5214,x5215,x5216))
% 155.94/155.63 [522]~E(x5221,x5222)+E(f520(x5223,x5224,x5221,x5225,x5226),f520(x5223,x5224,x5222,x5225,x5226))
% 155.94/155.63 [523]~E(x5231,x5232)+E(f520(x5233,x5234,x5235,x5231,x5236),f520(x5233,x5234,x5235,x5232,x5236))
% 155.94/155.63 [524]~E(x5241,x5242)+E(f520(x5243,x5244,x5245,x5246,x5241),f520(x5243,x5244,x5245,x5246,x5242))
% 155.94/155.63 [525]~E(x5251,x5252)+E(f356(x5251,x5253,x5254),f356(x5252,x5253,x5254))
% 155.94/155.63 [526]~E(x5261,x5262)+E(f356(x5263,x5261,x5264),f356(x5263,x5262,x5264))
% 155.94/155.63 [527]~E(x5271,x5272)+E(f356(x5273,x5274,x5271),f356(x5273,x5274,x5272))
% 155.94/155.63 [528]~E(x5281,x5282)+E(f537(x5281,x5283,x5284),f537(x5282,x5283,x5284))
% 155.94/155.63 [529]~E(x5291,x5292)+E(f537(x5293,x5291,x5294),f537(x5293,x5292,x5294))
% 155.94/155.63 [530]~E(x5301,x5302)+E(f537(x5303,x5304,x5301),f537(x5303,x5304,x5302))
% 155.94/155.63 [531]~E(x5311,x5312)+E(f49(x5311,x5313),f49(x5312,x5313))
% 155.94/155.63 [532]~E(x5321,x5322)+E(f49(x5323,x5321),f49(x5323,x5322))
% 155.94/155.63 [533]~E(x5331,x5332)+E(f797(x5331,x5333,x5334),f797(x5332,x5333,x5334))
% 155.94/155.63 [534]~E(x5341,x5342)+E(f797(x5343,x5341,x5344),f797(x5343,x5342,x5344))
% 155.94/155.63 [535]~E(x5351,x5352)+E(f797(x5353,x5354,x5351),f797(x5353,x5354,x5352))
% 155.94/155.63 [536]~E(x5361,x5362)+E(f136(x5361,x5363,x5364),f136(x5362,x5363,x5364))
% 155.94/155.63 [537]~E(x5371,x5372)+E(f136(x5373,x5371,x5374),f136(x5373,x5372,x5374))
% 155.94/155.63 [538]~E(x5381,x5382)+E(f136(x5383,x5384,x5381),f136(x5383,x5384,x5382))
% 155.94/155.63 [539]~E(x5391,x5392)+E(f286(x5391),f286(x5392))
% 155.94/155.63 [540]~E(x5401,x5402)+E(f680(x5401,x5403,x5404),f680(x5402,x5403,x5404))
% 155.94/155.63 [541]~E(x5411,x5412)+E(f680(x5413,x5411,x5414),f680(x5413,x5412,x5414))
% 155.94/155.63 [542]~E(x5421,x5422)+E(f680(x5423,x5424,x5421),f680(x5423,x5424,x5422))
% 155.94/155.63 [543]~E(x5431,x5432)+E(f280(x5431),f280(x5432))
% 155.94/155.63 [544]~E(x5441,x5442)+E(f509(x5441,x5443,x5444,x5445,x5446),f509(x5442,x5443,x5444,x5445,x5446))
% 155.94/155.63 [545]~E(x5451,x5452)+E(f509(x5453,x5451,x5454,x5455,x5456),f509(x5453,x5452,x5454,x5455,x5456))
% 155.94/155.63 [546]~E(x5461,x5462)+E(f509(x5463,x5464,x5461,x5465,x5466),f509(x5463,x5464,x5462,x5465,x5466))
% 155.94/155.63 [547]~E(x5471,x5472)+E(f509(x5473,x5474,x5475,x5471,x5476),f509(x5473,x5474,x5475,x5472,x5476))
% 155.94/155.63 [548]~E(x5481,x5482)+E(f509(x5483,x5484,x5485,x5486,x5481),f509(x5483,x5484,x5485,x5486,x5482))
% 155.94/155.63 [549]~E(x5491,x5492)+E(f420(x5491,x5493,x5494),f420(x5492,x5493,x5494))
% 155.94/155.63 [550]~E(x5501,x5502)+E(f420(x5503,x5501,x5504),f420(x5503,x5502,x5504))
% 155.94/155.63 [551]~E(x5511,x5512)+E(f420(x5513,x5514,x5511),f420(x5513,x5514,x5512))
% 155.94/155.63 [552]~E(x5521,x5522)+E(f366(x5521),f366(x5522))
% 155.94/155.63 [553]~E(x5531,x5532)+E(f757(x5531,x5533,x5534),f757(x5532,x5533,x5534))
% 155.94/155.63 [554]~E(x5541,x5542)+E(f757(x5543,x5541,x5544),f757(x5543,x5542,x5544))
% 155.94/155.63 [555]~E(x5551,x5552)+E(f757(x5553,x5554,x5551),f757(x5553,x5554,x5552))
% 155.94/155.63 [556]~E(x5561,x5562)+E(f234(x5561),f234(x5562))
% 155.94/155.63 [557]~E(x5571,x5572)+E(f223(x5571),f223(x5572))
% 155.94/155.63 [558]~E(x5581,x5582)+E(f760(x5581),f760(x5582))
% 155.94/155.63 [559]~E(x5591,x5592)+E(f767(x5591,x5593,x5594,x5595,x5596),f767(x5592,x5593,x5594,x5595,x5596))
% 155.94/155.63 [560]~E(x5601,x5602)+E(f767(x5603,x5601,x5604,x5605,x5606),f767(x5603,x5602,x5604,x5605,x5606))
% 155.94/155.63 [561]~E(x5611,x5612)+E(f767(x5613,x5614,x5611,x5615,x5616),f767(x5613,x5614,x5612,x5615,x5616))
% 155.94/155.63 [562]~E(x5621,x5622)+E(f767(x5623,x5624,x5625,x5621,x5626),f767(x5623,x5624,x5625,x5622,x5626))
% 155.94/155.63 [563]~E(x5631,x5632)+E(f767(x5633,x5634,x5635,x5636,x5631),f767(x5633,x5634,x5635,x5636,x5632))
% 155.94/155.63 [564]~E(x5641,x5642)+E(f507(x5641,x5643,x5644,x5645),f507(x5642,x5643,x5644,x5645))
% 155.94/155.63 [565]~E(x5651,x5652)+E(f507(x5653,x5651,x5654,x5655),f507(x5653,x5652,x5654,x5655))
% 155.94/155.63 [566]~E(x5661,x5662)+E(f507(x5663,x5664,x5661,x5665),f507(x5663,x5664,x5662,x5665))
% 155.94/155.63 [567]~E(x5671,x5672)+E(f507(x5673,x5674,x5675,x5671),f507(x5673,x5674,x5675,x5672))
% 155.94/155.63 [568]~E(x5681,x5682)+E(f806(x5681,x5683,x5684,x5685),f806(x5682,x5683,x5684,x5685))
% 155.94/155.63 [569]~E(x5691,x5692)+E(f806(x5693,x5691,x5694,x5695),f806(x5693,x5692,x5694,x5695))
% 155.94/155.63 [570]~E(x5701,x5702)+E(f806(x5703,x5704,x5701,x5705),f806(x5703,x5704,x5702,x5705))
% 155.94/155.63 [571]~E(x5711,x5712)+E(f806(x5713,x5714,x5715,x5711),f806(x5713,x5714,x5715,x5712))
% 155.94/155.63 [572]~E(x5721,x5722)+E(f301(x5721,x5723),f301(x5722,x5723))
% 155.94/155.63 [573]~E(x5731,x5732)+E(f301(x5733,x5731),f301(x5733,x5732))
% 155.94/155.63 [574]~E(x5741,x5742)+E(f68(x5741,x5743,x5744,x5745),f68(x5742,x5743,x5744,x5745))
% 155.94/155.63 [575]~E(x5751,x5752)+E(f68(x5753,x5751,x5754,x5755),f68(x5753,x5752,x5754,x5755))
% 155.94/155.63 [576]~E(x5761,x5762)+E(f68(x5763,x5764,x5761,x5765),f68(x5763,x5764,x5762,x5765))
% 155.94/155.63 [577]~E(x5771,x5772)+E(f68(x5773,x5774,x5775,x5771),f68(x5773,x5774,x5775,x5772))
% 155.94/155.63 [578]~E(x5781,x5782)+E(f55(x5781,x5783),f55(x5782,x5783))
% 155.94/155.63 [579]~E(x5791,x5792)+E(f55(x5793,x5791),f55(x5793,x5792))
% 155.94/155.63 [580]~E(x5801,x5802)+E(f108(x5801),f108(x5802))
% 155.94/155.63 [581]~E(x5811,x5812)+E(f141(x5811,x5813),f141(x5812,x5813))
% 155.94/155.63 [582]~E(x5821,x5822)+E(f141(x5823,x5821),f141(x5823,x5822))
% 155.94/155.63 [583]~E(x5831,x5832)+E(f617(x5831,x5833,x5834),f617(x5832,x5833,x5834))
% 155.94/155.63 [584]~E(x5841,x5842)+E(f617(x5843,x5841,x5844),f617(x5843,x5842,x5844))
% 155.94/155.63 [585]~E(x5851,x5852)+E(f617(x5853,x5854,x5851),f617(x5853,x5854,x5852))
% 155.94/155.63 [586]~E(x5861,x5862)+E(f131(x5861,x5863,x5864,x5865),f131(x5862,x5863,x5864,x5865))
% 155.94/155.63 [587]~E(x5871,x5872)+E(f131(x5873,x5871,x5874,x5875),f131(x5873,x5872,x5874,x5875))
% 155.94/155.63 [588]~E(x5881,x5882)+E(f131(x5883,x5884,x5881,x5885),f131(x5883,x5884,x5882,x5885))
% 155.94/155.63 [589]~E(x5891,x5892)+E(f131(x5893,x5894,x5895,x5891),f131(x5893,x5894,x5895,x5892))
% 155.94/155.63 [590]~E(x5901,x5902)+E(f333(x5901,x5903,x5904),f333(x5902,x5903,x5904))
% 155.94/155.63 [591]~E(x5911,x5912)+E(f333(x5913,x5911,x5914),f333(x5913,x5912,x5914))
% 155.94/155.63 [592]~E(x5921,x5922)+E(f333(x5923,x5924,x5921),f333(x5923,x5924,x5922))
% 155.94/155.63 [593]~E(x5931,x5932)+E(f57(x5931,x5933),f57(x5932,x5933))
% 155.94/155.63 [594]~E(x5941,x5942)+E(f57(x5943,x5941),f57(x5943,x5942))
% 155.94/155.63 [595]~E(x5951,x5952)+E(f467(x5951,x5953,x5954,x5955),f467(x5952,x5953,x5954,x5955))
% 155.94/155.63 [596]~E(x5961,x5962)+E(f467(x5963,x5961,x5964,x5965),f467(x5963,x5962,x5964,x5965))
% 155.94/155.63 [597]~E(x5971,x5972)+E(f467(x5973,x5974,x5971,x5975),f467(x5973,x5974,x5972,x5975))
% 155.94/155.63 [598]~E(x5981,x5982)+E(f467(x5983,x5984,x5985,x5981),f467(x5983,x5984,x5985,x5982))
% 155.94/155.63 [599]~E(x5991,x5992)+E(f692(x5991,x5993,x5994),f692(x5992,x5993,x5994))
% 155.94/155.63 [600]~E(x6001,x6002)+E(f692(x6003,x6001,x6004),f692(x6003,x6002,x6004))
% 155.94/155.63 [601]~E(x6011,x6012)+E(f692(x6013,x6014,x6011),f692(x6013,x6014,x6012))
% 155.94/155.63 [602]~E(x6021,x6022)+E(f742(x6021,x6023,x6024,x6025,x6026),f742(x6022,x6023,x6024,x6025,x6026))
% 155.94/155.63 [603]~E(x6031,x6032)+E(f742(x6033,x6031,x6034,x6035,x6036),f742(x6033,x6032,x6034,x6035,x6036))
% 155.94/155.63 [604]~E(x6041,x6042)+E(f742(x6043,x6044,x6041,x6045,x6046),f742(x6043,x6044,x6042,x6045,x6046))
% 155.94/155.63 [605]~E(x6051,x6052)+E(f742(x6053,x6054,x6055,x6051,x6056),f742(x6053,x6054,x6055,x6052,x6056))
% 155.94/155.63 [606]~E(x6061,x6062)+E(f742(x6063,x6064,x6065,x6066,x6061),f742(x6063,x6064,x6065,x6066,x6062))
% 155.94/155.63 [607]~E(x6071,x6072)+E(f221(x6071,x6073,x6074,x6075),f221(x6072,x6073,x6074,x6075))
% 155.94/155.63 [608]~E(x6081,x6082)+E(f221(x6083,x6081,x6084,x6085),f221(x6083,x6082,x6084,x6085))
% 155.94/155.63 [609]~E(x6091,x6092)+E(f221(x6093,x6094,x6091,x6095),f221(x6093,x6094,x6092,x6095))
% 155.94/155.63 [610]~E(x6101,x6102)+E(f221(x6103,x6104,x6105,x6101),f221(x6103,x6104,x6105,x6102))
% 155.94/155.63 [611]~E(x6111,x6112)+E(f440(x6111,x6113,x6114),f440(x6112,x6113,x6114))
% 155.94/155.63 [612]~E(x6121,x6122)+E(f440(x6123,x6121,x6124),f440(x6123,x6122,x6124))
% 155.94/155.63 [613]~E(x6131,x6132)+E(f440(x6133,x6134,x6131),f440(x6133,x6134,x6132))
% 155.94/155.63 [614]~E(x6141,x6142)+E(f156(x6141,x6143),f156(x6142,x6143))
% 155.94/155.63 [615]~E(x6151,x6152)+E(f156(x6153,x6151),f156(x6153,x6152))
% 155.94/155.63 [616]~E(x6161,x6162)+E(f491(x6161,x6163,x6164,x6165),f491(x6162,x6163,x6164,x6165))
% 155.94/155.63 [617]~E(x6171,x6172)+E(f491(x6173,x6171,x6174,x6175),f491(x6173,x6172,x6174,x6175))
% 155.94/155.63 [618]~E(x6181,x6182)+E(f491(x6183,x6184,x6181,x6185),f491(x6183,x6184,x6182,x6185))
% 155.94/155.63 [619]~E(x6191,x6192)+E(f491(x6193,x6194,x6195,x6191),f491(x6193,x6194,x6195,x6192))
% 155.94/155.63 [620]~E(x6201,x6202)+E(f52(x6201),f52(x6202))
% 155.94/155.63 [621]~E(x6211,x6212)+E(f242(x6211,x6213,x6214),f242(x6212,x6213,x6214))
% 155.94/155.63 [622]~E(x6221,x6222)+E(f242(x6223,x6221,x6224),f242(x6223,x6222,x6224))
% 155.94/155.63 [623]~E(x6231,x6232)+E(f242(x6233,x6234,x6231),f242(x6233,x6234,x6232))
% 155.94/155.63 [624]~E(x6241,x6242)+E(f519(x6241,x6243,x6244,x6245,x6246),f519(x6242,x6243,x6244,x6245,x6246))
% 155.94/155.63 [625]~E(x6251,x6252)+E(f519(x6253,x6251,x6254,x6255,x6256),f519(x6253,x6252,x6254,x6255,x6256))
% 155.94/155.63 [626]~E(x6261,x6262)+E(f519(x6263,x6264,x6261,x6265,x6266),f519(x6263,x6264,x6262,x6265,x6266))
% 155.94/155.63 [627]~E(x6271,x6272)+E(f519(x6273,x6274,x6275,x6271,x6276),f519(x6273,x6274,x6275,x6272,x6276))
% 155.94/155.63 [628]~E(x6281,x6282)+E(f519(x6283,x6284,x6285,x6286,x6281),f519(x6283,x6284,x6285,x6286,x6282))
% 155.94/155.63 [629]~E(x6291,x6292)+E(f603(x6291,x6293,x6294,x6295),f603(x6292,x6293,x6294,x6295))
% 155.94/155.63 [630]~E(x6301,x6302)+E(f603(x6303,x6301,x6304,x6305),f603(x6303,x6302,x6304,x6305))
% 155.94/155.63 [631]~E(x6311,x6312)+E(f603(x6313,x6314,x6311,x6315),f603(x6313,x6314,x6312,x6315))
% 155.94/155.63 [632]~E(x6321,x6322)+E(f603(x6323,x6324,x6325,x6321),f603(x6323,x6324,x6325,x6322))
% 155.94/155.63 [633]~E(x6331,x6332)+E(f645(x6331,x6333,x6334),f645(x6332,x6333,x6334))
% 155.94/155.63 [634]~E(x6341,x6342)+E(f645(x6343,x6341,x6344),f645(x6343,x6342,x6344))
% 155.94/155.63 [635]~E(x6351,x6352)+E(f645(x6353,x6354,x6351),f645(x6353,x6354,x6352))
% 155.94/155.63 [636]~E(x6361,x6362)+E(f341(x6361,x6363,x6364,x6365,x6366),f341(x6362,x6363,x6364,x6365,x6366))
% 155.94/155.63 [637]~E(x6371,x6372)+E(f341(x6373,x6371,x6374,x6375,x6376),f341(x6373,x6372,x6374,x6375,x6376))
% 155.94/155.63 [638]~E(x6381,x6382)+E(f341(x6383,x6384,x6381,x6385,x6386),f341(x6383,x6384,x6382,x6385,x6386))
% 155.94/155.63 [639]~E(x6391,x6392)+E(f341(x6393,x6394,x6395,x6391,x6396),f341(x6393,x6394,x6395,x6392,x6396))
% 155.94/155.63 [640]~E(x6401,x6402)+E(f341(x6403,x6404,x6405,x6406,x6401),f341(x6403,x6404,x6405,x6406,x6402))
% 155.94/155.63 [641]~E(x6411,x6412)+E(f218(x6411,x6413),f218(x6412,x6413))
% 155.94/155.63 [642]~E(x6421,x6422)+E(f218(x6423,x6421),f218(x6423,x6422))
% 155.94/155.63 [643]~E(x6431,x6432)+E(f193(x6431,x6433),f193(x6432,x6433))
% 155.94/155.63 [644]~E(x6441,x6442)+E(f193(x6443,x6441),f193(x6443,x6442))
% 155.94/155.63 [645]~E(x6451,x6452)+E(f814(x6451,x6453,x6454),f814(x6452,x6453,x6454))
% 155.94/155.63 [646]~E(x6461,x6462)+E(f814(x6463,x6461,x6464),f814(x6463,x6462,x6464))
% 155.94/155.63 [647]~E(x6471,x6472)+E(f814(x6473,x6474,x6471),f814(x6473,x6474,x6472))
% 155.94/155.63 [648]~E(x6481,x6482)+E(f674(x6481,x6483,x6484,x6485,x6486,x6487,x6488,x6489),f674(x6482,x6483,x6484,x6485,x6486,x6487,x6488,x6489))
% 155.94/155.63 [649]~E(x6491,x6492)+E(f674(x6493,x6491,x6494,x6495,x6496,x6497,x6498,x6499),f674(x6493,x6492,x6494,x6495,x6496,x6497,x6498,x6499))
% 155.94/155.63 [650]~E(x6501,x6502)+E(f674(x6503,x6504,x6501,x6505,x6506,x6507,x6508,x6509),f674(x6503,x6504,x6502,x6505,x6506,x6507,x6508,x6509))
% 155.94/155.63 [651]~E(x6511,x6512)+E(f674(x6513,x6514,x6515,x6511,x6516,x6517,x6518,x6519),f674(x6513,x6514,x6515,x6512,x6516,x6517,x6518,x6519))
% 155.94/155.63 [652]~E(x6521,x6522)+E(f674(x6523,x6524,x6525,x6526,x6521,x6527,x6528,x6529),f674(x6523,x6524,x6525,x6526,x6522,x6527,x6528,x6529))
% 155.94/155.63 [653]~E(x6531,x6532)+E(f674(x6533,x6534,x6535,x6536,x6537,x6531,x6538,x6539),f674(x6533,x6534,x6535,x6536,x6537,x6532,x6538,x6539))
% 155.94/155.63 [654]~E(x6541,x6542)+E(f674(x6543,x6544,x6545,x6546,x6547,x6548,x6541,x6549),f674(x6543,x6544,x6545,x6546,x6547,x6548,x6542,x6549))
% 155.94/155.63 [655]~E(x6551,x6552)+E(f674(x6553,x6554,x6555,x6556,x6557,x6558,x6559,x6551),f674(x6553,x6554,x6555,x6556,x6557,x6558,x6559,x6552))
% 155.94/155.63 [656]~E(x6561,x6562)+E(f577(x6561,x6563,x6564,x6565),f577(x6562,x6563,x6564,x6565))
% 155.94/155.63 [657]~E(x6571,x6572)+E(f577(x6573,x6571,x6574,x6575),f577(x6573,x6572,x6574,x6575))
% 155.94/155.63 [658]~E(x6581,x6582)+E(f577(x6583,x6584,x6581,x6585),f577(x6583,x6584,x6582,x6585))
% 155.94/155.63 [659]~E(x6591,x6592)+E(f577(x6593,x6594,x6595,x6591),f577(x6593,x6594,x6595,x6592))
% 155.94/155.63 [660]~E(x6601,x6602)+E(f666(x6601,x6603),f666(x6602,x6603))
% 155.94/155.63 [661]~E(x6611,x6612)+E(f666(x6613,x6611),f666(x6613,x6612))
% 155.94/155.63 [662]~E(x6621,x6622)+E(f285(x6621,x6623,x6624),f285(x6622,x6623,x6624))
% 155.94/155.63 [663]~E(x6631,x6632)+E(f285(x6633,x6631,x6634),f285(x6633,x6632,x6634))
% 155.94/155.63 [664]~E(x6641,x6642)+E(f285(x6643,x6644,x6641),f285(x6643,x6644,x6642))
% 155.94/155.63 [665]~E(x6651,x6652)+E(f134(x6651),f134(x6652))
% 155.94/155.63 [666]~E(x6661,x6662)+E(f586(x6661,x6663,x6664,x6665,x6666),f586(x6662,x6663,x6664,x6665,x6666))
% 155.94/155.63 [667]~E(x6671,x6672)+E(f586(x6673,x6671,x6674,x6675,x6676),f586(x6673,x6672,x6674,x6675,x6676))
% 155.94/155.63 [668]~E(x6681,x6682)+E(f586(x6683,x6684,x6681,x6685,x6686),f586(x6683,x6684,x6682,x6685,x6686))
% 155.94/155.63 [669]~E(x6691,x6692)+E(f586(x6693,x6694,x6695,x6691,x6696),f586(x6693,x6694,x6695,x6692,x6696))
% 155.94/155.63 [670]~E(x6701,x6702)+E(f586(x6703,x6704,x6705,x6706,x6701),f586(x6703,x6704,x6705,x6706,x6702))
% 155.94/155.63 [671]~E(x6711,x6712)+E(f544(x6711,x6713,x6714),f544(x6712,x6713,x6714))
% 155.94/155.63 [672]~E(x6721,x6722)+E(f544(x6723,x6721,x6724),f544(x6723,x6722,x6724))
% 155.94/155.63 [673]~E(x6731,x6732)+E(f544(x6733,x6734,x6731),f544(x6733,x6734,x6732))
% 155.94/155.63 [674]~E(x6741,x6742)+E(f792(x6741,x6743,x6744),f792(x6742,x6743,x6744))
% 155.94/155.63 [675]~E(x6751,x6752)+E(f792(x6753,x6751,x6754),f792(x6753,x6752,x6754))
% 155.94/155.63 [676]~E(x6761,x6762)+E(f792(x6763,x6764,x6761),f792(x6763,x6764,x6762))
% 155.94/155.63 [677]~E(x6771,x6772)+E(f521(x6771,x6773,x6774,x6775,x6776),f521(x6772,x6773,x6774,x6775,x6776))
% 155.94/155.63 [678]~E(x6781,x6782)+E(f521(x6783,x6781,x6784,x6785,x6786),f521(x6783,x6782,x6784,x6785,x6786))
% 155.94/155.63 [679]~E(x6791,x6792)+E(f521(x6793,x6794,x6791,x6795,x6796),f521(x6793,x6794,x6792,x6795,x6796))
% 155.94/155.63 [680]~E(x6801,x6802)+E(f521(x6803,x6804,x6805,x6801,x6806),f521(x6803,x6804,x6805,x6802,x6806))
% 155.94/155.63 [681]~E(x6811,x6812)+E(f521(x6813,x6814,x6815,x6816,x6811),f521(x6813,x6814,x6815,x6816,x6812))
% 155.94/155.63 [682]~E(x6821,x6822)+E(f601(x6821,x6823,x6824),f601(x6822,x6823,x6824))
% 155.94/155.63 [683]~E(x6831,x6832)+E(f601(x6833,x6831,x6834),f601(x6833,x6832,x6834))
% 155.94/155.63 [684]~E(x6841,x6842)+E(f601(x6843,x6844,x6841),f601(x6843,x6844,x6842))
% 155.94/155.63 [685]~E(x6851,x6852)+E(f493(x6851,x6853,x6854,x6855),f493(x6852,x6853,x6854,x6855))
% 155.94/155.63 [686]~E(x6861,x6862)+E(f493(x6863,x6861,x6864,x6865),f493(x6863,x6862,x6864,x6865))
% 155.94/155.63 [687]~E(x6871,x6872)+E(f493(x6873,x6874,x6871,x6875),f493(x6873,x6874,x6872,x6875))
% 155.94/155.63 [688]~E(x6881,x6882)+E(f493(x6883,x6884,x6885,x6881),f493(x6883,x6884,x6885,x6882))
% 155.94/155.63 [689]~E(x6891,x6892)+E(f696(x6891,x6893,x6894,x6895,x6896),f696(x6892,x6893,x6894,x6895,x6896))
% 155.94/155.63 [690]~E(x6901,x6902)+E(f696(x6903,x6901,x6904,x6905,x6906),f696(x6903,x6902,x6904,x6905,x6906))
% 155.94/155.63 [691]~E(x6911,x6912)+E(f696(x6913,x6914,x6911,x6915,x6916),f696(x6913,x6914,x6912,x6915,x6916))
% 155.94/155.63 [692]~E(x6921,x6922)+E(f696(x6923,x6924,x6925,x6921,x6926),f696(x6923,x6924,x6925,x6922,x6926))
% 155.94/155.63 [693]~E(x6931,x6932)+E(f696(x6933,x6934,x6935,x6936,x6931),f696(x6933,x6934,x6935,x6936,x6932))
% 155.94/155.63 [694]~E(x6941,x6942)+E(f567(x6941,x6943,x6944,x6945),f567(x6942,x6943,x6944,x6945))
% 155.94/155.63 [695]~E(x6951,x6952)+E(f567(x6953,x6951,x6954,x6955),f567(x6953,x6952,x6954,x6955))
% 155.94/155.63 [696]~E(x6961,x6962)+E(f567(x6963,x6964,x6961,x6965),f567(x6963,x6964,x6962,x6965))
% 155.94/155.63 [697]~E(x6971,x6972)+E(f567(x6973,x6974,x6975,x6971),f567(x6973,x6974,x6975,x6972))
% 155.94/155.63 [698]~E(x6981,x6982)+E(f697(x6981,x6983,x6984,x6985,x6986,x6987),f697(x6982,x6983,x6984,x6985,x6986,x6987))
% 155.94/155.63 [699]~E(x6991,x6992)+E(f697(x6993,x6991,x6994,x6995,x6996,x6997),f697(x6993,x6992,x6994,x6995,x6996,x6997))
% 155.94/155.63 [700]~E(x7001,x7002)+E(f697(x7003,x7004,x7001,x7005,x7006,x7007),f697(x7003,x7004,x7002,x7005,x7006,x7007))
% 155.94/155.63 [701]~E(x7011,x7012)+E(f697(x7013,x7014,x7015,x7011,x7016,x7017),f697(x7013,x7014,x7015,x7012,x7016,x7017))
% 155.94/155.63 [702]~E(x7021,x7022)+E(f697(x7023,x7024,x7025,x7026,x7021,x7027),f697(x7023,x7024,x7025,x7026,x7022,x7027))
% 155.94/155.63 [703]~E(x7031,x7032)+E(f697(x7033,x7034,x7035,x7036,x7037,x7031),f697(x7033,x7034,x7035,x7036,x7037,x7032))
% 155.94/155.63 [704]~E(x7041,x7042)+E(f385(x7041),f385(x7042))
% 155.94/155.63 [705]~E(x7051,x7052)+E(f731(x7051,x7053,x7054,x7055,x7056,x7057),f731(x7052,x7053,x7054,x7055,x7056,x7057))
% 155.94/155.63 [706]~E(x7061,x7062)+E(f731(x7063,x7061,x7064,x7065,x7066,x7067),f731(x7063,x7062,x7064,x7065,x7066,x7067))
% 155.94/155.63 [707]~E(x7071,x7072)+E(f731(x7073,x7074,x7071,x7075,x7076,x7077),f731(x7073,x7074,x7072,x7075,x7076,x7077))
% 155.94/155.63 [708]~E(x7081,x7082)+E(f731(x7083,x7084,x7085,x7081,x7086,x7087),f731(x7083,x7084,x7085,x7082,x7086,x7087))
% 155.94/155.63 [709]~E(x7091,x7092)+E(f731(x7093,x7094,x7095,x7096,x7091,x7097),f731(x7093,x7094,x7095,x7096,x7092,x7097))
% 155.94/155.63 [710]~E(x7101,x7102)+E(f731(x7103,x7104,x7105,x7106,x7107,x7101),f731(x7103,x7104,x7105,x7106,x7107,x7102))
% 155.94/155.63 [711]~E(x7111,x7112)+E(f152(x7111,x7113,x7114,x7115),f152(x7112,x7113,x7114,x7115))
% 155.94/155.63 [712]~E(x7121,x7122)+E(f152(x7123,x7121,x7124,x7125),f152(x7123,x7122,x7124,x7125))
% 155.94/155.63 [713]~E(x7131,x7132)+E(f152(x7133,x7134,x7131,x7135),f152(x7133,x7134,x7132,x7135))
% 155.94/155.63 [714]~E(x7141,x7142)+E(f152(x7143,x7144,x7145,x7141),f152(x7143,x7144,x7145,x7142))
% 155.94/155.63 [715]~E(x7151,x7152)+E(f61(x7151,x7153),f61(x7152,x7153))
% 155.94/155.63 [716]~E(x7161,x7162)+E(f61(x7163,x7161),f61(x7163,x7162))
% 155.94/155.63 [717]~E(x7171,x7172)+E(f95(x7171,x7173),f95(x7172,x7173))
% 155.94/155.63 [718]~E(x7181,x7182)+E(f95(x7183,x7181),f95(x7183,x7182))
% 155.94/155.63 [719]~E(x7191,x7192)+E(f484(x7191,x7193),f484(x7192,x7193))
% 155.94/155.63 [720]~E(x7201,x7202)+E(f484(x7203,x7201),f484(x7203,x7202))
% 155.94/155.63 [721]~E(x7211,x7212)+E(f378(x7211,x7213),f378(x7212,x7213))
% 155.94/155.63 [722]~E(x7221,x7222)+E(f378(x7223,x7221),f378(x7223,x7222))
% 155.94/155.63 [723]~E(x7231,x7232)+E(f163(x7231,x7233,x7234),f163(x7232,x7233,x7234))
% 155.94/155.63 [724]~E(x7241,x7242)+E(f163(x7243,x7241,x7244),f163(x7243,x7242,x7244))
% 155.94/155.63 [725]~E(x7251,x7252)+E(f163(x7253,x7254,x7251),f163(x7253,x7254,x7252))
% 155.94/155.63 [726]~E(x7261,x7262)+E(f721(x7261,x7263,x7264,x7265),f721(x7262,x7263,x7264,x7265))
% 155.94/155.63 [727]~E(x7271,x7272)+E(f721(x7273,x7271,x7274,x7275),f721(x7273,x7272,x7274,x7275))
% 155.94/155.63 [728]~E(x7281,x7282)+E(f721(x7283,x7284,x7281,x7285),f721(x7283,x7284,x7282,x7285))
% 155.94/155.63 [729]~E(x7291,x7292)+E(f721(x7293,x7294,x7295,x7291),f721(x7293,x7294,x7295,x7292))
% 155.94/155.63 [730]~E(x7301,x7302)+E(f44(x7301,x7303,x7304,x7305),f44(x7302,x7303,x7304,x7305))
% 155.94/155.63 [731]~E(x7311,x7312)+E(f44(x7313,x7311,x7314,x7315),f44(x7313,x7312,x7314,x7315))
% 155.94/155.63 [732]~E(x7321,x7322)+E(f44(x7323,x7324,x7321,x7325),f44(x7323,x7324,x7322,x7325))
% 155.94/155.63 [733]~E(x7331,x7332)+E(f44(x7333,x7334,x7335,x7331),f44(x7333,x7334,x7335,x7332))
% 155.94/155.63 [734]~E(x7341,x7342)+E(f352(x7341,x7343,x7344,x7345),f352(x7342,x7343,x7344,x7345))
% 155.94/155.63 [735]~E(x7351,x7352)+E(f352(x7353,x7351,x7354,x7355),f352(x7353,x7352,x7354,x7355))
% 155.94/155.63 [736]~E(x7361,x7362)+E(f352(x7363,x7364,x7361,x7365),f352(x7363,x7364,x7362,x7365))
% 155.94/155.63 [737]~E(x7371,x7372)+E(f352(x7373,x7374,x7375,x7371),f352(x7373,x7374,x7375,x7372))
% 155.94/155.63 [738]~E(x7381,x7382)+E(f64(x7381),f64(x7382))
% 155.94/155.63 [739]~E(x7391,x7392)+E(f653(x7391,x7393),f653(x7392,x7393))
% 155.94/155.63 [740]~E(x7401,x7402)+E(f653(x7403,x7401),f653(x7403,x7402))
% 155.94/155.63 [741]~E(x7411,x7412)+E(f220(x7411,x7413,x7414),f220(x7412,x7413,x7414))
% 155.94/155.63 [742]~E(x7421,x7422)+E(f220(x7423,x7421,x7424),f220(x7423,x7422,x7424))
% 155.94/155.63 [743]~E(x7431,x7432)+E(f220(x7433,x7434,x7431),f220(x7433,x7434,x7432))
% 155.94/155.63 [744]~E(x7441,x7442)+E(f455(x7441,x7443),f455(x7442,x7443))
% 155.94/155.63 [745]~E(x7451,x7452)+E(f455(x7453,x7451),f455(x7453,x7452))
% 155.94/155.63 [746]~E(x7461,x7462)+E(f616(x7461,x7463,x7464),f616(x7462,x7463,x7464))
% 155.94/155.63 [747]~E(x7471,x7472)+E(f616(x7473,x7471,x7474),f616(x7473,x7472,x7474))
% 155.94/155.63 [748]~E(x7481,x7482)+E(f616(x7483,x7484,x7481),f616(x7483,x7484,x7482))
% 155.94/155.63 [749]~E(x7491,x7492)+E(f558(x7491,x7493,x7494,x7495),f558(x7492,x7493,x7494,x7495))
% 155.94/155.63 [750]~E(x7501,x7502)+E(f558(x7503,x7501,x7504,x7505),f558(x7503,x7502,x7504,x7505))
% 155.94/155.63 [751]~E(x7511,x7512)+E(f558(x7513,x7514,x7511,x7515),f558(x7513,x7514,x7512,x7515))
% 155.94/155.63 [752]~E(x7521,x7522)+E(f558(x7523,x7524,x7525,x7521),f558(x7523,x7524,x7525,x7522))
% 155.94/155.63 [753]~E(x7531,x7532)+E(f582(x7531,x7533),f582(x7532,x7533))
% 155.94/155.63 [754]~E(x7541,x7542)+E(f582(x7543,x7541),f582(x7543,x7542))
% 155.94/155.63 [755]~E(x7551,x7552)+E(f441(x7551,x7553,x7554),f441(x7552,x7553,x7554))
% 155.94/155.63 [756]~E(x7561,x7562)+E(f441(x7563,x7561,x7564),f441(x7563,x7562,x7564))
% 155.94/155.63 [757]~E(x7571,x7572)+E(f441(x7573,x7574,x7571),f441(x7573,x7574,x7572))
% 155.94/155.63 [758]~E(x7581,x7582)+E(f665(x7581,x7583,x7584,x7585,x7586),f665(x7582,x7583,x7584,x7585,x7586))
% 155.94/155.63 [759]~E(x7591,x7592)+E(f665(x7593,x7591,x7594,x7595,x7596),f665(x7593,x7592,x7594,x7595,x7596))
% 155.94/155.63 [760]~E(x7601,x7602)+E(f665(x7603,x7604,x7601,x7605,x7606),f665(x7603,x7604,x7602,x7605,x7606))
% 155.94/155.63 [761]~E(x7611,x7612)+E(f665(x7613,x7614,x7615,x7611,x7616),f665(x7613,x7614,x7615,x7612,x7616))
% 155.94/155.63 [762]~E(x7621,x7622)+E(f665(x7623,x7624,x7625,x7626,x7621),f665(x7623,x7624,x7625,x7626,x7622))
% 155.94/155.63 [763]~E(x7631,x7632)+E(f358(x7631,x7633,x7634),f358(x7632,x7633,x7634))
% 155.94/155.63 [764]~E(x7641,x7642)+E(f358(x7643,x7641,x7644),f358(x7643,x7642,x7644))
% 155.94/155.63 [765]~E(x7651,x7652)+E(f358(x7653,x7654,x7651),f358(x7653,x7654,x7652))
% 155.94/155.63 [766]~E(x7661,x7662)+E(f578(x7661,x7663,x7664,x7665),f578(x7662,x7663,x7664,x7665))
% 155.94/155.63 [767]~E(x7671,x7672)+E(f578(x7673,x7671,x7674,x7675),f578(x7673,x7672,x7674,x7675))
% 155.94/155.63 [768]~E(x7681,x7682)+E(f578(x7683,x7684,x7681,x7685),f578(x7683,x7684,x7682,x7685))
% 155.94/155.63 [769]~E(x7691,x7692)+E(f578(x7693,x7694,x7695,x7691),f578(x7693,x7694,x7695,x7692))
% 155.94/155.63 [770]~E(x7701,x7702)+E(f38(x7701,x7703,x7704,x7705,x7706,x7707,x7708,x7709,x77010,x77011),f38(x7702,x7703,x7704,x7705,x7706,x7707,x7708,x7709,x77010,x77011))
% 155.94/155.63 [771]~E(x7711,x7712)+E(f38(x7713,x7711,x7714,x7715,x7716,x7717,x7718,x7719,x77110,x77111),f38(x7713,x7712,x7714,x7715,x7716,x7717,x7718,x7719,x77110,x77111))
% 155.94/155.63 [772]~E(x7721,x7722)+E(f38(x7723,x7724,x7721,x7725,x7726,x7727,x7728,x7729,x77210,x77211),f38(x7723,x7724,x7722,x7725,x7726,x7727,x7728,x7729,x77210,x77211))
% 155.94/155.63 [773]~E(x7731,x7732)+E(f38(x7733,x7734,x7735,x7731,x7736,x7737,x7738,x7739,x77310,x77311),f38(x7733,x7734,x7735,x7732,x7736,x7737,x7738,x7739,x77310,x77311))
% 155.94/155.63 [774]~E(x7741,x7742)+E(f38(x7743,x7744,x7745,x7746,x7741,x7747,x7748,x7749,x77410,x77411),f38(x7743,x7744,x7745,x7746,x7742,x7747,x7748,x7749,x77410,x77411))
% 155.94/155.63 [775]~E(x7751,x7752)+E(f38(x7753,x7754,x7755,x7756,x7757,x7751,x7758,x7759,x77510,x77511),f38(x7753,x7754,x7755,x7756,x7757,x7752,x7758,x7759,x77510,x77511))
% 155.94/155.63 [776]~E(x7761,x7762)+E(f38(x7763,x7764,x7765,x7766,x7767,x7768,x7761,x7769,x77610,x77611),f38(x7763,x7764,x7765,x7766,x7767,x7768,x7762,x7769,x77610,x77611))
% 155.94/155.63 [777]~E(x7771,x7772)+E(f38(x7773,x7774,x7775,x7776,x7777,x7778,x7779,x7771,x77710,x77711),f38(x7773,x7774,x7775,x7776,x7777,x7778,x7779,x7772,x77710,x77711))
% 155.94/155.63 [778]~E(x7781,x7782)+E(f38(x7783,x7784,x7785,x7786,x7787,x7788,x7789,x77810,x7781,x77811),f38(x7783,x7784,x7785,x7786,x7787,x7788,x7789,x77810,x7782,x77811))
% 155.94/155.63 [779]~E(x7791,x7792)+E(f38(x7793,x7794,x7795,x7796,x7797,x7798,x7799,x77910,x77911,x7791),f38(x7793,x7794,x7795,x7796,x7797,x7798,x7799,x77910,x77911,x7792))
% 155.94/155.63 [780]~E(x7801,x7802)+E(f595(x7801,x7803,x7804,x7805,x7806),f595(x7802,x7803,x7804,x7805,x7806))
% 155.94/155.63 [781]~E(x7811,x7812)+E(f595(x7813,x7811,x7814,x7815,x7816),f595(x7813,x7812,x7814,x7815,x7816))
% 155.94/155.63 [782]~E(x7821,x7822)+E(f595(x7823,x7824,x7821,x7825,x7826),f595(x7823,x7824,x7822,x7825,x7826))
% 155.94/155.63 [783]~E(x7831,x7832)+E(f595(x7833,x7834,x7835,x7831,x7836),f595(x7833,x7834,x7835,x7832,x7836))
% 155.94/155.63 [784]~E(x7841,x7842)+E(f595(x7843,x7844,x7845,x7846,x7841),f595(x7843,x7844,x7845,x7846,x7842))
% 155.94/155.63 [785]~E(x7851,x7852)+E(f392(x7851,x7853),f392(x7852,x7853))
% 155.94/155.63 [786]~E(x7861,x7862)+E(f392(x7863,x7861),f392(x7863,x7862))
% 155.94/155.63 [787]~E(x7871,x7872)+E(f393(x7871,x7873,x7874),f393(x7872,x7873,x7874))
% 155.94/155.63 [788]~E(x7881,x7882)+E(f393(x7883,x7881,x7884),f393(x7883,x7882,x7884))
% 155.94/155.63 [789]~E(x7891,x7892)+E(f393(x7893,x7894,x7891),f393(x7893,x7894,x7892))
% 155.94/155.63 [790]~E(x7901,x7902)+E(f841(x7901,x7903),f841(x7902,x7903))
% 155.94/155.63 [791]~E(x7911,x7912)+E(f841(x7913,x7911),f841(x7913,x7912))
% 155.94/155.63 [792]~E(x7921,x7922)+E(f413(x7921,x7923,x7924,x7925),f413(x7922,x7923,x7924,x7925))
% 155.94/155.63 [793]~E(x7931,x7932)+E(f413(x7933,x7931,x7934,x7935),f413(x7933,x7932,x7934,x7935))
% 155.94/155.63 [794]~E(x7941,x7942)+E(f413(x7943,x7944,x7941,x7945),f413(x7943,x7944,x7942,x7945))
% 155.94/155.63 [795]~E(x7951,x7952)+E(f413(x7953,x7954,x7955,x7951),f413(x7953,x7954,x7955,x7952))
% 155.94/155.63 [796]~E(x7961,x7962)+E(f448(x7961,x7963,x7964,x7965),f448(x7962,x7963,x7964,x7965))
% 155.94/155.63 [797]~E(x7971,x7972)+E(f448(x7973,x7971,x7974,x7975),f448(x7973,x7972,x7974,x7975))
% 155.94/155.63 [798]~E(x7981,x7982)+E(f448(x7983,x7984,x7981,x7985),f448(x7983,x7984,x7982,x7985))
% 155.94/155.63 [799]~E(x7991,x7992)+E(f448(x7993,x7994,x7995,x7991),f448(x7993,x7994,x7995,x7992))
% 155.94/155.63 [800]~E(x8001,x8002)+E(f209(x8001,x8003,x8004,x8005),f209(x8002,x8003,x8004,x8005))
% 155.94/155.63 [801]~E(x8011,x8012)+E(f209(x8013,x8011,x8014,x8015),f209(x8013,x8012,x8014,x8015))
% 155.94/155.63 [802]~E(x8021,x8022)+E(f209(x8023,x8024,x8021,x8025),f209(x8023,x8024,x8022,x8025))
% 155.94/155.63 [803]~E(x8031,x8032)+E(f209(x8033,x8034,x8035,x8031),f209(x8033,x8034,x8035,x8032))
% 155.94/155.63 [804]~E(x8041,x8042)+E(f819(x8041),f819(x8042))
% 155.94/155.63 [805]~E(x8051,x8052)+E(f278(x8051,x8053,x8054,x8055,x8056),f278(x8052,x8053,x8054,x8055,x8056))
% 155.94/155.63 [806]~E(x8061,x8062)+E(f278(x8063,x8061,x8064,x8065,x8066),f278(x8063,x8062,x8064,x8065,x8066))
% 155.94/155.63 [807]~E(x8071,x8072)+E(f278(x8073,x8074,x8071,x8075,x8076),f278(x8073,x8074,x8072,x8075,x8076))
% 155.94/155.63 [808]~E(x8081,x8082)+E(f278(x8083,x8084,x8085,x8081,x8086),f278(x8083,x8084,x8085,x8082,x8086))
% 155.94/155.63 [809]~E(x8091,x8092)+E(f278(x8093,x8094,x8095,x8096,x8091),f278(x8093,x8094,x8095,x8096,x8092))
% 155.94/155.63 [810]~E(x8101,x8102)+E(f682(x8101,x8103,x8104),f682(x8102,x8103,x8104))
% 155.94/155.63 [811]~E(x8111,x8112)+E(f682(x8113,x8111,x8114),f682(x8113,x8112,x8114))
% 155.94/155.63 [812]~E(x8121,x8122)+E(f682(x8123,x8124,x8121),f682(x8123,x8124,x8122))
% 155.94/155.63 [813]~E(x8131,x8132)+E(f606(x8131,x8133,x8134,x8135),f606(x8132,x8133,x8134,x8135))
% 155.94/155.63 [814]~E(x8141,x8142)+E(f606(x8143,x8141,x8144,x8145),f606(x8143,x8142,x8144,x8145))
% 155.94/155.63 [815]~E(x8151,x8152)+E(f606(x8153,x8154,x8151,x8155),f606(x8153,x8154,x8152,x8155))
% 155.94/155.63 [816]~E(x8161,x8162)+E(f606(x8163,x8164,x8165,x8161),f606(x8163,x8164,x8165,x8162))
% 155.94/155.63 [817]~E(x8171,x8172)+E(f620(x8171,x8173,x8174,x8175,x8176,x8177),f620(x8172,x8173,x8174,x8175,x8176,x8177))
% 155.94/155.63 [818]~E(x8181,x8182)+E(f620(x8183,x8181,x8184,x8185,x8186,x8187),f620(x8183,x8182,x8184,x8185,x8186,x8187))
% 155.94/155.63 [819]~E(x8191,x8192)+E(f620(x8193,x8194,x8191,x8195,x8196,x8197),f620(x8193,x8194,x8192,x8195,x8196,x8197))
% 155.94/155.63 [820]~E(x8201,x8202)+E(f620(x8203,x8204,x8205,x8201,x8206,x8207),f620(x8203,x8204,x8205,x8202,x8206,x8207))
% 155.94/155.63 [821]~E(x8211,x8212)+E(f620(x8213,x8214,x8215,x8216,x8211,x8217),f620(x8213,x8214,x8215,x8216,x8212,x8217))
% 155.94/155.63 [822]~E(x8221,x8222)+E(f620(x8223,x8224,x8225,x8226,x8227,x8221),f620(x8223,x8224,x8225,x8226,x8227,x8222))
% 155.94/155.63 [823]~E(x8231,x8232)+E(f336(x8231,x8233,x8234),f336(x8232,x8233,x8234))
% 155.94/155.63 [824]~E(x8241,x8242)+E(f336(x8243,x8241,x8244),f336(x8243,x8242,x8244))
% 155.94/155.63 [825]~E(x8251,x8252)+E(f336(x8253,x8254,x8251),f336(x8253,x8254,x8252))
% 155.94/155.63 [826]~E(x8261,x8262)+E(f720(x8261,x8263,x8264,x8265),f720(x8262,x8263,x8264,x8265))
% 155.94/155.63 [827]~E(x8271,x8272)+E(f720(x8273,x8271,x8274,x8275),f720(x8273,x8272,x8274,x8275))
% 155.94/155.63 [828]~E(x8281,x8282)+E(f720(x8283,x8284,x8281,x8285),f720(x8283,x8284,x8282,x8285))
% 155.94/155.63 [829]~E(x8291,x8292)+E(f720(x8293,x8294,x8295,x8291),f720(x8293,x8294,x8295,x8292))
% 155.94/155.63 [830]~E(x8301,x8302)+E(f73(x8301,x8303,x8304),f73(x8302,x8303,x8304))
% 155.94/155.63 [831]~E(x8311,x8312)+E(f73(x8313,x8311,x8314),f73(x8313,x8312,x8314))
% 155.94/155.63 [832]~E(x8321,x8322)+E(f73(x8323,x8324,x8321),f73(x8323,x8324,x8322))
% 155.94/155.63 [833]~E(x8331,x8332)+E(f830(x8331,x8333,x8334,x8335),f830(x8332,x8333,x8334,x8335))
% 155.94/155.63 [834]~E(x8341,x8342)+E(f830(x8343,x8341,x8344,x8345),f830(x8343,x8342,x8344,x8345))
% 155.94/155.63 [835]~E(x8351,x8352)+E(f830(x8353,x8354,x8351,x8355),f830(x8353,x8354,x8352,x8355))
% 155.94/155.63 [836]~E(x8361,x8362)+E(f830(x8363,x8364,x8365,x8361),f830(x8363,x8364,x8365,x8362))
% 155.94/155.63 [837]~E(x8371,x8372)+E(f398(x8371,x8373,x8374),f398(x8372,x8373,x8374))
% 155.94/155.63 [838]~E(x8381,x8382)+E(f398(x8383,x8381,x8384),f398(x8383,x8382,x8384))
% 155.94/155.63 [839]~E(x8391,x8392)+E(f398(x8393,x8394,x8391),f398(x8393,x8394,x8392))
% 155.94/155.63 [840]~E(x8401,x8402)+E(f123(x8401),f123(x8402))
% 155.94/155.63 [841]~E(x8411,x8412)+E(f176(x8411),f176(x8412))
% 155.94/155.63 [842]~E(x8421,x8422)+E(f817(x8421,x8423),f817(x8422,x8423))
% 155.94/155.63 [843]~E(x8431,x8432)+E(f817(x8433,x8431),f817(x8433,x8432))
% 155.94/155.63 [844]~E(x8441,x8442)+E(f506(x8441,x8443,x8444,x8445),f506(x8442,x8443,x8444,x8445))
% 155.94/155.63 [845]~E(x8451,x8452)+E(f506(x8453,x8451,x8454,x8455),f506(x8453,x8452,x8454,x8455))
% 155.94/155.63 [846]~E(x8461,x8462)+E(f506(x8463,x8464,x8461,x8465),f506(x8463,x8464,x8462,x8465))
% 155.94/155.63 [847]~E(x8471,x8472)+E(f506(x8473,x8474,x8475,x8471),f506(x8473,x8474,x8475,x8472))
% 155.94/155.63 [848]~E(x8481,x8482)+E(f395(x8481,x8483,x8484),f395(x8482,x8483,x8484))
% 155.94/155.63 [849]~E(x8491,x8492)+E(f395(x8493,x8491,x8494),f395(x8493,x8492,x8494))
% 155.94/155.63 [850]~E(x8501,x8502)+E(f395(x8503,x8504,x8501),f395(x8503,x8504,x8502))
% 155.94/155.63 [851]~E(x8511,x8512)+E(f74(x8511,x8513,x8514),f74(x8512,x8513,x8514))
% 155.94/155.63 [852]~E(x8521,x8522)+E(f74(x8523,x8521,x8524),f74(x8523,x8522,x8524))
% 155.94/155.63 [853]~E(x8531,x8532)+E(f74(x8533,x8534,x8531),f74(x8533,x8534,x8532))
% 155.94/155.63 [854]~E(x8541,x8542)+E(f791(x8541,x8543,x8544),f791(x8542,x8543,x8544))
% 155.94/155.63 [855]~E(x8551,x8552)+E(f791(x8553,x8551,x8554),f791(x8553,x8552,x8554))
% 155.94/155.63 [856]~E(x8561,x8562)+E(f791(x8563,x8564,x8561),f791(x8563,x8564,x8562))
% 155.94/155.63 [857]~E(x8571,x8572)+E(f622(x8571,x8573,x8574,x8575,x8576),f622(x8572,x8573,x8574,x8575,x8576))
% 155.94/155.63 [858]~E(x8581,x8582)+E(f622(x8583,x8581,x8584,x8585,x8586),f622(x8583,x8582,x8584,x8585,x8586))
% 155.94/155.63 [859]~E(x8591,x8592)+E(f622(x8593,x8594,x8591,x8595,x8596),f622(x8593,x8594,x8592,x8595,x8596))
% 155.94/155.63 [860]~E(x8601,x8602)+E(f622(x8603,x8604,x8605,x8601,x8606),f622(x8603,x8604,x8605,x8602,x8606))
% 155.94/155.63 [861]~E(x8611,x8612)+E(f622(x8613,x8614,x8615,x8616,x8611),f622(x8613,x8614,x8615,x8616,x8612))
% 155.94/155.63 [862]~E(x8621,x8622)+E(f594(x8621,x8623,x8624,x8625,x8626),f594(x8622,x8623,x8624,x8625,x8626))
% 155.94/155.63 [863]~E(x8631,x8632)+E(f594(x8633,x8631,x8634,x8635,x8636),f594(x8633,x8632,x8634,x8635,x8636))
% 155.94/155.63 [864]~E(x8641,x8642)+E(f594(x8643,x8644,x8641,x8645,x8646),f594(x8643,x8644,x8642,x8645,x8646))
% 155.94/155.63 [865]~E(x8651,x8652)+E(f594(x8653,x8654,x8655,x8651,x8656),f594(x8653,x8654,x8655,x8652,x8656))
% 155.94/155.63 [866]~E(x8661,x8662)+E(f594(x8663,x8664,x8665,x8666,x8661),f594(x8663,x8664,x8665,x8666,x8662))
% 155.94/155.63 [867]~E(x8671,x8672)+E(f571(x8671,x8673,x8674,x8675),f571(x8672,x8673,x8674,x8675))
% 155.94/155.63 [868]~E(x8681,x8682)+E(f571(x8683,x8681,x8684,x8685),f571(x8683,x8682,x8684,x8685))
% 155.94/155.63 [869]~E(x8691,x8692)+E(f571(x8693,x8694,x8691,x8695),f571(x8693,x8694,x8692,x8695))
% 155.94/155.63 [870]~E(x8701,x8702)+E(f571(x8703,x8704,x8705,x8701),f571(x8703,x8704,x8705,x8702))
% 155.94/155.63 [871]~E(x8711,x8712)+E(f419(x8711,x8713,x8714),f419(x8712,x8713,x8714))
% 155.94/155.63 [872]~E(x8721,x8722)+E(f419(x8723,x8721,x8724),f419(x8723,x8722,x8724))
% 155.94/155.63 [873]~E(x8731,x8732)+E(f419(x8733,x8734,x8731),f419(x8733,x8734,x8732))
% 155.94/155.63 [874]~E(x8741,x8742)+E(f62(x8741,x8743),f62(x8742,x8743))
% 155.94/155.63 [875]~E(x8751,x8752)+E(f62(x8753,x8751),f62(x8753,x8752))
% 155.94/155.63 [876]~E(x8761,x8762)+E(f207(x8761,x8763),f207(x8762,x8763))
% 155.94/155.63 [877]~E(x8771,x8772)+E(f207(x8773,x8771),f207(x8773,x8772))
% 155.94/155.63 [878]~E(x8781,x8782)+E(f610(x8781,x8783,x8784,x8785),f610(x8782,x8783,x8784,x8785))
% 155.94/155.63 [879]~E(x8791,x8792)+E(f610(x8793,x8791,x8794,x8795),f610(x8793,x8792,x8794,x8795))
% 155.94/155.63 [880]~E(x8801,x8802)+E(f610(x8803,x8804,x8801,x8805),f610(x8803,x8804,x8802,x8805))
% 155.94/155.63 [881]~E(x8811,x8812)+E(f610(x8813,x8814,x8815,x8811),f610(x8813,x8814,x8815,x8812))
% 155.94/155.63 [882]~E(x8821,x8822)+E(f15(x8821,x8823),f15(x8822,x8823))
% 155.94/155.63 [883]~E(x8831,x8832)+E(f15(x8833,x8831),f15(x8833,x8832))
% 155.94/155.63 [884]~E(x8841,x8842)+E(f803(x8841,x8843,x8844,x8845),f803(x8842,x8843,x8844,x8845))
% 155.94/155.63 [885]~E(x8851,x8852)+E(f803(x8853,x8851,x8854,x8855),f803(x8853,x8852,x8854,x8855))
% 155.94/155.63 [886]~E(x8861,x8862)+E(f803(x8863,x8864,x8861,x8865),f803(x8863,x8864,x8862,x8865))
% 155.94/155.63 [887]~E(x8871,x8872)+E(f803(x8873,x8874,x8875,x8871),f803(x8873,x8874,x8875,x8872))
% 155.94/155.63 [888]~E(x8881,x8882)+E(f529(x8881,x8883,x8884,x8885,x8886,x8887),f529(x8882,x8883,x8884,x8885,x8886,x8887))
% 155.94/155.63 [889]~E(x8891,x8892)+E(f529(x8893,x8891,x8894,x8895,x8896,x8897),f529(x8893,x8892,x8894,x8895,x8896,x8897))
% 155.94/155.63 [890]~E(x8901,x8902)+E(f529(x8903,x8904,x8901,x8905,x8906,x8907),f529(x8903,x8904,x8902,x8905,x8906,x8907))
% 155.94/155.63 [891]~E(x8911,x8912)+E(f529(x8913,x8914,x8915,x8911,x8916,x8917),f529(x8913,x8914,x8915,x8912,x8916,x8917))
% 155.94/155.63 [892]~E(x8921,x8922)+E(f529(x8923,x8924,x8925,x8926,x8921,x8927),f529(x8923,x8924,x8925,x8926,x8922,x8927))
% 155.94/155.63 [893]~E(x8931,x8932)+E(f529(x8933,x8934,x8935,x8936,x8937,x8931),f529(x8933,x8934,x8935,x8936,x8937,x8932))
% 155.94/155.63 [894]~E(x8941,x8942)+E(f512(x8941,x8943,x8944,x8945,x8946),f512(x8942,x8943,x8944,x8945,x8946))
% 155.94/155.63 [895]~E(x8951,x8952)+E(f512(x8953,x8951,x8954,x8955,x8956),f512(x8953,x8952,x8954,x8955,x8956))
% 155.94/155.63 [896]~E(x8961,x8962)+E(f512(x8963,x8964,x8961,x8965,x8966),f512(x8963,x8964,x8962,x8965,x8966))
% 155.94/155.63 [897]~E(x8971,x8972)+E(f512(x8973,x8974,x8975,x8971,x8976),f512(x8973,x8974,x8975,x8972,x8976))
% 155.94/155.63 [898]~E(x8981,x8982)+E(f512(x8983,x8984,x8985,x8986,x8981),f512(x8983,x8984,x8985,x8986,x8982))
% 155.94/155.63 [899]~E(x8991,x8992)+E(f137(x8991),f137(x8992))
% 155.94/155.63 [900]~E(x9001,x9002)+E(f259(x9001,x9003,x9004,x9005),f259(x9002,x9003,x9004,x9005))
% 155.94/155.63 [901]~E(x9011,x9012)+E(f259(x9013,x9011,x9014,x9015),f259(x9013,x9012,x9014,x9015))
% 155.94/155.63 [902]~E(x9021,x9022)+E(f259(x9023,x9024,x9021,x9025),f259(x9023,x9024,x9022,x9025))
% 155.94/155.63 [903]~E(x9031,x9032)+E(f259(x9033,x9034,x9035,x9031),f259(x9033,x9034,x9035,x9032))
% 155.94/155.63 [904]~E(x9041,x9042)+E(f197(x9041,x9043),f197(x9042,x9043))
% 155.94/155.63 [905]~E(x9051,x9052)+E(f197(x9053,x9051),f197(x9053,x9052))
% 155.94/155.63 [906]~E(x9061,x9062)+E(f652(x9061,x9063),f652(x9062,x9063))
% 155.94/155.63 [907]~E(x9071,x9072)+E(f652(x9073,x9071),f652(x9073,x9072))
% 155.94/155.63 [908]~E(x9081,x9082)+E(f85(x9081,x9083,x9084,x9085,x9086),f85(x9082,x9083,x9084,x9085,x9086))
% 155.94/155.63 [909]~E(x9091,x9092)+E(f85(x9093,x9091,x9094,x9095,x9096),f85(x9093,x9092,x9094,x9095,x9096))
% 155.94/155.63 [910]~E(x9101,x9102)+E(f85(x9103,x9104,x9101,x9105,x9106),f85(x9103,x9104,x9102,x9105,x9106))
% 155.94/155.63 [911]~E(x9111,x9112)+E(f85(x9113,x9114,x9115,x9111,x9116),f85(x9113,x9114,x9115,x9112,x9116))
% 155.94/155.63 [912]~E(x9121,x9122)+E(f85(x9123,x9124,x9125,x9126,x9121),f85(x9123,x9124,x9125,x9126,x9122))
% 155.94/155.63 [913]~E(x9131,x9132)+E(f404(x9131,x9133,x9134,x9135,x9136),f404(x9132,x9133,x9134,x9135,x9136))
% 155.94/155.63 [914]~E(x9141,x9142)+E(f404(x9143,x9141,x9144,x9145,x9146),f404(x9143,x9142,x9144,x9145,x9146))
% 155.94/155.63 [915]~E(x9151,x9152)+E(f404(x9153,x9154,x9151,x9155,x9156),f404(x9153,x9154,x9152,x9155,x9156))
% 155.94/155.63 [916]~E(x9161,x9162)+E(f404(x9163,x9164,x9165,x9161,x9166),f404(x9163,x9164,x9165,x9162,x9166))
% 155.94/155.63 [917]~E(x9171,x9172)+E(f404(x9173,x9174,x9175,x9176,x9171),f404(x9173,x9174,x9175,x9176,x9172))
% 155.94/155.63 [918]~E(x9181,x9182)+E(f778(x9181,x9183,x9184,x9185,x9186),f778(x9182,x9183,x9184,x9185,x9186))
% 155.94/155.63 [919]~E(x9191,x9192)+E(f778(x9193,x9191,x9194,x9195,x9196),f778(x9193,x9192,x9194,x9195,x9196))
% 155.94/155.63 [920]~E(x9201,x9202)+E(f778(x9203,x9204,x9201,x9205,x9206),f778(x9203,x9204,x9202,x9205,x9206))
% 155.94/155.63 [921]~E(x9211,x9212)+E(f778(x9213,x9214,x9215,x9211,x9216),f778(x9213,x9214,x9215,x9212,x9216))
% 155.94/155.63 [922]~E(x9221,x9222)+E(f778(x9223,x9224,x9225,x9226,x9221),f778(x9223,x9224,x9225,x9226,x9222))
% 155.94/155.63 [923]~E(x9231,x9232)+E(f347(x9231,x9233,x9234),f347(x9232,x9233,x9234))
% 155.94/155.63 [924]~E(x9241,x9242)+E(f347(x9243,x9241,x9244),f347(x9243,x9242,x9244))
% 155.94/155.63 [925]~E(x9251,x9252)+E(f347(x9253,x9254,x9251),f347(x9253,x9254,x9252))
% 155.94/155.63 [926]~E(x9261,x9262)+E(f784(x9261,x9263,x9264),f784(x9262,x9263,x9264))
% 155.94/155.63 [927]~E(x9271,x9272)+E(f784(x9273,x9271,x9274),f784(x9273,x9272,x9274))
% 155.94/155.63 [928]~E(x9281,x9282)+E(f784(x9283,x9284,x9281),f784(x9283,x9284,x9282))
% 155.94/155.63 [929]~E(x9291,x9292)+E(f613(x9291,x9293,x9294,x9295,x9296),f613(x9292,x9293,x9294,x9295,x9296))
% 155.94/155.63 [930]~E(x9301,x9302)+E(f613(x9303,x9301,x9304,x9305,x9306),f613(x9303,x9302,x9304,x9305,x9306))
% 155.94/155.63 [931]~E(x9311,x9312)+E(f613(x9313,x9314,x9311,x9315,x9316),f613(x9313,x9314,x9312,x9315,x9316))
% 155.94/155.63 [932]~E(x9321,x9322)+E(f613(x9323,x9324,x9325,x9321,x9326),f613(x9323,x9324,x9325,x9322,x9326))
% 155.94/155.63 [933]~E(x9331,x9332)+E(f613(x9333,x9334,x9335,x9336,x9331),f613(x9333,x9334,x9335,x9336,x9332))
% 155.94/155.63 [934]~E(x9341,x9342)+E(f295(x9341,x9343,x9344),f295(x9342,x9343,x9344))
% 155.94/155.63 [935]~E(x9351,x9352)+E(f295(x9353,x9351,x9354),f295(x9353,x9352,x9354))
% 155.94/155.63 [936]~E(x9361,x9362)+E(f295(x9363,x9364,x9361),f295(x9363,x9364,x9362))
% 155.94/155.63 [937]~E(x9371,x9372)+E(f252(x9371,x9373,x9374,x9375,x9376),f252(x9372,x9373,x9374,x9375,x9376))
% 155.94/155.63 [938]~E(x9381,x9382)+E(f252(x9383,x9381,x9384,x9385,x9386),f252(x9383,x9382,x9384,x9385,x9386))
% 155.94/155.63 [939]~E(x9391,x9392)+E(f252(x9393,x9394,x9391,x9395,x9396),f252(x9393,x9394,x9392,x9395,x9396))
% 155.94/155.63 [940]~E(x9401,x9402)+E(f252(x9403,x9404,x9405,x9401,x9406),f252(x9403,x9404,x9405,x9402,x9406))
% 155.94/155.63 [941]~E(x9411,x9412)+E(f252(x9413,x9414,x9415,x9416,x9411),f252(x9413,x9414,x9415,x9416,x9412))
% 155.94/155.63 [942]~E(x9421,x9422)+E(f773(x9421,x9423,x9424,x9425,x9426),f773(x9422,x9423,x9424,x9425,x9426))
% 155.94/155.63 [943]~E(x9431,x9432)+E(f773(x9433,x9431,x9434,x9435,x9436),f773(x9433,x9432,x9434,x9435,x9436))
% 155.94/155.63 [944]~E(x9441,x9442)+E(f773(x9443,x9444,x9441,x9445,x9446),f773(x9443,x9444,x9442,x9445,x9446))
% 155.94/155.63 [945]~E(x9451,x9452)+E(f773(x9453,x9454,x9455,x9451,x9456),f773(x9453,x9454,x9455,x9452,x9456))
% 155.94/155.63 [946]~E(x9461,x9462)+E(f773(x9463,x9464,x9465,x9466,x9461),f773(x9463,x9464,x9465,x9466,x9462))
% 155.94/155.63 [947]~E(x9471,x9472)+E(f768(x9471,x9473,x9474,x9475,x9476),f768(x9472,x9473,x9474,x9475,x9476))
% 155.94/155.63 [948]~E(x9481,x9482)+E(f768(x9483,x9481,x9484,x9485,x9486),f768(x9483,x9482,x9484,x9485,x9486))
% 155.94/155.63 [949]~E(x9491,x9492)+E(f768(x9493,x9494,x9491,x9495,x9496),f768(x9493,x9494,x9492,x9495,x9496))
% 155.94/155.63 [950]~E(x9501,x9502)+E(f768(x9503,x9504,x9505,x9501,x9506),f768(x9503,x9504,x9505,x9502,x9506))
% 155.94/155.63 [951]~E(x9511,x9512)+E(f768(x9513,x9514,x9515,x9516,x9511),f768(x9513,x9514,x9515,x9516,x9512))
% 155.94/155.63 [952]~E(x9521,x9522)+E(f477(x9521,x9523,x9524,x9525,x9526),f477(x9522,x9523,x9524,x9525,x9526))
% 155.94/155.63 [953]~E(x9531,x9532)+E(f477(x9533,x9531,x9534,x9535,x9536),f477(x9533,x9532,x9534,x9535,x9536))
% 155.94/155.63 [954]~E(x9541,x9542)+E(f477(x9543,x9544,x9541,x9545,x9546),f477(x9543,x9544,x9542,x9545,x9546))
% 155.94/155.63 [955]~E(x9551,x9552)+E(f477(x9553,x9554,x9555,x9551,x9556),f477(x9553,x9554,x9555,x9552,x9556))
% 155.94/155.63 [956]~E(x9561,x9562)+E(f477(x9563,x9564,x9565,x9566,x9561),f477(x9563,x9564,x9565,x9566,x9562))
% 155.94/155.63 [957]~E(x9571,x9572)+E(f827(x9571,x9573,x9574),f827(x9572,x9573,x9574))
% 155.94/155.63 [958]~E(x9581,x9582)+E(f827(x9583,x9581,x9584),f827(x9583,x9582,x9584))
% 155.94/155.63 [959]~E(x9591,x9592)+E(f827(x9593,x9594,x9591),f827(x9593,x9594,x9592))
% 155.94/155.63 [960]~E(x9601,x9602)+E(f324(x9601,x9603,x9604,x9605),f324(x9602,x9603,x9604,x9605))
% 155.94/155.63 [961]~E(x9611,x9612)+E(f324(x9613,x9611,x9614,x9615),f324(x9613,x9612,x9614,x9615))
% 155.94/155.63 [962]~E(x9621,x9622)+E(f324(x9623,x9624,x9621,x9625),f324(x9623,x9624,x9622,x9625))
% 155.94/155.63 [963]~E(x9631,x9632)+E(f324(x9633,x9634,x9635,x9631),f324(x9633,x9634,x9635,x9632))
% 155.94/155.63 [964]~E(x9641,x9642)+E(f435(x9641,x9643,x9644),f435(x9642,x9643,x9644))
% 155.94/155.63 [965]~E(x9651,x9652)+E(f435(x9653,x9651,x9654),f435(x9653,x9652,x9654))
% 155.94/155.63 [966]~E(x9661,x9662)+E(f435(x9663,x9664,x9661),f435(x9663,x9664,x9662))
% 155.94/155.63 [967]~E(x9671,x9672)+E(f391(x9671,x9673),f391(x9672,x9673))
% 155.94/155.63 [968]~E(x9681,x9682)+E(f391(x9683,x9681),f391(x9683,x9682))
% 155.94/155.63 [969]~E(x9691,x9692)+E(f688(x9691,x9693),f688(x9692,x9693))
% 155.94/155.63 [970]~E(x9701,x9702)+E(f688(x9703,x9701),f688(x9703,x9702))
% 155.94/155.63 [971]~E(x9711,x9712)+E(f619(x9711,x9713,x9714),f619(x9712,x9713,x9714))
% 155.94/155.63 [972]~E(x9721,x9722)+E(f619(x9723,x9721,x9724),f619(x9723,x9722,x9724))
% 155.94/155.63 [973]~E(x9731,x9732)+E(f619(x9733,x9734,x9731),f619(x9733,x9734,x9732))
% 155.94/155.63 [974]~E(x9741,x9742)+E(f371(x9741,x9743),f371(x9742,x9743))
% 155.94/155.63 [975]~E(x9751,x9752)+E(f371(x9753,x9751),f371(x9753,x9752))
% 155.94/155.63 [976]~E(x9761,x9762)+E(f381(x9761,x9763),f381(x9762,x9763))
% 155.94/155.63 [977]~E(x9771,x9772)+E(f381(x9773,x9771),f381(x9773,x9772))
% 155.94/155.63 [978]~E(x9781,x9782)+E(f588(x9781,x9783,x9784),f588(x9782,x9783,x9784))
% 155.94/155.63 [979]~E(x9791,x9792)+E(f588(x9793,x9791,x9794),f588(x9793,x9792,x9794))
% 155.94/155.63 [980]~E(x9801,x9802)+E(f588(x9803,x9804,x9801),f588(x9803,x9804,x9802))
% 155.94/155.63 [981]~E(x9811,x9812)+E(f255(x9811),f255(x9812))
% 155.94/155.63 [982]~E(x9821,x9822)+E(f574(x9821,x9823,x9824,x9825),f574(x9822,x9823,x9824,x9825))
% 155.94/155.63 [983]~E(x9831,x9832)+E(f574(x9833,x9831,x9834,x9835),f574(x9833,x9832,x9834,x9835))
% 155.94/155.63 [984]~E(x9841,x9842)+E(f574(x9843,x9844,x9841,x9845),f574(x9843,x9844,x9842,x9845))
% 155.94/155.63 [985]~E(x9851,x9852)+E(f574(x9853,x9854,x9855,x9851),f574(x9853,x9854,x9855,x9852))
% 155.94/155.63 [986]~E(x9861,x9862)+E(f299(x9861,x9863,x9864,x9865,x9866),f299(x9862,x9863,x9864,x9865,x9866))
% 155.94/155.63 [987]~E(x9871,x9872)+E(f299(x9873,x9871,x9874,x9875,x9876),f299(x9873,x9872,x9874,x9875,x9876))
% 155.94/155.63 [988]~E(x9881,x9882)+E(f299(x9883,x9884,x9881,x9885,x9886),f299(x9883,x9884,x9882,x9885,x9886))
% 155.94/155.63 [989]~E(x9891,x9892)+E(f299(x9893,x9894,x9895,x9891,x9896),f299(x9893,x9894,x9895,x9892,x9896))
% 155.94/155.63 [990]~E(x9901,x9902)+E(f299(x9903,x9904,x9905,x9906,x9901),f299(x9903,x9904,x9905,x9906,x9902))
% 155.94/155.63 [991]~E(x9911,x9912)+E(f763(x9911,x9913,x9914,x9915),f763(x9912,x9913,x9914,x9915))
% 155.94/155.63 [992]~E(x9921,x9922)+E(f763(x9923,x9921,x9924,x9925),f763(x9923,x9922,x9924,x9925))
% 155.94/155.63 [993]~E(x9931,x9932)+E(f763(x9933,x9934,x9931,x9935),f763(x9933,x9934,x9932,x9935))
% 155.94/155.63 [994]~E(x9941,x9942)+E(f763(x9943,x9944,x9945,x9941),f763(x9943,x9944,x9945,x9942))
% 155.94/155.63 [995]~E(x9951,x9952)+E(f185(x9951,x9953,x9954),f185(x9952,x9953,x9954))
% 155.94/155.63 [996]~E(x9961,x9962)+E(f185(x9963,x9961,x9964),f185(x9963,x9962,x9964))
% 155.94/155.63 [997]~E(x9971,x9972)+E(f185(x9973,x9974,x9971),f185(x9973,x9974,x9972))
% 155.94/155.63 [998]~E(x9981,x9982)+E(f97(x9981),f97(x9982))
% 155.94/155.63 [999]~E(x9991,x9992)+E(f335(x9991,x9993,x9994),f335(x9992,x9993,x9994))
% 155.94/155.63 [1000]~E(x10001,x10002)+E(f335(x10003,x10001,x10004),f335(x10003,x10002,x10004))
% 155.94/155.63 [1001]~E(x10011,x10012)+E(f335(x10013,x10014,x10011),f335(x10013,x10014,x10012))
% 155.94/155.63 [1002]~E(x10021,x10022)+E(f809(x10021,x10023,x10024,x10025),f809(x10022,x10023,x10024,x10025))
% 155.94/155.63 [1003]~E(x10031,x10032)+E(f809(x10033,x10031,x10034,x10035),f809(x10033,x10032,x10034,x10035))
% 155.94/155.63 [1004]~E(x10041,x10042)+E(f809(x10043,x10044,x10041,x10045),f809(x10043,x10044,x10042,x10045))
% 155.94/155.63 [1005]~E(x10051,x10052)+E(f809(x10053,x10054,x10055,x10051),f809(x10053,x10054,x10055,x10052))
% 155.94/155.63 [1006]~E(x10061,x10062)+E(f103(x10061,x10063,x10064),f103(x10062,x10063,x10064))
% 155.94/155.63 [1007]~E(x10071,x10072)+E(f103(x10073,x10071,x10074),f103(x10073,x10072,x10074))
% 155.94/155.63 [1008]~E(x10081,x10082)+E(f103(x10083,x10084,x10081),f103(x10083,x10084,x10082))
% 155.94/155.63 [1009]~E(x10091,x10092)+E(f490(x10091,x10093,x10094,x10095),f490(x10092,x10093,x10094,x10095))
% 155.94/155.63 [1010]~E(x10101,x10102)+E(f490(x10103,x10101,x10104,x10105),f490(x10103,x10102,x10104,x10105))
% 155.94/155.63 [1011]~E(x10111,x10112)+E(f490(x10113,x10114,x10111,x10115),f490(x10113,x10114,x10112,x10115))
% 155.94/155.63 [1012]~E(x10121,x10122)+E(f490(x10123,x10124,x10125,x10121),f490(x10123,x10124,x10125,x10122))
% 155.94/155.63 [1013]~E(x10131,x10132)+E(f243(x10131,x10133),f243(x10132,x10133))
% 155.94/155.63 [1014]~E(x10141,x10142)+E(f243(x10143,x10141),f243(x10143,x10142))
% 155.94/155.63 [1015]~E(x10151,x10152)+E(f382(x10151,x10153),f382(x10152,x10153))
% 155.94/155.63 [1016]~E(x10161,x10162)+E(f382(x10163,x10161),f382(x10163,x10162))
% 155.94/155.63 [1017]~E(x10171,x10172)+E(f801(x10171,x10173,x10174,x10175,x10176,x10177,x10178),f801(x10172,x10173,x10174,x10175,x10176,x10177,x10178))
% 155.94/155.63 [1018]~E(x10181,x10182)+E(f801(x10183,x10181,x10184,x10185,x10186,x10187,x10188),f801(x10183,x10182,x10184,x10185,x10186,x10187,x10188))
% 155.94/155.63 [1019]~E(x10191,x10192)+E(f801(x10193,x10194,x10191,x10195,x10196,x10197,x10198),f801(x10193,x10194,x10192,x10195,x10196,x10197,x10198))
% 155.94/155.63 [1020]~E(x10201,x10202)+E(f801(x10203,x10204,x10205,x10201,x10206,x10207,x10208),f801(x10203,x10204,x10205,x10202,x10206,x10207,x10208))
% 155.94/155.63 [1021]~E(x10211,x10212)+E(f801(x10213,x10214,x10215,x10216,x10211,x10217,x10218),f801(x10213,x10214,x10215,x10216,x10212,x10217,x10218))
% 155.94/155.63 [1022]~E(x10221,x10222)+E(f801(x10223,x10224,x10225,x10226,x10227,x10221,x10228),f801(x10223,x10224,x10225,x10226,x10227,x10222,x10228))
% 155.94/155.63 [1023]~E(x10231,x10232)+E(f801(x10233,x10234,x10235,x10236,x10237,x10238,x10231),f801(x10233,x10234,x10235,x10236,x10237,x10238,x10232))
% 155.94/155.63 [1024]~E(x10241,x10242)+E(f733(x10241,x10243,x10244,x10245,x10246,x10247),f733(x10242,x10243,x10244,x10245,x10246,x10247))
% 155.94/155.63 [1025]~E(x10251,x10252)+E(f733(x10253,x10251,x10254,x10255,x10256,x10257),f733(x10253,x10252,x10254,x10255,x10256,x10257))
% 155.94/155.63 [1026]~E(x10261,x10262)+E(f733(x10263,x10264,x10261,x10265,x10266,x10267),f733(x10263,x10264,x10262,x10265,x10266,x10267))
% 155.94/155.63 [1027]~E(x10271,x10272)+E(f733(x10273,x10274,x10275,x10271,x10276,x10277),f733(x10273,x10274,x10275,x10272,x10276,x10277))
% 155.94/155.63 [1028]~E(x10281,x10282)+E(f733(x10283,x10284,x10285,x10286,x10281,x10287),f733(x10283,x10284,x10285,x10286,x10282,x10287))
% 155.94/155.63 [1029]~E(x10291,x10292)+E(f733(x10293,x10294,x10295,x10296,x10297,x10291),f733(x10293,x10294,x10295,x10296,x10297,x10292))
% 155.94/155.63 [1030]~E(x10301,x10302)+E(f256(x10301,x10303),f256(x10302,x10303))
% 155.94/155.63 [1031]~E(x10311,x10312)+E(f256(x10313,x10311),f256(x10313,x10312))
% 155.94/155.63 [1032]~E(x10321,x10322)+E(f304(x10321,x10323,x10324,x10325),f304(x10322,x10323,x10324,x10325))
% 155.94/155.63 [1033]~E(x10331,x10332)+E(f304(x10333,x10331,x10334,x10335),f304(x10333,x10332,x10334,x10335))
% 155.94/155.63 [1034]~E(x10341,x10342)+E(f304(x10343,x10344,x10341,x10345),f304(x10343,x10344,x10342,x10345))
% 155.94/155.63 [1035]~E(x10351,x10352)+E(f304(x10353,x10354,x10355,x10351),f304(x10353,x10354,x10355,x10352))
% 155.94/155.63 [1036]~E(x10361,x10362)+E(f501(x10361,x10363,x10364,x10365,x10366),f501(x10362,x10363,x10364,x10365,x10366))
% 155.94/155.63 [1037]~E(x10371,x10372)+E(f501(x10373,x10371,x10374,x10375,x10376),f501(x10373,x10372,x10374,x10375,x10376))
% 155.94/155.64 [1038]~E(x10381,x10382)+E(f501(x10383,x10384,x10381,x10385,x10386),f501(x10383,x10384,x10382,x10385,x10386))
% 155.94/155.64 [1039]~E(x10391,x10392)+E(f501(x10393,x10394,x10395,x10391,x10396),f501(x10393,x10394,x10395,x10392,x10396))
% 155.94/155.64 [1040]~E(x10401,x10402)+E(f501(x10403,x10404,x10405,x10406,x10401),f501(x10403,x10404,x10405,x10406,x10402))
% 155.94/155.64 [1041]~E(x10411,x10412)+E(f738(x10411,x10413,x10414),f738(x10412,x10413,x10414))
% 155.94/155.64 [1042]~E(x10421,x10422)+E(f738(x10423,x10421,x10424),f738(x10423,x10422,x10424))
% 155.94/155.64 [1043]~E(x10431,x10432)+E(f738(x10433,x10434,x10431),f738(x10433,x10434,x10432))
% 155.94/155.64 [1044]~E(x10441,x10442)+E(f396(x10441,x10443,x10444,x10445),f396(x10442,x10443,x10444,x10445))
% 155.94/155.64 [1045]~E(x10451,x10452)+E(f396(x10453,x10451,x10454,x10455),f396(x10453,x10452,x10454,x10455))
% 155.94/155.64 [1046]~E(x10461,x10462)+E(f396(x10463,x10464,x10461,x10465),f396(x10463,x10464,x10462,x10465))
% 155.94/155.64 [1047]~E(x10471,x10472)+E(f396(x10473,x10474,x10475,x10471),f396(x10473,x10474,x10475,x10472))
% 155.94/155.64 [1048]~E(x10481,x10482)+E(f342(x10481,x10483),f342(x10482,x10483))
% 155.94/155.64 [1049]~E(x10491,x10492)+E(f342(x10493,x10491),f342(x10493,x10492))
% 155.94/155.64 [1050]~E(x10501,x10502)+E(f740(x10501,x10503,x10504,x10505,x10506),f740(x10502,x10503,x10504,x10505,x10506))
% 155.94/155.64 [1051]~E(x10511,x10512)+E(f740(x10513,x10511,x10514,x10515,x10516),f740(x10513,x10512,x10514,x10515,x10516))
% 155.94/155.64 [1052]~E(x10521,x10522)+E(f740(x10523,x10524,x10521,x10525,x10526),f740(x10523,x10524,x10522,x10525,x10526))
% 155.94/155.64 [1053]~E(x10531,x10532)+E(f740(x10533,x10534,x10535,x10531,x10536),f740(x10533,x10534,x10535,x10532,x10536))
% 155.94/155.64 [1054]~E(x10541,x10542)+E(f740(x10543,x10544,x10545,x10546,x10541),f740(x10543,x10544,x10545,x10546,x10542))
% 155.94/155.64 [1055]~E(x10551,x10552)+E(f818(x10551,x10553),f818(x10552,x10553))
% 155.94/155.64 [1056]~E(x10561,x10562)+E(f818(x10563,x10561),f818(x10563,x10562))
% 155.94/155.64 [1057]~E(x10571,x10572)+E(f751(x10571,x10573,x10574,x10575),f751(x10572,x10573,x10574,x10575))
% 155.94/155.64 [1058]~E(x10581,x10582)+E(f751(x10583,x10581,x10584,x10585),f751(x10583,x10582,x10584,x10585))
% 155.94/155.64 [1059]~E(x10591,x10592)+E(f751(x10593,x10594,x10591,x10595),f751(x10593,x10594,x10592,x10595))
% 155.94/155.64 [1060]~E(x10601,x10602)+E(f751(x10603,x10604,x10605,x10601),f751(x10603,x10604,x10605,x10602))
% 155.94/155.64 [1061]~E(x10611,x10612)+E(f549(x10611,x10613,x10614,x10615,x10616),f549(x10612,x10613,x10614,x10615,x10616))
% 155.94/155.64 [1062]~E(x10621,x10622)+E(f549(x10623,x10621,x10624,x10625,x10626),f549(x10623,x10622,x10624,x10625,x10626))
% 155.94/155.64 [1063]~E(x10631,x10632)+E(f549(x10633,x10634,x10631,x10635,x10636),f549(x10633,x10634,x10632,x10635,x10636))
% 155.94/155.64 [1064]~E(x10641,x10642)+E(f549(x10643,x10644,x10645,x10641,x10646),f549(x10643,x10644,x10645,x10642,x10646))
% 155.94/155.64 [1065]~E(x10651,x10652)+E(f549(x10653,x10654,x10655,x10656,x10651),f549(x10653,x10654,x10655,x10656,x10652))
% 155.94/155.64 [1066]~E(x10661,x10662)+E(f210(x10661,x10663),f210(x10662,x10663))
% 155.94/155.64 [1067]~E(x10671,x10672)+E(f210(x10673,x10671),f210(x10673,x10672))
% 155.94/155.64 [1068]~E(x10681,x10682)+E(f468(x10681,x10683,x10684,x10685),f468(x10682,x10683,x10684,x10685))
% 155.94/155.64 [1069]~E(x10691,x10692)+E(f468(x10693,x10691,x10694,x10695),f468(x10693,x10692,x10694,x10695))
% 155.94/155.64 [1070]~E(x10701,x10702)+E(f468(x10703,x10704,x10701,x10705),f468(x10703,x10704,x10702,x10705))
% 155.94/155.64 [1071]~E(x10711,x10712)+E(f468(x10713,x10714,x10715,x10711),f468(x10713,x10714,x10715,x10712))
% 155.94/155.64 [1072]~E(x10721,x10722)+E(f518(x10721,x10723,x10724,x10725,x10726),f518(x10722,x10723,x10724,x10725,x10726))
% 155.94/155.64 [1073]~E(x10731,x10732)+E(f518(x10733,x10731,x10734,x10735,x10736),f518(x10733,x10732,x10734,x10735,x10736))
% 155.94/155.64 [1074]~E(x10741,x10742)+E(f518(x10743,x10744,x10741,x10745,x10746),f518(x10743,x10744,x10742,x10745,x10746))
% 155.94/155.64 [1075]~E(x10751,x10752)+E(f518(x10753,x10754,x10755,x10751,x10756),f518(x10753,x10754,x10755,x10752,x10756))
% 155.94/155.64 [1076]~E(x10761,x10762)+E(f518(x10763,x10764,x10765,x10766,x10761),f518(x10763,x10764,x10765,x10766,x10762))
% 155.94/155.64 [1077]~E(x10771,x10772)+E(f159(x10771,x10773,x10774,x10775),f159(x10772,x10773,x10774,x10775))
% 155.94/155.64 [1078]~E(x10781,x10782)+E(f159(x10783,x10781,x10784,x10785),f159(x10783,x10782,x10784,x10785))
% 155.94/155.64 [1079]~E(x10791,x10792)+E(f159(x10793,x10794,x10791,x10795),f159(x10793,x10794,x10792,x10795))
% 155.94/155.64 [1080]~E(x10801,x10802)+E(f159(x10803,x10804,x10805,x10801),f159(x10803,x10804,x10805,x10802))
% 155.94/155.64 [1081]~E(x10811,x10812)+E(f556(x10811,x10813),f556(x10812,x10813))
% 155.94/155.64 [1082]~E(x10821,x10822)+E(f556(x10823,x10821),f556(x10823,x10822))
% 155.94/155.64 [1083]~E(x10831,x10832)+E(f37(x10831,x10833,x10834,x10835,x10836,x10837,x10838,x10839,x108310,x108311),f37(x10832,x10833,x10834,x10835,x10836,x10837,x10838,x10839,x108310,x108311))
% 155.94/155.64 [1084]~E(x10841,x10842)+E(f37(x10843,x10841,x10844,x10845,x10846,x10847,x10848,x10849,x108410,x108411),f37(x10843,x10842,x10844,x10845,x10846,x10847,x10848,x10849,x108410,x108411))
% 155.94/155.64 [1085]~E(x10851,x10852)+E(f37(x10853,x10854,x10851,x10855,x10856,x10857,x10858,x10859,x108510,x108511),f37(x10853,x10854,x10852,x10855,x10856,x10857,x10858,x10859,x108510,x108511))
% 155.94/155.64 [1086]~E(x10861,x10862)+E(f37(x10863,x10864,x10865,x10861,x10866,x10867,x10868,x10869,x108610,x108611),f37(x10863,x10864,x10865,x10862,x10866,x10867,x10868,x10869,x108610,x108611))
% 155.94/155.64 [1087]~E(x10871,x10872)+E(f37(x10873,x10874,x10875,x10876,x10871,x10877,x10878,x10879,x108710,x108711),f37(x10873,x10874,x10875,x10876,x10872,x10877,x10878,x10879,x108710,x108711))
% 155.94/155.64 [1088]~E(x10881,x10882)+E(f37(x10883,x10884,x10885,x10886,x10887,x10881,x10888,x10889,x108810,x108811),f37(x10883,x10884,x10885,x10886,x10887,x10882,x10888,x10889,x108810,x108811))
% 155.94/155.64 [1089]~E(x10891,x10892)+E(f37(x10893,x10894,x10895,x10896,x10897,x10898,x10891,x10899,x108910,x108911),f37(x10893,x10894,x10895,x10896,x10897,x10898,x10892,x10899,x108910,x108911))
% 155.94/155.64 [1090]~E(x10901,x10902)+E(f37(x10903,x10904,x10905,x10906,x10907,x10908,x10909,x10901,x109010,x109011),f37(x10903,x10904,x10905,x10906,x10907,x10908,x10909,x10902,x109010,x109011))
% 155.94/155.64 [1091]~E(x10911,x10912)+E(f37(x10913,x10914,x10915,x10916,x10917,x10918,x10919,x109110,x10911,x109111),f37(x10913,x10914,x10915,x10916,x10917,x10918,x10919,x109110,x10912,x109111))
% 155.94/155.64 [1092]~E(x10921,x10922)+E(f37(x10923,x10924,x10925,x10926,x10927,x10928,x10929,x109210,x109211,x10921),f37(x10923,x10924,x10925,x10926,x10927,x10928,x10929,x109210,x109211,x10922))
% 155.94/155.64 [1093]~E(x10931,x10932)+E(f752(x10931,x10933,x10934,x10935,x10936,x10937,x10938,x10939),f752(x10932,x10933,x10934,x10935,x10936,x10937,x10938,x10939))
% 155.94/155.64 [1094]~E(x10941,x10942)+E(f752(x10943,x10941,x10944,x10945,x10946,x10947,x10948,x10949),f752(x10943,x10942,x10944,x10945,x10946,x10947,x10948,x10949))
% 155.94/155.64 [1095]~E(x10951,x10952)+E(f752(x10953,x10954,x10951,x10955,x10956,x10957,x10958,x10959),f752(x10953,x10954,x10952,x10955,x10956,x10957,x10958,x10959))
% 155.94/155.64 [1096]~E(x10961,x10962)+E(f752(x10963,x10964,x10965,x10961,x10966,x10967,x10968,x10969),f752(x10963,x10964,x10965,x10962,x10966,x10967,x10968,x10969))
% 155.94/155.64 [1097]~E(x10971,x10972)+E(f752(x10973,x10974,x10975,x10976,x10971,x10977,x10978,x10979),f752(x10973,x10974,x10975,x10976,x10972,x10977,x10978,x10979))
% 155.94/155.64 [1098]~E(x10981,x10982)+E(f752(x10983,x10984,x10985,x10986,x10987,x10981,x10988,x10989),f752(x10983,x10984,x10985,x10986,x10987,x10982,x10988,x10989))
% 155.94/155.64 [1099]~E(x10991,x10992)+E(f752(x10993,x10994,x10995,x10996,x10997,x10998,x10991,x10999),f752(x10993,x10994,x10995,x10996,x10997,x10998,x10992,x10999))
% 155.94/155.64 [1100]~E(x11001,x11002)+E(f752(x11003,x11004,x11005,x11006,x11007,x11008,x11009,x11001),f752(x11003,x11004,x11005,x11006,x11007,x11008,x11009,x11002))
% 155.94/155.64 [1101]~E(x11011,x11012)+E(f770(x11011,x11013,x11014,x11015,x11016),f770(x11012,x11013,x11014,x11015,x11016))
% 155.94/155.64 [1102]~E(x11021,x11022)+E(f770(x11023,x11021,x11024,x11025,x11026),f770(x11023,x11022,x11024,x11025,x11026))
% 155.94/155.64 [1103]~E(x11031,x11032)+E(f770(x11033,x11034,x11031,x11035,x11036),f770(x11033,x11034,x11032,x11035,x11036))
% 155.94/155.64 [1104]~E(x11041,x11042)+E(f770(x11043,x11044,x11045,x11041,x11046),f770(x11043,x11044,x11045,x11042,x11046))
% 155.94/155.64 [1105]~E(x11051,x11052)+E(f770(x11053,x11054,x11055,x11056,x11051),f770(x11053,x11054,x11055,x11056,x11052))
% 155.94/155.64 [1106]~E(x11061,x11062)+E(f728(x11061,x11063,x11064,x11065,x11066),f728(x11062,x11063,x11064,x11065,x11066))
% 155.94/155.64 [1107]~E(x11071,x11072)+E(f728(x11073,x11071,x11074,x11075,x11076),f728(x11073,x11072,x11074,x11075,x11076))
% 155.94/155.64 [1108]~E(x11081,x11082)+E(f728(x11083,x11084,x11081,x11085,x11086),f728(x11083,x11084,x11082,x11085,x11086))
% 155.94/155.64 [1109]~E(x11091,x11092)+E(f728(x11093,x11094,x11095,x11091,x11096),f728(x11093,x11094,x11095,x11092,x11096))
% 155.94/155.64 [1110]~E(x11101,x11102)+E(f728(x11103,x11104,x11105,x11106,x11101),f728(x11103,x11104,x11105,x11106,x11102))
% 155.94/155.64 [1111]~E(x11111,x11112)+E(f638(x11111,x11113,x11114,x11115,x11116),f638(x11112,x11113,x11114,x11115,x11116))
% 155.94/155.64 [1112]~E(x11121,x11122)+E(f638(x11123,x11121,x11124,x11125,x11126),f638(x11123,x11122,x11124,x11125,x11126))
% 155.94/155.64 [1113]~E(x11131,x11132)+E(f638(x11133,x11134,x11131,x11135,x11136),f638(x11133,x11134,x11132,x11135,x11136))
% 155.94/155.64 [1114]~E(x11141,x11142)+E(f638(x11143,x11144,x11145,x11141,x11146),f638(x11143,x11144,x11145,x11142,x11146))
% 155.94/155.64 [1115]~E(x11151,x11152)+E(f638(x11153,x11154,x11155,x11156,x11151),f638(x11153,x11154,x11155,x11156,x11152))
% 155.94/155.64 [1116]~E(x11161,x11162)+E(f338(x11161,x11163,x11164),f338(x11162,x11163,x11164))
% 155.94/155.64 [1117]~E(x11171,x11172)+E(f338(x11173,x11171,x11174),f338(x11173,x11172,x11174))
% 155.94/155.64 [1118]~E(x11181,x11182)+E(f338(x11183,x11184,x11181),f338(x11183,x11184,x11182))
% 155.94/155.64 [1119]~E(x11191,x11192)+E(f723(x11191,x11193,x11194),f723(x11192,x11193,x11194))
% 155.94/155.64 [1120]~E(x11201,x11202)+E(f723(x11203,x11201,x11204),f723(x11203,x11202,x11204))
% 155.94/155.64 [1121]~E(x11211,x11212)+E(f723(x11213,x11214,x11211),f723(x11213,x11214,x11212))
% 155.94/155.64 [1122]~E(x11221,x11222)+E(f643(x11221,x11223,x11224),f643(x11222,x11223,x11224))
% 155.94/155.64 [1123]~E(x11231,x11232)+E(f643(x11233,x11231,x11234),f643(x11233,x11232,x11234))
% 155.94/155.64 [1124]~E(x11241,x11242)+E(f643(x11243,x11244,x11241),f643(x11243,x11244,x11242))
% 155.94/155.64 [1125]~E(x11251,x11252)+E(f151(x11251,x11253,x11254),f151(x11252,x11253,x11254))
% 155.94/155.64 [1126]~E(x11261,x11262)+E(f151(x11263,x11261,x11264),f151(x11263,x11262,x11264))
% 155.94/155.64 [1127]~E(x11271,x11272)+E(f151(x11273,x11274,x11271),f151(x11273,x11274,x11272))
% 155.94/155.64 [1128]~E(x11281,x11282)+E(f191(x11281,x11283,x11284,x11285),f191(x11282,x11283,x11284,x11285))
% 155.94/155.64 [1129]~E(x11291,x11292)+E(f191(x11293,x11291,x11294,x11295),f191(x11293,x11292,x11294,x11295))
% 155.94/155.64 [1130]~E(x11301,x11302)+E(f191(x11303,x11304,x11301,x11305),f191(x11303,x11304,x11302,x11305))
% 155.94/155.64 [1131]~E(x11311,x11312)+E(f191(x11313,x11314,x11315,x11311),f191(x11313,x11314,x11315,x11312))
% 155.94/155.64 [1132]~E(x11321,x11322)+E(f43(x11321,x11323,x11324,x11325),f43(x11322,x11323,x11324,x11325))
% 155.94/155.64 [1133]~E(x11331,x11332)+E(f43(x11333,x11331,x11334,x11335),f43(x11333,x11332,x11334,x11335))
% 155.94/155.64 [1134]~E(x11341,x11342)+E(f43(x11343,x11344,x11341,x11345),f43(x11343,x11344,x11342,x11345))
% 155.94/155.64 [1135]~E(x11351,x11352)+E(f43(x11353,x11354,x11355,x11351),f43(x11353,x11354,x11355,x11352))
% 155.94/155.64 [1136]~E(x11361,x11362)+E(f410(x11361,x11363,x11364,x11365,x11366,x11367,x11368,x11369),f410(x11362,x11363,x11364,x11365,x11366,x11367,x11368,x11369))
% 155.94/155.64 [1137]~E(x11371,x11372)+E(f410(x11373,x11371,x11374,x11375,x11376,x11377,x11378,x11379),f410(x11373,x11372,x11374,x11375,x11376,x11377,x11378,x11379))
% 155.94/155.64 [1138]~E(x11381,x11382)+E(f410(x11383,x11384,x11381,x11385,x11386,x11387,x11388,x11389),f410(x11383,x11384,x11382,x11385,x11386,x11387,x11388,x11389))
% 155.94/155.64 [1139]~E(x11391,x11392)+E(f410(x11393,x11394,x11395,x11391,x11396,x11397,x11398,x11399),f410(x11393,x11394,x11395,x11392,x11396,x11397,x11398,x11399))
% 155.94/155.64 [1140]~E(x11401,x11402)+E(f410(x11403,x11404,x11405,x11406,x11401,x11407,x11408,x11409),f410(x11403,x11404,x11405,x11406,x11402,x11407,x11408,x11409))
% 155.94/155.64 [1141]~E(x11411,x11412)+E(f410(x11413,x11414,x11415,x11416,x11417,x11411,x11418,x11419),f410(x11413,x11414,x11415,x11416,x11417,x11412,x11418,x11419))
% 155.94/155.64 [1142]~E(x11421,x11422)+E(f410(x11423,x11424,x11425,x11426,x11427,x11428,x11421,x11429),f410(x11423,x11424,x11425,x11426,x11427,x11428,x11422,x11429))
% 155.94/155.64 [1143]~E(x11431,x11432)+E(f410(x11433,x11434,x11435,x11436,x11437,x11438,x11439,x11431),f410(x11433,x11434,x11435,x11436,x11437,x11438,x11439,x11432))
% 155.94/155.64 [1144]~E(x11441,x11442)+E(f357(x11441,x11443,x11444),f357(x11442,x11443,x11444))
% 155.94/155.64 [1145]~E(x11451,x11452)+E(f357(x11453,x11451,x11454),f357(x11453,x11452,x11454))
% 155.94/155.64 [1146]~E(x11461,x11462)+E(f357(x11463,x11464,x11461),f357(x11463,x11464,x11462))
% 155.94/155.64 [1147]~E(x11471,x11472)+E(f83(x11471,x11473),f83(x11472,x11473))
% 155.94/155.64 [1148]~E(x11481,x11482)+E(f83(x11483,x11481),f83(x11483,x11482))
% 155.94/155.64 [1149]~E(x11491,x11492)+E(f446(x11491,x11493,x11494,x11495,x11496),f446(x11492,x11493,x11494,x11495,x11496))
% 155.94/155.64 [1150]~E(x11501,x11502)+E(f446(x11503,x11501,x11504,x11505,x11506),f446(x11503,x11502,x11504,x11505,x11506))
% 155.94/155.64 [1151]~E(x11511,x11512)+E(f446(x11513,x11514,x11511,x11515,x11516),f446(x11513,x11514,x11512,x11515,x11516))
% 155.94/155.64 [1152]~E(x11521,x11522)+E(f446(x11523,x11524,x11525,x11521,x11526),f446(x11523,x11524,x11525,x11522,x11526))
% 155.94/155.64 [1153]~E(x11531,x11532)+E(f446(x11533,x11534,x11535,x11536,x11531),f446(x11533,x11534,x11535,x11536,x11532))
% 155.94/155.64 [1154]~E(x11541,x11542)+E(f353(x11541,x11543,x11544,x11545),f353(x11542,x11543,x11544,x11545))
% 155.94/155.64 [1155]~E(x11551,x11552)+E(f353(x11553,x11551,x11554,x11555),f353(x11553,x11552,x11554,x11555))
% 155.94/155.64 [1156]~E(x11561,x11562)+E(f353(x11563,x11564,x11561,x11565),f353(x11563,x11564,x11562,x11565))
% 155.94/155.64 [1157]~E(x11571,x11572)+E(f353(x11573,x11574,x11575,x11571),f353(x11573,x11574,x11575,x11572))
% 155.94/155.64 [1158]~E(x11581,x11582)+E(f432(x11581,x11583,x11584),f432(x11582,x11583,x11584))
% 155.94/155.64 [1159]~E(x11591,x11592)+E(f432(x11593,x11591,x11594),f432(x11593,x11592,x11594))
% 155.94/155.64 [1160]~E(x11601,x11602)+E(f432(x11603,x11604,x11601),f432(x11603,x11604,x11602))
% 155.94/155.64 [1161]~E(x11611,x11612)+E(f844(x11611,x11613,x11614),f844(x11612,x11613,x11614))
% 155.94/155.64 [1162]~E(x11621,x11622)+E(f844(x11623,x11621,x11624),f844(x11623,x11622,x11624))
% 155.94/155.64 [1163]~E(x11631,x11632)+E(f844(x11633,x11634,x11631),f844(x11633,x11634,x11632))
% 155.94/155.64 [1164]~E(x11641,x11642)+E(f196(x11641,x11643),f196(x11642,x11643))
% 155.94/155.64 [1165]~E(x11651,x11652)+E(f196(x11653,x11651),f196(x11653,x11652))
% 155.94/155.64 [1166]~E(x11661,x11662)+E(f499(x11661,x11663,x11664),f499(x11662,x11663,x11664))
% 155.94/155.64 [1167]~E(x11671,x11672)+E(f499(x11673,x11671,x11674),f499(x11673,x11672,x11674))
% 155.94/155.64 [1168]~E(x11681,x11682)+E(f499(x11683,x11684,x11681),f499(x11683,x11684,x11682))
% 155.94/155.64 [1169]~E(x11691,x11692)+E(f480(x11691,x11693,x11694,x11695),f480(x11692,x11693,x11694,x11695))
% 155.94/155.64 [1170]~E(x11701,x11702)+E(f480(x11703,x11701,x11704,x11705),f480(x11703,x11702,x11704,x11705))
% 155.94/155.64 [1171]~E(x11711,x11712)+E(f480(x11713,x11714,x11711,x11715),f480(x11713,x11714,x11712,x11715))
% 155.94/155.64 [1172]~E(x11721,x11722)+E(f480(x11723,x11724,x11725,x11721),f480(x11723,x11724,x11725,x11722))
% 155.94/155.64 [1173]~E(x11731,x11732)+E(f744(x11731,x11733,x11734),f744(x11732,x11733,x11734))
% 155.94/155.64 [1174]~E(x11741,x11742)+E(f744(x11743,x11741,x11744),f744(x11743,x11742,x11744))
% 155.94/155.64 [1175]~E(x11751,x11752)+E(f744(x11753,x11754,x11751),f744(x11753,x11754,x11752))
% 155.94/155.64 [1176]~E(x11761,x11762)+E(f321(x11761),f321(x11762))
% 155.94/155.64 [1177]~E(x11771,x11772)+E(f386(x11771,x11773,x11774,x11775,x11776),f386(x11772,x11773,x11774,x11775,x11776))
% 155.94/155.64 [1178]~E(x11781,x11782)+E(f386(x11783,x11781,x11784,x11785,x11786),f386(x11783,x11782,x11784,x11785,x11786))
% 155.94/155.64 [1179]~E(x11791,x11792)+E(f386(x11793,x11794,x11791,x11795,x11796),f386(x11793,x11794,x11792,x11795,x11796))
% 155.94/155.64 [1180]~E(x11801,x11802)+E(f386(x11803,x11804,x11805,x11801,x11806),f386(x11803,x11804,x11805,x11802,x11806))
% 155.94/155.64 [1181]~E(x11811,x11812)+E(f386(x11813,x11814,x11815,x11816,x11811),f386(x11813,x11814,x11815,x11816,x11812))
% 155.94/155.64 [1182]~E(x11821,x11822)+E(f677(x11821,x11823,x11824),f677(x11822,x11823,x11824))
% 155.94/155.64 [1183]~E(x11831,x11832)+E(f677(x11833,x11831,x11834),f677(x11833,x11832,x11834))
% 155.94/155.64 [1184]~E(x11841,x11842)+E(f677(x11843,x11844,x11841),f677(x11843,x11844,x11842))
% 155.94/155.64 [1185]~E(x11851,x11852)+E(f705(x11851,x11853,x11854),f705(x11852,x11853,x11854))
% 155.94/155.64 [1186]~E(x11861,x11862)+E(f705(x11863,x11861,x11864),f705(x11863,x11862,x11864))
% 155.94/155.64 [1187]~E(x11871,x11872)+E(f705(x11873,x11874,x11871),f705(x11873,x11874,x11872))
% 155.94/155.64 [1188]~E(x11881,x11882)+E(f334(x11881,x11883,x11884),f334(x11882,x11883,x11884))
% 155.94/155.64 [1189]~E(x11891,x11892)+E(f334(x11893,x11891,x11894),f334(x11893,x11892,x11894))
% 155.94/155.64 [1190]~E(x11901,x11902)+E(f334(x11903,x11904,x11901),f334(x11903,x11904,x11902))
% 155.94/155.64 [1191]~E(x11911,x11912)+E(f495(x11911,x11913,x11914),f495(x11912,x11913,x11914))
% 155.94/155.64 [1192]~E(x11921,x11922)+E(f495(x11923,x11921,x11924),f495(x11923,x11922,x11924))
% 155.94/155.64 [1193]~E(x11931,x11932)+E(f495(x11933,x11934,x11931),f495(x11933,x11934,x11932))
% 155.94/155.64 [1194]~E(x11941,x11942)+E(f370(x11941,x11943,x11944,x11945,x11946,x11947,x11948,x11949,x119410),f370(x11942,x11943,x11944,x11945,x11946,x11947,x11948,x11949,x119410))
% 155.94/155.64 [1195]~E(x11951,x11952)+E(f370(x11953,x11951,x11954,x11955,x11956,x11957,x11958,x11959,x119510),f370(x11953,x11952,x11954,x11955,x11956,x11957,x11958,x11959,x119510))
% 155.94/155.64 [1196]~E(x11961,x11962)+E(f370(x11963,x11964,x11961,x11965,x11966,x11967,x11968,x11969,x119610),f370(x11963,x11964,x11962,x11965,x11966,x11967,x11968,x11969,x119610))
% 155.94/155.64 [1197]~E(x11971,x11972)+E(f370(x11973,x11974,x11975,x11971,x11976,x11977,x11978,x11979,x119710),f370(x11973,x11974,x11975,x11972,x11976,x11977,x11978,x11979,x119710))
% 155.94/155.64 [1198]~E(x11981,x11982)+E(f370(x11983,x11984,x11985,x11986,x11981,x11987,x11988,x11989,x119810),f370(x11983,x11984,x11985,x11986,x11982,x11987,x11988,x11989,x119810))
% 155.94/155.64 [1199]~E(x11991,x11992)+E(f370(x11993,x11994,x11995,x11996,x11997,x11991,x11998,x11999,x119910),f370(x11993,x11994,x11995,x11996,x11997,x11992,x11998,x11999,x119910))
% 155.94/155.64 [1200]~E(x12001,x12002)+E(f370(x12003,x12004,x12005,x12006,x12007,x12008,x12001,x12009,x120010),f370(x12003,x12004,x12005,x12006,x12007,x12008,x12002,x12009,x120010))
% 155.94/155.64 [1201]~E(x12011,x12012)+E(f370(x12013,x12014,x12015,x12016,x12017,x12018,x12019,x12011,x120110),f370(x12013,x12014,x12015,x12016,x12017,x12018,x12019,x12012,x120110))
% 155.94/155.64 [1202]~E(x12021,x12022)+E(f370(x12023,x12024,x12025,x12026,x12027,x12028,x12029,x120210,x12021),f370(x12023,x12024,x12025,x12026,x12027,x12028,x12029,x120210,x12022))
% 155.94/155.64 [1203]~E(x12031,x12032)+E(f708(x12031,x12033,x12034,x12035,x12036,x12037),f708(x12032,x12033,x12034,x12035,x12036,x12037))
% 155.94/155.64 [1204]~E(x12041,x12042)+E(f708(x12043,x12041,x12044,x12045,x12046,x12047),f708(x12043,x12042,x12044,x12045,x12046,x12047))
% 155.94/155.64 [1205]~E(x12051,x12052)+E(f708(x12053,x12054,x12051,x12055,x12056,x12057),f708(x12053,x12054,x12052,x12055,x12056,x12057))
% 155.94/155.64 [1206]~E(x12061,x12062)+E(f708(x12063,x12064,x12065,x12061,x12066,x12067),f708(x12063,x12064,x12065,x12062,x12066,x12067))
% 155.94/155.64 [1207]~E(x12071,x12072)+E(f708(x12073,x12074,x12075,x12076,x12071,x12077),f708(x12073,x12074,x12075,x12076,x12072,x12077))
% 155.94/155.64 [1208]~E(x12081,x12082)+E(f708(x12083,x12084,x12085,x12086,x12087,x12081),f708(x12083,x12084,x12085,x12086,x12087,x12082))
% 155.94/155.64 [1209]~E(x12091,x12092)+E(f826(x12091,x12093,x12094,x12095,x12096),f826(x12092,x12093,x12094,x12095,x12096))
% 155.94/155.64 [1210]~E(x12101,x12102)+E(f826(x12103,x12101,x12104,x12105,x12106),f826(x12103,x12102,x12104,x12105,x12106))
% 155.94/155.64 [1211]~E(x12111,x12112)+E(f826(x12113,x12114,x12111,x12115,x12116),f826(x12113,x12114,x12112,x12115,x12116))
% 155.94/155.64 [1212]~E(x12121,x12122)+E(f826(x12123,x12124,x12125,x12121,x12126),f826(x12123,x12124,x12125,x12122,x12126))
% 155.94/155.64 [1213]~E(x12131,x12132)+E(f826(x12133,x12134,x12135,x12136,x12131),f826(x12133,x12134,x12135,x12136,x12132))
% 155.94/155.64 [1214]~E(x12141,x12142)+E(f842(x12141,x12143,x12144),f842(x12142,x12143,x12144))
% 155.94/155.64 [1215]~E(x12151,x12152)+E(f842(x12153,x12151,x12154),f842(x12153,x12152,x12154))
% 155.94/155.64 [1216]~E(x12161,x12162)+E(f842(x12163,x12164,x12161),f842(x12163,x12164,x12162))
% 155.94/155.64 [1217]~E(x12171,x12172)+E(f750(x12171,x12173),f750(x12172,x12173))
% 155.94/155.64 [1218]~E(x12181,x12182)+E(f750(x12183,x12181),f750(x12183,x12182))
% 155.94/155.64 [1219]~E(x12191,x12192)+E(f745(x12191,x12193,x12194),f745(x12192,x12193,x12194))
% 155.94/155.64 [1220]~E(x12201,x12202)+E(f745(x12203,x12201,x12204),f745(x12203,x12202,x12204))
% 155.94/155.64 [1221]~E(x12211,x12212)+E(f745(x12213,x12214,x12211),f745(x12213,x12214,x12212))
% 155.94/155.64 [1222]~E(x12221,x12222)+E(f623(x12221,x12223,x12224,x12225,x12226),f623(x12222,x12223,x12224,x12225,x12226))
% 155.94/155.64 [1223]~E(x12231,x12232)+E(f623(x12233,x12231,x12234,x12235,x12236),f623(x12233,x12232,x12234,x12235,x12236))
% 155.94/155.64 [1224]~E(x12241,x12242)+E(f623(x12243,x12244,x12241,x12245,x12246),f623(x12243,x12244,x12242,x12245,x12246))
% 155.94/155.64 [1225]~E(x12251,x12252)+E(f623(x12253,x12254,x12255,x12251,x12256),f623(x12253,x12254,x12255,x12252,x12256))
% 155.94/155.64 [1226]~E(x12261,x12262)+E(f623(x12263,x12264,x12265,x12266,x12261),f623(x12263,x12264,x12265,x12266,x12262))
% 155.94/155.64 [1227]~E(x12271,x12272)+E(f349(x12271,x12273,x12274),f349(x12272,x12273,x12274))
% 155.94/155.64 [1228]~E(x12281,x12282)+E(f349(x12283,x12281,x12284),f349(x12283,x12282,x12284))
% 155.94/155.64 [1229]~E(x12291,x12292)+E(f349(x12293,x12294,x12291),f349(x12293,x12294,x12292))
% 155.94/155.64 [1230]~E(x12301,x12302)+E(f747(x12301,x12303,x12304,x12305,x12306,x12307),f747(x12302,x12303,x12304,x12305,x12306,x12307))
% 155.94/155.64 [1231]~E(x12311,x12312)+E(f747(x12313,x12311,x12314,x12315,x12316,x12317),f747(x12313,x12312,x12314,x12315,x12316,x12317))
% 155.94/155.64 [1232]~E(x12321,x12322)+E(f747(x12323,x12324,x12321,x12325,x12326,x12327),f747(x12323,x12324,x12322,x12325,x12326,x12327))
% 155.94/155.64 [1233]~E(x12331,x12332)+E(f747(x12333,x12334,x12335,x12331,x12336,x12337),f747(x12333,x12334,x12335,x12332,x12336,x12337))
% 155.94/155.64 [1234]~E(x12341,x12342)+E(f747(x12343,x12344,x12345,x12346,x12341,x12347),f747(x12343,x12344,x12345,x12346,x12342,x12347))
% 155.94/155.64 [1235]~E(x12351,x12352)+E(f747(x12353,x12354,x12355,x12356,x12357,x12351),f747(x12353,x12354,x12355,x12356,x12357,x12352))
% 155.94/155.64 [1236]~E(x12361,x12362)+E(f687(x12361,x12363),f687(x12362,x12363))
% 155.94/155.64 [1237]~E(x12371,x12372)+E(f687(x12373,x12371),f687(x12373,x12372))
% 155.94/155.64 [1238]~E(x12381,x12382)+E(f754(x12381,x12383,x12384),f754(x12382,x12383,x12384))
% 155.94/155.64 [1239]~E(x12391,x12392)+E(f754(x12393,x12391,x12394),f754(x12393,x12392,x12394))
% 155.94/155.64 [1240]~E(x12401,x12402)+E(f754(x12403,x12404,x12401),f754(x12403,x12404,x12402))
% 155.94/155.64 [1241]~E(x12411,x12412)+E(f769(x12411,x12413,x12414,x12415,x12416),f769(x12412,x12413,x12414,x12415,x12416))
% 155.94/155.64 [1242]~E(x12421,x12422)+E(f769(x12423,x12421,x12424,x12425,x12426),f769(x12423,x12422,x12424,x12425,x12426))
% 155.94/155.64 [1243]~E(x12431,x12432)+E(f769(x12433,x12434,x12431,x12435,x12436),f769(x12433,x12434,x12432,x12435,x12436))
% 155.94/155.64 [1244]~E(x12441,x12442)+E(f769(x12443,x12444,x12445,x12441,x12446),f769(x12443,x12444,x12445,x12442,x12446))
% 155.94/155.64 [1245]~E(x12451,x12452)+E(f769(x12453,x12454,x12455,x12456,x12451),f769(x12453,x12454,x12455,x12456,x12452))
% 155.94/155.64 [1246]~E(x12461,x12462)+E(f672(x12461,x12463,x12464,x12465),f672(x12462,x12463,x12464,x12465))
% 155.94/155.64 [1247]~E(x12471,x12472)+E(f672(x12473,x12471,x12474,x12475),f672(x12473,x12472,x12474,x12475))
% 155.94/155.64 [1248]~E(x12481,x12482)+E(f672(x12483,x12484,x12481,x12485),f672(x12483,x12484,x12482,x12485))
% 155.94/155.64 [1249]~E(x12491,x12492)+E(f672(x12493,x12494,x12495,x12491),f672(x12493,x12494,x12495,x12492))
% 155.94/155.64 [1250]~E(x12501,x12502)+E(f293(x12501,x12503,x12504),f293(x12502,x12503,x12504))
% 155.94/155.64 [1251]~E(x12511,x12512)+E(f293(x12513,x12511,x12514),f293(x12513,x12512,x12514))
% 155.94/155.64 [1252]~E(x12521,x12522)+E(f293(x12523,x12524,x12521),f293(x12523,x12524,x12522))
% 155.94/155.64 [1253]~E(x12531,x12532)+E(f298(x12531,x12533,x12534,x12535),f298(x12532,x12533,x12534,x12535))
% 155.94/155.64 [1254]~E(x12541,x12542)+E(f298(x12543,x12541,x12544,x12545),f298(x12543,x12542,x12544,x12545))
% 155.94/155.64 [1255]~E(x12551,x12552)+E(f298(x12553,x12554,x12551,x12555),f298(x12553,x12554,x12552,x12555))
% 155.94/155.64 [1256]~E(x12561,x12562)+E(f298(x12563,x12564,x12565,x12561),f298(x12563,x12564,x12565,x12562))
% 155.94/155.64 [1257]~E(x12571,x12572)+E(f261(x12571,x12573),f261(x12572,x12573))
% 155.94/155.64 [1258]~E(x12581,x12582)+E(f261(x12583,x12581),f261(x12583,x12582))
% 155.94/155.64 [1259]~E(x12591,x12592)+E(f445(x12591,x12593,x12594,x12595,x12596,x12597,x12598,x12599),f445(x12592,x12593,x12594,x12595,x12596,x12597,x12598,x12599))
% 155.94/155.64 [1260]~E(x12601,x12602)+E(f445(x12603,x12601,x12604,x12605,x12606,x12607,x12608,x12609),f445(x12603,x12602,x12604,x12605,x12606,x12607,x12608,x12609))
% 155.94/155.64 [1261]~E(x12611,x12612)+E(f445(x12613,x12614,x12611,x12615,x12616,x12617,x12618,x12619),f445(x12613,x12614,x12612,x12615,x12616,x12617,x12618,x12619))
% 155.94/155.64 [1262]~E(x12621,x12622)+E(f445(x12623,x12624,x12625,x12621,x12626,x12627,x12628,x12629),f445(x12623,x12624,x12625,x12622,x12626,x12627,x12628,x12629))
% 155.94/155.64 [1263]~E(x12631,x12632)+E(f445(x12633,x12634,x12635,x12636,x12631,x12637,x12638,x12639),f445(x12633,x12634,x12635,x12636,x12632,x12637,x12638,x12639))
% 155.94/155.64 [1264]~E(x12641,x12642)+E(f445(x12643,x12644,x12645,x12646,x12647,x12641,x12648,x12649),f445(x12643,x12644,x12645,x12646,x12647,x12642,x12648,x12649))
% 155.94/155.64 [1265]~E(x12651,x12652)+E(f445(x12653,x12654,x12655,x12656,x12657,x12658,x12651,x12659),f445(x12653,x12654,x12655,x12656,x12657,x12658,x12652,x12659))
% 155.94/155.64 [1266]~E(x12661,x12662)+E(f445(x12663,x12664,x12665,x12666,x12667,x12668,x12669,x12661),f445(x12663,x12664,x12665,x12666,x12667,x12668,x12669,x12662))
% 155.94/155.64 [1267]~E(x12671,x12672)+E(f777(x12671,x12673,x12674,x12675,x12676),f777(x12672,x12673,x12674,x12675,x12676))
% 155.94/155.64 [1268]~E(x12681,x12682)+E(f777(x12683,x12681,x12684,x12685,x12686),f777(x12683,x12682,x12684,x12685,x12686))
% 155.94/155.64 [1269]~E(x12691,x12692)+E(f777(x12693,x12694,x12691,x12695,x12696),f777(x12693,x12694,x12692,x12695,x12696))
% 155.94/155.64 [1270]~E(x12701,x12702)+E(f777(x12703,x12704,x12705,x12701,x12706),f777(x12703,x12704,x12705,x12702,x12706))
% 155.94/155.64 [1271]~E(x12711,x12712)+E(f777(x12713,x12714,x12715,x12716,x12711),f777(x12713,x12714,x12715,x12716,x12712))
% 155.94/155.64 [1272]~E(x12721,x12722)+E(f566(x12721,x12723,x12724,x12725,x12726,x12727),f566(x12722,x12723,x12724,x12725,x12726,x12727))
% 155.94/155.64 [1273]~E(x12731,x12732)+E(f566(x12733,x12731,x12734,x12735,x12736,x12737),f566(x12733,x12732,x12734,x12735,x12736,x12737))
% 155.94/155.64 [1274]~E(x12741,x12742)+E(f566(x12743,x12744,x12741,x12745,x12746,x12747),f566(x12743,x12744,x12742,x12745,x12746,x12747))
% 155.94/155.64 [1275]~E(x12751,x12752)+E(f566(x12753,x12754,x12755,x12751,x12756,x12757),f566(x12753,x12754,x12755,x12752,x12756,x12757))
% 155.94/155.64 [1276]~E(x12761,x12762)+E(f566(x12763,x12764,x12765,x12766,x12761,x12767),f566(x12763,x12764,x12765,x12766,x12762,x12767))
% 155.94/155.64 [1277]~E(x12771,x12772)+E(f566(x12773,x12774,x12775,x12776,x12777,x12771),f566(x12773,x12774,x12775,x12776,x12777,x12772))
% 155.94/155.64 [1278]~E(x12781,x12782)+E(f294(x12781,x12783,x12784),f294(x12782,x12783,x12784))
% 155.94/155.64 [1279]~E(x12791,x12792)+E(f294(x12793,x12791,x12794),f294(x12793,x12792,x12794))
% 155.94/155.64 [1280]~E(x12801,x12802)+E(f294(x12803,x12804,x12801),f294(x12803,x12804,x12802))
% 155.94/155.64 [1281]~E(x12811,x12812)+E(f433(x12811,x12813,x12814),f433(x12812,x12813,x12814))
% 155.94/155.64 [1282]~E(x12821,x12822)+E(f433(x12823,x12821,x12824),f433(x12823,x12822,x12824))
% 155.94/155.64 [1283]~E(x12831,x12832)+E(f433(x12833,x12834,x12831),f433(x12833,x12834,x12832))
% 155.94/155.64 [1284]~E(x12841,x12842)+E(f331(x12841,x12843,x12844),f331(x12842,x12843,x12844))
% 155.94/155.64 [1285]~E(x12851,x12852)+E(f331(x12853,x12851,x12854),f331(x12853,x12852,x12854))
% 155.94/155.64 [1286]~E(x12861,x12862)+E(f331(x12863,x12864,x12861),f331(x12863,x12864,x12862))
% 155.94/155.64 [1287]~E(x12871,x12872)+E(f497(x12871,x12873,x12874),f497(x12872,x12873,x12874))
% 155.94/155.64 [1288]~E(x12881,x12882)+E(f497(x12883,x12881,x12884),f497(x12883,x12882,x12884))
% 155.94/155.64 [1289]~E(x12891,x12892)+E(f497(x12893,x12894,x12891),f497(x12893,x12894,x12892))
% 155.94/155.64 [1290]~E(x12901,x12902)+E(f641(x12901,x12903,x12904,x12905,x12906),f641(x12902,x12903,x12904,x12905,x12906))
% 155.94/155.64 [1291]~E(x12911,x12912)+E(f641(x12913,x12911,x12914,x12915,x12916),f641(x12913,x12912,x12914,x12915,x12916))
% 155.94/155.64 [1292]~E(x12921,x12922)+E(f641(x12923,x12924,x12921,x12925,x12926),f641(x12923,x12924,x12922,x12925,x12926))
% 155.94/155.64 [1293]~E(x12931,x12932)+E(f641(x12933,x12934,x12935,x12931,x12936),f641(x12933,x12934,x12935,x12932,x12936))
% 155.94/155.64 [1294]~E(x12941,x12942)+E(f641(x12943,x12944,x12945,x12946,x12941),f641(x12943,x12944,x12945,x12946,x12942))
% 155.94/155.64 [1295]~E(x12951,x12952)+E(f713(x12951,x12953,x12954,x12955,x12956),f713(x12952,x12953,x12954,x12955,x12956))
% 155.94/155.64 [1296]~E(x12961,x12962)+E(f713(x12963,x12961,x12964,x12965,x12966),f713(x12963,x12962,x12964,x12965,x12966))
% 155.94/155.64 [1297]~E(x12971,x12972)+E(f713(x12973,x12974,x12971,x12975,x12976),f713(x12973,x12974,x12972,x12975,x12976))
% 155.94/155.64 [1298]~E(x12981,x12982)+E(f713(x12983,x12984,x12985,x12981,x12986),f713(x12983,x12984,x12985,x12982,x12986))
% 155.94/155.64 [1299]~E(x12991,x12992)+E(f713(x12993,x12994,x12995,x12996,x12991),f713(x12993,x12994,x12995,x12996,x12992))
% 155.94/155.64 [1300]~E(x13001,x13002)+E(f775(x13001,x13003,x13004,x13005),f775(x13002,x13003,x13004,x13005))
% 155.94/155.64 [1301]~E(x13011,x13012)+E(f775(x13013,x13011,x13014,x13015),f775(x13013,x13012,x13014,x13015))
% 155.94/155.64 [1302]~E(x13021,x13022)+E(f775(x13023,x13024,x13021,x13025),f775(x13023,x13024,x13022,x13025))
% 155.94/155.64 [1303]~E(x13031,x13032)+E(f775(x13033,x13034,x13035,x13031),f775(x13033,x13034,x13035,x13032))
% 155.94/155.64 [1304]~E(x13041,x13042)+E(f442(x13041,x13043,x13044),f442(x13042,x13043,x13044))
% 155.94/155.64 [1305]~E(x13051,x13052)+E(f442(x13053,x13051,x13054),f442(x13053,x13052,x13054))
% 155.94/155.64 [1306]~E(x13061,x13062)+E(f442(x13063,x13064,x13061),f442(x13063,x13064,x13062))
% 155.94/155.64 [1307]~E(x13071,x13072)+E(f411(x13071,x13073,x13074,x13075,x13076),f411(x13072,x13073,x13074,x13075,x13076))
% 155.94/155.64 [1308]~E(x13081,x13082)+E(f411(x13083,x13081,x13084,x13085,x13086),f411(x13083,x13082,x13084,x13085,x13086))
% 155.94/155.64 [1309]~E(x13091,x13092)+E(f411(x13093,x13094,x13091,x13095,x13096),f411(x13093,x13094,x13092,x13095,x13096))
% 155.94/155.64 [1310]~E(x13101,x13102)+E(f411(x13103,x13104,x13105,x13101,x13106),f411(x13103,x13104,x13105,x13102,x13106))
% 155.94/155.64 [1311]~E(x13111,x13112)+E(f411(x13113,x13114,x13115,x13116,x13111),f411(x13113,x13114,x13115,x13116,x13112))
% 155.94/155.64 [1312]~E(x13121,x13122)+E(f802(x13121,x13123,x13124,x13125,x13126,x13127,x13128),f802(x13122,x13123,x13124,x13125,x13126,x13127,x13128))
% 155.94/155.64 [1313]~E(x13131,x13132)+E(f802(x13133,x13131,x13134,x13135,x13136,x13137,x13138),f802(x13133,x13132,x13134,x13135,x13136,x13137,x13138))
% 155.94/155.64 [1314]~E(x13141,x13142)+E(f802(x13143,x13144,x13141,x13145,x13146,x13147,x13148),f802(x13143,x13144,x13142,x13145,x13146,x13147,x13148))
% 155.94/155.64 [1315]~E(x13151,x13152)+E(f802(x13153,x13154,x13155,x13151,x13156,x13157,x13158),f802(x13153,x13154,x13155,x13152,x13156,x13157,x13158))
% 155.94/155.64 [1316]~E(x13161,x13162)+E(f802(x13163,x13164,x13165,x13166,x13161,x13167,x13168),f802(x13163,x13164,x13165,x13166,x13162,x13167,x13168))
% 155.94/155.64 [1317]~E(x13171,x13172)+E(f802(x13173,x13174,x13175,x13176,x13177,x13171,x13178),f802(x13173,x13174,x13175,x13176,x13177,x13172,x13178))
% 155.94/155.64 [1318]~E(x13181,x13182)+E(f802(x13183,x13184,x13185,x13186,x13187,x13188,x13181),f802(x13183,x13184,x13185,x13186,x13187,x13188,x13182))
% 155.94/155.64 [1319]~E(x13191,x13192)+E(f274(x13191,x13193,x13194,x13195),f274(x13192,x13193,x13194,x13195))
% 155.94/155.64 [1320]~E(x13201,x13202)+E(f274(x13203,x13201,x13204,x13205),f274(x13203,x13202,x13204,x13205))
% 155.94/155.64 [1321]~E(x13211,x13212)+E(f274(x13213,x13214,x13211,x13215),f274(x13213,x13214,x13212,x13215))
% 155.94/155.64 [1322]~E(x13221,x13222)+E(f274(x13223,x13224,x13225,x13221),f274(x13223,x13224,x13225,x13222))
% 155.94/155.64 [1323]~E(x13231,x13232)+E(f406(x13231,x13233,x13234,x13235,x13236),f406(x13232,x13233,x13234,x13235,x13236))
% 155.94/155.64 [1324]~E(x13241,x13242)+E(f406(x13243,x13241,x13244,x13245,x13246),f406(x13243,x13242,x13244,x13245,x13246))
% 155.94/155.64 [1325]~E(x13251,x13252)+E(f406(x13253,x13254,x13251,x13255,x13256),f406(x13253,x13254,x13252,x13255,x13256))
% 155.94/155.64 [1326]~E(x13261,x13262)+E(f406(x13263,x13264,x13265,x13261,x13266),f406(x13263,x13264,x13265,x13262,x13266))
% 155.94/155.64 [1327]~E(x13271,x13272)+E(f406(x13273,x13274,x13275,x13276,x13271),f406(x13273,x13274,x13275,x13276,x13272))
% 155.94/155.64 [1328]~E(x13281,x13282)+E(f500(x13281,x13283,x13284,x13285,x13286),f500(x13282,x13283,x13284,x13285,x13286))
% 155.94/155.64 [1329]~E(x13291,x13292)+E(f500(x13293,x13291,x13294,x13295,x13296),f500(x13293,x13292,x13294,x13295,x13296))
% 155.94/155.64 [1330]~E(x13301,x13302)+E(f500(x13303,x13304,x13301,x13305,x13306),f500(x13303,x13304,x13302,x13305,x13306))
% 155.94/155.64 [1331]~E(x13311,x13312)+E(f500(x13313,x13314,x13315,x13311,x13316),f500(x13313,x13314,x13315,x13312,x13316))
% 155.94/155.64 [1332]~E(x13321,x13322)+E(f500(x13323,x13324,x13325,x13326,x13321),f500(x13323,x13324,x13325,x13326,x13322))
% 155.94/155.64 [1333]~E(x13331,x13332)+E(f732(x13331,x13333,x13334,x13335,x13336,x13337,x13338),f732(x13332,x13333,x13334,x13335,x13336,x13337,x13338))
% 155.94/155.64 [1334]~E(x13341,x13342)+E(f732(x13343,x13341,x13344,x13345,x13346,x13347,x13348),f732(x13343,x13342,x13344,x13345,x13346,x13347,x13348))
% 155.94/155.64 [1335]~E(x13351,x13352)+E(f732(x13353,x13354,x13351,x13355,x13356,x13357,x13358),f732(x13353,x13354,x13352,x13355,x13356,x13357,x13358))
% 155.94/155.64 [1336]~E(x13361,x13362)+E(f732(x13363,x13364,x13365,x13361,x13366,x13367,x13368),f732(x13363,x13364,x13365,x13362,x13366,x13367,x13368))
% 155.94/155.64 [1337]~E(x13371,x13372)+E(f732(x13373,x13374,x13375,x13376,x13371,x13377,x13378),f732(x13373,x13374,x13375,x13376,x13372,x13377,x13378))
% 155.94/155.64 [1338]~E(x13381,x13382)+E(f732(x13383,x13384,x13385,x13386,x13387,x13381,x13388),f732(x13383,x13384,x13385,x13386,x13387,x13382,x13388))
% 155.94/155.64 [1339]~E(x13391,x13392)+E(f732(x13393,x13394,x13395,x13396,x13397,x13398,x13391),f732(x13393,x13394,x13395,x13396,x13397,x13398,x13392))
% 155.94/155.64 [1340]~E(x13401,x13402)+E(f804(x13401,x13403,x13404,x13405),f804(x13402,x13403,x13404,x13405))
% 155.94/155.64 [1341]~E(x13411,x13412)+E(f804(x13413,x13411,x13414,x13415),f804(x13413,x13412,x13414,x13415))
% 155.94/155.64 [1342]~E(x13421,x13422)+E(f804(x13423,x13424,x13421,x13425),f804(x13423,x13424,x13422,x13425))
% 155.94/155.64 [1343]~E(x13431,x13432)+E(f804(x13433,x13434,x13435,x13431),f804(x13433,x13434,x13435,x13432))
% 155.94/155.64 [1344]~E(x13441,x13442)+E(f505(x13441,x13443,x13444),f505(x13442,x13443,x13444))
% 155.94/155.64 [1345]~E(x13451,x13452)+E(f505(x13453,x13451,x13454),f505(x13453,x13452,x13454))
% 155.94/155.64 [1346]~E(x13461,x13462)+E(f505(x13463,x13464,x13461),f505(x13463,x13464,x13462))
% 155.94/155.64 [1347]~E(x13471,x13472)+E(f614(x13471,x13473,x13474),f614(x13472,x13473,x13474))
% 155.94/155.64 [1348]~E(x13481,x13482)+E(f614(x13483,x13481,x13484),f614(x13483,x13482,x13484))
% 155.94/155.64 [1349]~E(x13491,x13492)+E(f614(x13493,x13494,x13491),f614(x13493,x13494,x13492))
% 155.94/155.64 [1350]~E(x13501,x13502)+E(f458(x13501,x13503,x13504),f458(x13502,x13503,x13504))
% 155.94/155.64 [1351]~E(x13511,x13512)+E(f458(x13513,x13511,x13514),f458(x13513,x13512,x13514))
% 155.94/155.64 [1352]~E(x13521,x13522)+E(f458(x13523,x13524,x13521),f458(x13523,x13524,x13522))
% 155.94/155.64 [1353]~E(x13531,x13532)+E(f296(x13531),f296(x13532))
% 155.94/155.64 [1354]~E(x13541,x13542)+E(f702(x13541,x13543),f702(x13542,x13543))
% 155.94/155.64 [1355]~E(x13551,x13552)+E(f702(x13553,x13551),f702(x13553,x13552))
% 155.94/155.64 [1356]~E(x13561,x13562)+E(f328(x13561),f328(x13562))
% 155.94/155.64 [1357]~E(x13571,x13572)+E(f106(x13571,x13573,x13574,x13575),f106(x13572,x13573,x13574,x13575))
% 155.94/155.64 [1358]~E(x13581,x13582)+E(f106(x13583,x13581,x13584,x13585),f106(x13583,x13582,x13584,x13585))
% 155.94/155.64 [1359]~E(x13591,x13592)+E(f106(x13593,x13594,x13591,x13595),f106(x13593,x13594,x13592,x13595))
% 155.94/155.64 [1360]~E(x13601,x13602)+E(f106(x13603,x13604,x13605,x13601),f106(x13603,x13604,x13605,x13602))
% 155.94/155.64 [1361]~E(x13611,x13612)+E(f139(x13611,x13613),f139(x13612,x13613))
% 155.94/155.64 [1362]~E(x13621,x13622)+E(f139(x13623,x13621),f139(x13623,x13622))
% 155.94/155.64 [1363]~E(x13631,x13632)+E(f531(x13631,x13633,x13634,x13635,x13636,x13637),f531(x13632,x13633,x13634,x13635,x13636,x13637))
% 155.94/155.64 [1364]~E(x13641,x13642)+E(f531(x13643,x13641,x13644,x13645,x13646,x13647),f531(x13643,x13642,x13644,x13645,x13646,x13647))
% 155.94/155.64 [1365]~E(x13651,x13652)+E(f531(x13653,x13654,x13651,x13655,x13656,x13657),f531(x13653,x13654,x13652,x13655,x13656,x13657))
% 155.94/155.64 [1366]~E(x13661,x13662)+E(f531(x13663,x13664,x13665,x13661,x13666,x13667),f531(x13663,x13664,x13665,x13662,x13666,x13667))
% 155.94/155.64 [1367]~E(x13671,x13672)+E(f531(x13673,x13674,x13675,x13676,x13671,x13677),f531(x13673,x13674,x13675,x13676,x13672,x13677))
% 155.94/155.64 [1368]~E(x13681,x13682)+E(f531(x13683,x13684,x13685,x13686,x13687,x13681),f531(x13683,x13684,x13685,x13686,x13687,x13682))
% 155.94/155.64 [1369]~E(x13691,x13692)+E(f611(x13691,x13693),f611(x13692,x13693))
% 155.94/155.64 [1370]~E(x13701,x13702)+E(f611(x13703,x13701),f611(x13703,x13702))
% 155.94/155.64 [1371]~E(x13711,x13712)+E(f241(x13711,x13713,x13714),f241(x13712,x13713,x13714))
% 155.94/155.64 [1372]~E(x13721,x13722)+E(f241(x13723,x13721,x13724),f241(x13723,x13722,x13724))
% 155.94/155.64 [1373]~E(x13731,x13732)+E(f241(x13733,x13734,x13731),f241(x13733,x13734,x13732))
% 155.94/155.64 [1374]~E(x13741,x13742)+E(f727(x13741,x13743,x13744,x13745,x13746),f727(x13742,x13743,x13744,x13745,x13746))
% 155.94/155.64 [1375]~E(x13751,x13752)+E(f727(x13753,x13751,x13754,x13755,x13756),f727(x13753,x13752,x13754,x13755,x13756))
% 155.94/155.64 [1376]~E(x13761,x13762)+E(f727(x13763,x13764,x13761,x13765,x13766),f727(x13763,x13764,x13762,x13765,x13766))
% 155.94/155.64 [1377]~E(x13771,x13772)+E(f727(x13773,x13774,x13775,x13771,x13776),f727(x13773,x13774,x13775,x13772,x13776))
% 155.94/155.64 [1378]~E(x13781,x13782)+E(f727(x13783,x13784,x13785,x13786,x13781),f727(x13783,x13784,x13785,x13786,x13782))
% 155.94/155.64 [1379]~E(x13791,x13792)+E(f815(x13791,x13793,x13794,x13795),f815(x13792,x13793,x13794,x13795))
% 155.94/155.64 [1380]~E(x13801,x13802)+E(f815(x13803,x13801,x13804,x13805),f815(x13803,x13802,x13804,x13805))
% 155.94/155.64 [1381]~E(x13811,x13812)+E(f815(x13813,x13814,x13811,x13815),f815(x13813,x13814,x13812,x13815))
% 155.94/155.64 [1382]~E(x13821,x13822)+E(f815(x13823,x13824,x13825,x13821),f815(x13823,x13824,x13825,x13822))
% 155.94/155.64 [1383]~E(x13831,x13832)+E(f560(x13831,x13833,x13834,x13835),f560(x13832,x13833,x13834,x13835))
% 155.94/155.64 [1384]~E(x13841,x13842)+E(f560(x13843,x13841,x13844,x13845),f560(x13843,x13842,x13844,x13845))
% 155.94/155.64 [1385]~E(x13851,x13852)+E(f560(x13853,x13854,x13851,x13855),f560(x13853,x13854,x13852,x13855))
% 155.94/155.64 [1386]~E(x13861,x13862)+E(f560(x13863,x13864,x13865,x13861),f560(x13863,x13864,x13865,x13862))
% 155.94/155.64 [1387]~E(x13871,x13872)+E(f570(x13871,x13873),f570(x13872,x13873))
% 155.94/155.64 [1388]~E(x13881,x13882)+E(f570(x13883,x13881),f570(x13883,x13882))
% 155.94/155.64 [1389]~E(x13891,x13892)+E(f831(x13891,x13893,x13894,x13895,x13896),f831(x13892,x13893,x13894,x13895,x13896))
% 155.94/155.64 [1390]~E(x13901,x13902)+E(f831(x13903,x13901,x13904,x13905,x13906),f831(x13903,x13902,x13904,x13905,x13906))
% 155.94/155.64 [1391]~E(x13911,x13912)+E(f831(x13913,x13914,x13911,x13915,x13916),f831(x13913,x13914,x13912,x13915,x13916))
% 155.94/155.64 [1392]~E(x13921,x13922)+E(f831(x13923,x13924,x13925,x13921,x13926),f831(x13923,x13924,x13925,x13922,x13926))
% 155.94/155.64 [1393]~E(x13931,x13932)+E(f831(x13933,x13934,x13935,x13936,x13931),f831(x13933,x13934,x13935,x13936,x13932))
% 155.94/155.64 [1394]~E(x13941,x13942)+E(f230(x13941,x13943),f230(x13942,x13943))
% 155.94/155.64 [1395]~E(x13951,x13952)+E(f230(x13953,x13951),f230(x13953,x13952))
% 155.94/155.64 [1396]~E(x13961,x13962)+E(f561(x13961,x13963,x13964,x13965,x13966,x13967),f561(x13962,x13963,x13964,x13965,x13966,x13967))
% 155.94/155.64 [1397]~E(x13971,x13972)+E(f561(x13973,x13971,x13974,x13975,x13976,x13977),f561(x13973,x13972,x13974,x13975,x13976,x13977))
% 155.94/155.64 [1398]~E(x13981,x13982)+E(f561(x13983,x13984,x13981,x13985,x13986,x13987),f561(x13983,x13984,x13982,x13985,x13986,x13987))
% 155.94/155.64 [1399]~E(x13991,x13992)+E(f561(x13993,x13994,x13995,x13991,x13996,x13997),f561(x13993,x13994,x13995,x13992,x13996,x13997))
% 155.94/155.64 [1400]~E(x14001,x14002)+E(f561(x14003,x14004,x14005,x14006,x14001,x14007),f561(x14003,x14004,x14005,x14006,x14002,x14007))
% 155.94/155.64 [1401]~E(x14011,x14012)+E(f561(x14013,x14014,x14015,x14016,x14017,x14011),f561(x14013,x14014,x14015,x14016,x14017,x14012))
% 155.94/155.64 [1402]~E(x14021,x14022)+E(f724(x14021,x14023,x14024),f724(x14022,x14023,x14024))
% 155.94/155.64 [1403]~E(x14031,x14032)+E(f724(x14033,x14031,x14034),f724(x14033,x14032,x14034))
% 155.94/155.64 [1404]~E(x14041,x14042)+E(f724(x14043,x14044,x14041),f724(x14043,x14044,x14042))
% 155.94/155.64 [1405]~E(x14051,x14052)+E(f377(x14051,x14053),f377(x14052,x14053))
% 155.94/155.64 [1406]~E(x14061,x14062)+E(f377(x14063,x14061),f377(x14063,x14062))
% 155.94/155.64 [1407]~E(x14071,x14072)+E(f657(x14071,x14073,x14074),f657(x14072,x14073,x14074))
% 155.94/155.64 [1408]~E(x14081,x14082)+E(f657(x14083,x14081,x14084),f657(x14083,x14082,x14084))
% 155.94/155.64 [1409]~E(x14091,x14092)+E(f657(x14093,x14094,x14091),f657(x14093,x14094,x14092))
% 155.94/155.64 [1410]~E(x14101,x14102)+E(f229(x14101,x14103),f229(x14102,x14103))
% 155.94/155.64 [1411]~E(x14111,x14112)+E(f229(x14113,x14111),f229(x14113,x14112))
% 155.94/155.64 [1412]~E(x14121,x14122)+E(f722(x14121,x14123,x14124,x14125,x14126),f722(x14122,x14123,x14124,x14125,x14126))
% 155.94/155.64 [1413]~E(x14131,x14132)+E(f722(x14133,x14131,x14134,x14135,x14136),f722(x14133,x14132,x14134,x14135,x14136))
% 155.94/155.64 [1414]~E(x14141,x14142)+E(f722(x14143,x14144,x14141,x14145,x14146),f722(x14143,x14144,x14142,x14145,x14146))
% 155.94/155.64 [1415]~E(x14151,x14152)+E(f722(x14153,x14154,x14155,x14151,x14156),f722(x14153,x14154,x14155,x14152,x14156))
% 155.94/155.64 [1416]~E(x14161,x14162)+E(f722(x14163,x14164,x14165,x14166,x14161),f722(x14163,x14164,x14165,x14166,x14162))
% 155.94/155.64 [1417]~E(x14171,x14172)+E(f434(x14171,x14173,x14174),f434(x14172,x14173,x14174))
% 155.94/155.64 [1418]~E(x14181,x14182)+E(f434(x14183,x14181,x14184),f434(x14183,x14182,x14184))
% 155.94/155.64 [1419]~E(x14191,x14192)+E(f434(x14193,x14194,x14191),f434(x14193,x14194,x14192))
% 155.94/155.64 [1420]~E(x14201,x14202)+E(f483(x14201,x14203,x14204),f483(x14202,x14203,x14204))
% 155.94/155.64 [1421]~E(x14211,x14212)+E(f483(x14213,x14211,x14214),f483(x14213,x14212,x14214))
% 155.94/155.64 [1422]~E(x14221,x14222)+E(f483(x14223,x14224,x14221),f483(x14223,x14224,x14222))
% 155.94/155.64 [1423]~E(x14231,x14232)+E(f656(x14231,x14233),f656(x14232,x14233))
% 155.94/155.64 [1424]~E(x14241,x14242)+E(f656(x14243,x14241),f656(x14243,x14242))
% 155.94/155.64 [1425]~E(x14251,x14252)+E(f679(x14251,x14253,x14254),f679(x14252,x14253,x14254))
% 155.94/155.64 [1426]~E(x14261,x14262)+E(f679(x14263,x14261,x14264),f679(x14263,x14262,x14264))
% 155.94/155.64 [1427]~E(x14271,x14272)+E(f679(x14273,x14274,x14271),f679(x14273,x14274,x14272))
% 155.94/155.64 [1428]~E(x14281,x14282)+E(f562(x14281,x14283,x14284,x14285),f562(x14282,x14283,x14284,x14285))
% 155.94/155.64 [1429]~E(x14291,x14292)+E(f562(x14293,x14291,x14294,x14295),f562(x14293,x14292,x14294,x14295))
% 155.94/155.64 [1430]~E(x14301,x14302)+E(f562(x14303,x14304,x14301,x14305),f562(x14303,x14304,x14302,x14305))
% 155.94/155.64 [1431]~E(x14311,x14312)+E(f562(x14313,x14314,x14315,x14311),f562(x14313,x14314,x14315,x14312))
% 155.94/155.64 [1432]~E(x14321,x14322)+E(f383(x14321,x14323,x14324,x14325),f383(x14322,x14323,x14324,x14325))
% 155.94/155.64 [1433]~E(x14331,x14332)+E(f383(x14333,x14331,x14334,x14335),f383(x14333,x14332,x14334,x14335))
% 155.94/155.64 [1434]~E(x14341,x14342)+E(f383(x14343,x14344,x14341,x14345),f383(x14343,x14344,x14342,x14345))
% 155.94/155.64 [1435]~E(x14351,x14352)+E(f383(x14353,x14354,x14355,x14351),f383(x14353,x14354,x14355,x14352))
% 155.94/155.64 [1436]~E(x14361,x14362)+E(f186(x14361,x14363,x14364,x14365),f186(x14362,x14363,x14364,x14365))
% 155.94/155.64 [1437]~E(x14371,x14372)+E(f186(x14373,x14371,x14374,x14375),f186(x14373,x14372,x14374,x14375))
% 155.94/155.64 [1438]~E(x14381,x14382)+E(f186(x14383,x14384,x14381,x14385),f186(x14383,x14384,x14382,x14385))
% 155.94/155.64 [1439]~E(x14391,x14392)+E(f186(x14393,x14394,x14395,x14391),f186(x14393,x14394,x14395,x14392))
% 155.94/155.64 [1440]~E(x14401,x14402)+E(f292(x14401,x14403),f292(x14402,x14403))
% 155.94/155.64 [1441]~E(x14411,x14412)+E(f292(x14413,x14411),f292(x14413,x14412))
% 155.94/155.64 [1442]~E(x14421,x14422)+E(f415(x14421,x14423,x14424,x14425,x14426,x14427,x14428),f415(x14422,x14423,x14424,x14425,x14426,x14427,x14428))
% 155.94/155.64 [1443]~E(x14431,x14432)+E(f415(x14433,x14431,x14434,x14435,x14436,x14437,x14438),f415(x14433,x14432,x14434,x14435,x14436,x14437,x14438))
% 155.94/155.64 [1444]~E(x14441,x14442)+E(f415(x14443,x14444,x14441,x14445,x14446,x14447,x14448),f415(x14443,x14444,x14442,x14445,x14446,x14447,x14448))
% 155.94/155.64 [1445]~E(x14451,x14452)+E(f415(x14453,x14454,x14455,x14451,x14456,x14457,x14458),f415(x14453,x14454,x14455,x14452,x14456,x14457,x14458))
% 155.94/155.64 [1446]~E(x14461,x14462)+E(f415(x14463,x14464,x14465,x14466,x14461,x14467,x14468),f415(x14463,x14464,x14465,x14466,x14462,x14467,x14468))
% 155.94/155.64 [1447]~E(x14471,x14472)+E(f415(x14473,x14474,x14475,x14476,x14477,x14471,x14478),f415(x14473,x14474,x14475,x14476,x14477,x14472,x14478))
% 155.94/155.64 [1448]~E(x14481,x14482)+E(f415(x14483,x14484,x14485,x14486,x14487,x14488,x14481),f415(x14483,x14484,x14485,x14486,x14487,x14488,x14482))
% 155.94/155.64 [1449]~E(x14491,x14492)+E(f709(x14491,x14493,x14494,x14495,x14496,x14497,x14498,x14499),f709(x14492,x14493,x14494,x14495,x14496,x14497,x14498,x14499))
% 155.94/155.64 [1450]~E(x14501,x14502)+E(f709(x14503,x14501,x14504,x14505,x14506,x14507,x14508,x14509),f709(x14503,x14502,x14504,x14505,x14506,x14507,x14508,x14509))
% 155.94/155.64 [1451]~E(x14511,x14512)+E(f709(x14513,x14514,x14511,x14515,x14516,x14517,x14518,x14519),f709(x14513,x14514,x14512,x14515,x14516,x14517,x14518,x14519))
% 155.94/155.64 [1452]~E(x14521,x14522)+E(f709(x14523,x14524,x14525,x14521,x14526,x14527,x14528,x14529),f709(x14523,x14524,x14525,x14522,x14526,x14527,x14528,x14529))
% 155.94/155.64 [1453]~E(x14531,x14532)+E(f709(x14533,x14534,x14535,x14536,x14531,x14537,x14538,x14539),f709(x14533,x14534,x14535,x14536,x14532,x14537,x14538,x14539))
% 155.94/155.64 [1454]~E(x14541,x14542)+E(f709(x14543,x14544,x14545,x14546,x14547,x14541,x14548,x14549),f709(x14543,x14544,x14545,x14546,x14547,x14542,x14548,x14549))
% 155.94/155.64 [1455]~E(x14551,x14552)+E(f709(x14553,x14554,x14555,x14556,x14557,x14558,x14551,x14559),f709(x14553,x14554,x14555,x14556,x14557,x14558,x14552,x14559))
% 155.94/155.64 [1456]~E(x14561,x14562)+E(f709(x14563,x14564,x14565,x14566,x14567,x14568,x14569,x14561),f709(x14563,x14564,x14565,x14566,x14567,x14568,x14569,x14562))
% 155.94/155.64 [1457]~E(x14571,x14572)+E(f670(x14571,x14573),f670(x14572,x14573))
% 155.94/155.64 [1458]~E(x14581,x14582)+E(f670(x14583,x14581),f670(x14583,x14582))
% 155.94/155.64 [1459]~E(x14591,x14592)+E(f624(x14591,x14593,x14594,x14595,x14596),f624(x14592,x14593,x14594,x14595,x14596))
% 155.94/155.64 [1460]~E(x14601,x14602)+E(f624(x14603,x14601,x14604,x14605,x14606),f624(x14603,x14602,x14604,x14605,x14606))
% 155.94/155.64 [1461]~E(x14611,x14612)+E(f624(x14613,x14614,x14611,x14615,x14616),f624(x14613,x14614,x14612,x14615,x14616))
% 155.94/155.64 [1462]~E(x14621,x14622)+E(f624(x14623,x14624,x14625,x14621,x14626),f624(x14623,x14624,x14625,x14622,x14626))
% 155.94/155.64 [1463]~E(x14631,x14632)+E(f624(x14633,x14634,x14635,x14636,x14631),f624(x14633,x14634,x14635,x14636,x14632))
% 155.94/155.64 [1464]~E(x14641,x14642)+E(f421(x14641,x14643,x14644,x14645,x14646),f421(x14642,x14643,x14644,x14645,x14646))
% 155.94/155.64 [1465]~E(x14651,x14652)+E(f421(x14653,x14651,x14654,x14655,x14656),f421(x14653,x14652,x14654,x14655,x14656))
% 155.94/155.64 [1466]~E(x14661,x14662)+E(f421(x14663,x14664,x14661,x14665,x14666),f421(x14663,x14664,x14662,x14665,x14666))
% 155.94/155.64 [1467]~E(x14671,x14672)+E(f421(x14673,x14674,x14675,x14671,x14676),f421(x14673,x14674,x14675,x14672,x14676))
% 155.94/155.64 [1468]~E(x14681,x14682)+E(f421(x14683,x14684,x14685,x14686,x14681),f421(x14683,x14684,x14685,x14686,x14682))
% 155.94/155.64 [1469]~E(x14691,x14692)+E(f800(x14691,x14693,x14694,x14695,x14696),f800(x14692,x14693,x14694,x14695,x14696))
% 155.94/155.64 [1470]~E(x14701,x14702)+E(f800(x14703,x14701,x14704,x14705,x14706),f800(x14703,x14702,x14704,x14705,x14706))
% 155.94/155.64 [1471]~E(x14711,x14712)+E(f800(x14713,x14714,x14711,x14715,x14716),f800(x14713,x14714,x14712,x14715,x14716))
% 155.94/155.64 [1472]~E(x14721,x14722)+E(f800(x14723,x14724,x14725,x14721,x14726),f800(x14723,x14724,x14725,x14722,x14726))
% 155.94/155.64 [1473]~E(x14731,x14732)+E(f800(x14733,x14734,x14735,x14736,x14731),f800(x14733,x14734,x14735,x14736,x14732))
% 155.94/155.64 [1474]~E(x14741,x14742)+E(f834(x14741),f834(x14742))
% 155.94/155.64 [1475]~E(x14751,x14752)+E(f475(x14751,x14753),f475(x14752,x14753))
% 155.94/155.64 [1476]~E(x14761,x14762)+E(f475(x14763,x14761),f475(x14763,x14762))
% 155.94/155.64 [1477]~E(x14771,x14772)+E(f667(x14771,x14773,x14774),f667(x14772,x14773,x14774))
% 155.94/155.64 [1478]~E(x14781,x14782)+E(f667(x14783,x14781,x14784),f667(x14783,x14782,x14784))
% 155.94/155.64 [1479]~E(x14791,x14792)+E(f667(x14793,x14794,x14791),f667(x14793,x14794,x14792))
% 155.94/155.64 [1480]~E(x14801,x14802)+E(f840(x14801,x14803,x14804),f840(x14802,x14803,x14804))
% 155.94/155.64 [1481]~E(x14811,x14812)+E(f840(x14813,x14811,x14814),f840(x14813,x14812,x14814))
% 155.94/155.64 [1482]~E(x14821,x14822)+E(f840(x14823,x14824,x14821),f840(x14823,x14824,x14822))
% 155.94/155.64 [1483]~E(x14831,x14832)+E(f400(x14831,x14833,x14834),f400(x14832,x14833,x14834))
% 155.94/155.64 [1484]~E(x14841,x14842)+E(f400(x14843,x14841,x14844),f400(x14843,x14842,x14844))
% 155.94/155.64 [1485]~E(x14851,x14852)+E(f400(x14853,x14854,x14851),f400(x14853,x14854,x14852))
% 155.94/155.64 [1486]~E(x14861,x14862)+E(f746(x14861,x14863,x14864),f746(x14862,x14863,x14864))
% 155.94/155.64 [1487]~E(x14871,x14872)+E(f746(x14873,x14871,x14874),f746(x14873,x14872,x14874))
% 155.94/155.64 [1488]~E(x14881,x14882)+E(f746(x14883,x14884,x14881),f746(x14883,x14884,x14882))
% 155.94/155.64 [1489]~E(x14891,x14892)+E(f716(x14891,x14893,x14894,x14895,x14896,x14897),f716(x14892,x14893,x14894,x14895,x14896,x14897))
% 155.94/155.64 [1490]~E(x14901,x14902)+E(f716(x14903,x14901,x14904,x14905,x14906,x14907),f716(x14903,x14902,x14904,x14905,x14906,x14907))
% 155.94/155.64 [1491]~E(x14911,x14912)+E(f716(x14913,x14914,x14911,x14915,x14916,x14917),f716(x14913,x14914,x14912,x14915,x14916,x14917))
% 155.94/155.64 [1492]~E(x14921,x14922)+E(f716(x14923,x14924,x14925,x14921,x14926,x14927),f716(x14923,x14924,x14925,x14922,x14926,x14927))
% 155.94/155.64 [1493]~E(x14931,x14932)+E(f716(x14933,x14934,x14935,x14936,x14931,x14937),f716(x14933,x14934,x14935,x14936,x14932,x14937))
% 155.94/155.64 [1494]~E(x14941,x14942)+E(f716(x14943,x14944,x14945,x14946,x14947,x14941),f716(x14943,x14944,x14945,x14946,x14947,x14942))
% 155.94/155.64 [1495]~E(x14951,x14952)+E(f551(x14951,x14953,x14954,x14955,x14956,x14957),f551(x14952,x14953,x14954,x14955,x14956,x14957))
% 155.94/155.64 [1496]~E(x14961,x14962)+E(f551(x14963,x14961,x14964,x14965,x14966,x14967),f551(x14963,x14962,x14964,x14965,x14966,x14967))
% 155.94/155.64 [1497]~E(x14971,x14972)+E(f551(x14973,x14974,x14971,x14975,x14976,x14977),f551(x14973,x14974,x14972,x14975,x14976,x14977))
% 155.94/155.64 [1498]~E(x14981,x14982)+E(f551(x14983,x14984,x14985,x14981,x14986,x14987),f551(x14983,x14984,x14985,x14982,x14986,x14987))
% 155.94/155.64 [1499]~E(x14991,x14992)+E(f551(x14993,x14994,x14995,x14996,x14991,x14997),f551(x14993,x14994,x14995,x14996,x14992,x14997))
% 155.94/155.64 [1500]~E(x15001,x15002)+E(f551(x15003,x15004,x15005,x15006,x15007,x15001),f551(x15003,x15004,x15005,x15006,x15007,x15002))
% 155.94/155.64 [1501]~E(x15011,x15012)+E(f275(x15011,x15013,x15014,x15015,x15016),f275(x15012,x15013,x15014,x15015,x15016))
% 155.94/155.64 [1502]~E(x15021,x15022)+E(f275(x15023,x15021,x15024,x15025,x15026),f275(x15023,x15022,x15024,x15025,x15026))
% 155.94/155.64 [1503]~E(x15031,x15032)+E(f275(x15033,x15034,x15031,x15035,x15036),f275(x15033,x15034,x15032,x15035,x15036))
% 155.94/155.64 [1504]~E(x15041,x15042)+E(f275(x15043,x15044,x15045,x15041,x15046),f275(x15043,x15044,x15045,x15042,x15046))
% 155.94/155.64 [1505]~E(x15051,x15052)+E(f275(x15053,x15054,x15055,x15056,x15051),f275(x15053,x15054,x15055,x15056,x15052))
% 155.94/155.64 [1506]~E(x15061,x15062)+E(f350(x15061,x15063,x15064,x15065),f350(x15062,x15063,x15064,x15065))
% 155.94/155.64 [1507]~E(x15071,x15072)+E(f350(x15073,x15071,x15074,x15075),f350(x15073,x15072,x15074,x15075))
% 155.94/155.64 [1508]~E(x15081,x15082)+E(f350(x15083,x15084,x15081,x15085),f350(x15083,x15084,x15082,x15085))
% 155.94/155.64 [1509]~E(x15091,x15092)+E(f350(x15093,x15094,x15095,x15091),f350(x15093,x15094,x15095,x15092))
% 155.94/155.64 [1510]~E(x15101,x15102)+E(f650(x15101,x15103),f650(x15102,x15103))
% 155.94/155.64 [1511]~E(x15111,x15112)+E(f650(x15113,x15111),f650(x15113,x15112))
% 155.94/155.64 [1512]~E(x15121,x15122)+E(f478(x15121,x15123),f478(x15122,x15123))
% 155.94/155.64 [1513]~E(x15131,x15132)+E(f478(x15133,x15131),f478(x15133,x15132))
% 155.94/155.64 [1514]~E(x15141,x15142)+E(f355(x15141,x15143,x15144),f355(x15142,x15143,x15144))
% 155.94/155.64 [1515]~E(x15151,x15152)+E(f355(x15153,x15151,x15154),f355(x15153,x15152,x15154))
% 155.94/155.64 [1516]~E(x15161,x15162)+E(f355(x15163,x15164,x15161),f355(x15163,x15164,x15162))
% 155.94/155.64 [1517]~E(x15171,x15172)+E(f416(x15171,x15173,x15174,x15175,x15176,x15177,x15178),f416(x15172,x15173,x15174,x15175,x15176,x15177,x15178))
% 155.94/155.64 [1518]~E(x15181,x15182)+E(f416(x15183,x15181,x15184,x15185,x15186,x15187,x15188),f416(x15183,x15182,x15184,x15185,x15186,x15187,x15188))
% 155.94/155.64 [1519]~E(x15191,x15192)+E(f416(x15193,x15194,x15191,x15195,x15196,x15197,x15198),f416(x15193,x15194,x15192,x15195,x15196,x15197,x15198))
% 155.94/155.64 [1520]~E(x15201,x15202)+E(f416(x15203,x15204,x15205,x15201,x15206,x15207,x15208),f416(x15203,x15204,x15205,x15202,x15206,x15207,x15208))
% 155.94/155.64 [1521]~E(x15211,x15212)+E(f416(x15213,x15214,x15215,x15216,x15211,x15217,x15218),f416(x15213,x15214,x15215,x15216,x15212,x15217,x15218))
% 155.94/155.64 [1522]~E(x15221,x15222)+E(f416(x15223,x15224,x15225,x15226,x15227,x15221,x15228),f416(x15223,x15224,x15225,x15226,x15227,x15222,x15228))
% 155.94/155.64 [1523]~E(x15231,x15232)+E(f416(x15233,x15234,x15235,x15236,x15237,x15238,x15231),f416(x15233,x15234,x15235,x15236,x15237,x15238,x15232))
% 155.94/155.64 [1524]~E(x15241,x15242)+E(f639(x15241,x15243,x15244,x15245),f639(x15242,x15243,x15244,x15245))
% 155.94/155.64 [1525]~E(x15251,x15252)+E(f639(x15253,x15251,x15254,x15255),f639(x15253,x15252,x15254,x15255))
% 155.94/155.64 [1526]~E(x15261,x15262)+E(f639(x15263,x15264,x15261,x15265),f639(x15263,x15264,x15262,x15265))
% 155.94/155.64 [1527]~E(x15271,x15272)+E(f639(x15273,x15274,x15275,x15271),f639(x15273,x15274,x15275,x15272))
% 155.94/155.64 [1528]~E(x15281,x15282)+E(f636(x15281,x15283,x15284,x15285,x15286),f636(x15282,x15283,x15284,x15285,x15286))
% 155.94/155.64 [1529]~E(x15291,x15292)+E(f636(x15293,x15291,x15294,x15295,x15296),f636(x15293,x15292,x15294,x15295,x15296))
% 155.94/155.64 [1530]~E(x15301,x15302)+E(f636(x15303,x15304,x15301,x15305,x15306),f636(x15303,x15304,x15302,x15305,x15306))
% 155.94/155.64 [1531]~E(x15311,x15312)+E(f636(x15313,x15314,x15315,x15311,x15316),f636(x15313,x15314,x15315,x15312,x15316))
% 155.94/155.64 [1532]~E(x15321,x15322)+E(f636(x15323,x15324,x15325,x15326,x15321),f636(x15323,x15324,x15325,x15326,x15322))
% 155.94/155.64 [1533]~E(x15331,x15332)+E(f756(x15331,x15333,x15334),f756(x15332,x15333,x15334))
% 155.94/155.64 [1534]~E(x15341,x15342)+E(f756(x15343,x15341,x15344),f756(x15343,x15342,x15344))
% 155.94/155.64 [1535]~E(x15351,x15352)+E(f756(x15353,x15354,x15351),f756(x15353,x15354,x15352))
% 155.94/155.64 [1536]~E(x15361,x15362)+E(f422(x15361,x15363,x15364,x15365,x15366,x15367,x15368),f422(x15362,x15363,x15364,x15365,x15366,x15367,x15368))
% 155.94/155.64 [1537]~E(x15371,x15372)+E(f422(x15373,x15371,x15374,x15375,x15376,x15377,x15378),f422(x15373,x15372,x15374,x15375,x15376,x15377,x15378))
% 155.94/155.64 [1538]~E(x15381,x15382)+E(f422(x15383,x15384,x15381,x15385,x15386,x15387,x15388),f422(x15383,x15384,x15382,x15385,x15386,x15387,x15388))
% 155.94/155.64 [1539]~E(x15391,x15392)+E(f422(x15393,x15394,x15395,x15391,x15396,x15397,x15398),f422(x15393,x15394,x15395,x15392,x15396,x15397,x15398))
% 155.94/155.64 [1540]~E(x15401,x15402)+E(f422(x15403,x15404,x15405,x15406,x15401,x15407,x15408),f422(x15403,x15404,x15405,x15406,x15402,x15407,x15408))
% 155.94/155.64 [1541]~E(x15411,x15412)+E(f422(x15413,x15414,x15415,x15416,x15417,x15411,x15418),f422(x15413,x15414,x15415,x15416,x15417,x15412,x15418))
% 155.94/155.64 [1542]~E(x15421,x15422)+E(f422(x15423,x15424,x15425,x15426,x15427,x15428,x15421),f422(x15423,x15424,x15425,x15426,x15427,x15428,x15422))
% 155.94/155.64 [1543]~E(x15431,x15432)+E(f741(x15431,x15433,x15434,x15435),f741(x15432,x15433,x15434,x15435))
% 155.94/155.64 [1544]~E(x15441,x15442)+E(f741(x15443,x15441,x15444,x15445),f741(x15443,x15442,x15444,x15445))
% 155.94/155.64 [1545]~E(x15451,x15452)+E(f741(x15453,x15454,x15451,x15455),f741(x15453,x15454,x15452,x15455))
% 155.94/155.64 [1546]~E(x15461,x15462)+E(f741(x15463,x15464,x15465,x15461),f741(x15463,x15464,x15465,x15462))
% 155.94/155.64 [1547]~E(x15471,x15472)+E(f517(x15471,x15473,x15474,x15475,x15476),f517(x15472,x15473,x15474,x15475,x15476))
% 155.94/155.64 [1548]~E(x15481,x15482)+E(f517(x15483,x15481,x15484,x15485,x15486),f517(x15483,x15482,x15484,x15485,x15486))
% 155.94/155.64 [1549]~E(x15491,x15492)+E(f517(x15493,x15494,x15491,x15495,x15496),f517(x15493,x15494,x15492,x15495,x15496))
% 155.94/155.64 [1550]~E(x15501,x15502)+E(f517(x15503,x15504,x15505,x15501,x15506),f517(x15503,x15504,x15505,x15502,x15506))
% 155.94/155.64 [1551]~E(x15511,x15512)+E(f517(x15513,x15514,x15515,x15516,x15511),f517(x15513,x15514,x15515,x15516,x15512))
% 155.94/155.64 [1552]~E(x15521,x15522)+E(f253(x15521,x15523,x15524,x15525,x15526),f253(x15522,x15523,x15524,x15525,x15526))
% 155.94/155.64 [1553]~E(x15531,x15532)+E(f253(x15533,x15531,x15534,x15535,x15536),f253(x15533,x15532,x15534,x15535,x15536))
% 155.94/155.64 [1554]~E(x15541,x15542)+E(f253(x15543,x15544,x15541,x15545,x15546),f253(x15543,x15544,x15542,x15545,x15546))
% 155.94/155.64 [1555]~E(x15551,x15552)+E(f253(x15553,x15554,x15555,x15551,x15556),f253(x15553,x15554,x15555,x15552,x15556))
% 155.94/155.64 [1556]~E(x15561,x15562)+E(f253(x15563,x15564,x15565,x15566,x15561),f253(x15563,x15564,x15565,x15566,x15562))
% 155.94/155.64 [1557]~E(x15571,x15572)+E(f473(x15571,x15573,x15574,x15575),f473(x15572,x15573,x15574,x15575))
% 155.94/155.64 [1558]~E(x15581,x15582)+E(f473(x15583,x15581,x15584,x15585),f473(x15583,x15582,x15584,x15585))
% 155.94/155.64 [1559]~E(x15591,x15592)+E(f473(x15593,x15594,x15591,x15595),f473(x15593,x15594,x15592,x15595))
% 155.94/155.64 [1560]~E(x15601,x15602)+E(f473(x15603,x15604,x15605,x15601),f473(x15603,x15604,x15605,x15602))
% 155.94/155.64 [1561]~E(x15611,x15612)+E(f101(x15611,x15613,x15614),f101(x15612,x15613,x15614))
% 155.94/155.64 [1562]~E(x15621,x15622)+E(f101(x15623,x15621,x15624),f101(x15623,x15622,x15624))
% 155.94/155.64 [1563]~E(x15631,x15632)+E(f101(x15633,x15634,x15631),f101(x15633,x15634,x15632))
% 155.94/155.64 [1564]~E(x15641,x15642)+E(f323(x15641,x15643,x15644,x15645),f323(x15642,x15643,x15644,x15645))
% 155.94/155.64 [1565]~E(x15651,x15652)+E(f323(x15653,x15651,x15654,x15655),f323(x15653,x15652,x15654,x15655))
% 155.94/155.64 [1566]~E(x15661,x15662)+E(f323(x15663,x15664,x15661,x15665),f323(x15663,x15664,x15662,x15665))
% 155.94/155.64 [1567]~E(x15671,x15672)+E(f323(x15673,x15674,x15675,x15671),f323(x15673,x15674,x15675,x15672))
% 155.94/155.64 [1568]~E(x15681,x15682)+E(f743(x15681,x15683,x15684),f743(x15682,x15683,x15684))
% 155.94/155.64 [1569]~E(x15691,x15692)+E(f743(x15693,x15691,x15694),f743(x15693,x15692,x15694))
% 155.94/155.64 [1570]~E(x15701,x15702)+E(f743(x15703,x15704,x15701),f743(x15703,x15704,x15702))
% 155.94/155.64 [1571]~E(x15711,x15712)+E(f644(x15711,x15713,x15714),f644(x15712,x15713,x15714))
% 155.94/155.64 [1572]~E(x15721,x15722)+E(f644(x15723,x15721,x15724),f644(x15723,x15722,x15724))
% 155.94/155.64 [1573]~E(x15731,x15732)+E(f644(x15733,x15734,x15731),f644(x15733,x15734,x15732))
% 155.94/155.64 [1574]~E(x15741,x15742)+E(f772(x15741,x15743,x15744,x15745,x15746),f772(x15742,x15743,x15744,x15745,x15746))
% 155.94/155.64 [1575]~E(x15751,x15752)+E(f772(x15753,x15751,x15754,x15755,x15756),f772(x15753,x15752,x15754,x15755,x15756))
% 155.94/155.64 [1576]~E(x15761,x15762)+E(f772(x15763,x15764,x15761,x15765,x15766),f772(x15763,x15764,x15762,x15765,x15766))
% 155.94/155.64 [1577]~E(x15771,x15772)+E(f772(x15773,x15774,x15775,x15771,x15776),f772(x15773,x15774,x15775,x15772,x15776))
% 155.94/155.64 [1578]~E(x15781,x15782)+E(f772(x15783,x15784,x15785,x15786,x15781),f772(x15783,x15784,x15785,x15786,x15782))
% 155.94/155.64 [1579]~E(x15791,x15792)+E(f339(x15791,x15793,x15794),f339(x15792,x15793,x15794))
% 155.94/155.64 [1580]~E(x15801,x15802)+E(f339(x15803,x15801,x15804),f339(x15803,x15802,x15804))
% 155.94/155.64 [1581]~E(x15811,x15812)+E(f339(x15813,x15814,x15811),f339(x15813,x15814,x15812))
% 155.94/155.64 [1582]~E(x15821,x15822)+E(f810(x15821,x15823,x15824,x15825),f810(x15822,x15823,x15824,x15825))
% 155.94/155.64 [1583]~E(x15831,x15832)+E(f810(x15833,x15831,x15834,x15835),f810(x15833,x15832,x15834,x15835))
% 155.94/155.64 [1584]~E(x15841,x15842)+E(f810(x15843,x15844,x15841,x15845),f810(x15843,x15844,x15842,x15845))
% 155.94/155.64 [1585]~E(x15851,x15852)+E(f810(x15853,x15854,x15855,x15851),f810(x15853,x15854,x15855,x15852))
% 155.94/155.64 [1586]~E(x15861,x15862)+E(f569(x15861,x15863,x15864,x15865),f569(x15862,x15863,x15864,x15865))
% 155.94/155.64 [1587]~E(x15871,x15872)+E(f569(x15873,x15871,x15874,x15875),f569(x15873,x15872,x15874,x15875))
% 155.94/155.64 [1588]~E(x15881,x15882)+E(f569(x15883,x15884,x15881,x15885),f569(x15883,x15884,x15882,x15885))
% 155.94/155.64 [1589]~E(x15891,x15892)+E(f569(x15893,x15894,x15895,x15891),f569(x15893,x15894,x15895,x15892))
% 155.94/155.64 [1590]~E(x15901,x15902)+E(f425(x15901,x15903,x15904,x15905),f425(x15902,x15903,x15904,x15905))
% 155.94/155.64 [1591]~E(x15911,x15912)+E(f425(x15913,x15911,x15914,x15915),f425(x15913,x15912,x15914,x15915))
% 155.94/155.64 [1592]~E(x15921,x15922)+E(f425(x15923,x15924,x15921,x15925),f425(x15923,x15924,x15922,x15925))
% 155.94/155.64 [1593]~E(x15931,x15932)+E(f425(x15933,x15934,x15935,x15931),f425(x15933,x15934,x15935,x15932))
% 155.94/155.64 [1594]~E(x15941,x15942)+E(f710(x15941,x15943,x15944,x15945,x15946,x15947),f710(x15942,x15943,x15944,x15945,x15946,x15947))
% 155.94/155.64 [1595]~E(x15951,x15952)+E(f710(x15953,x15951,x15954,x15955,x15956,x15957),f710(x15953,x15952,x15954,x15955,x15956,x15957))
% 155.94/155.64 [1596]~E(x15961,x15962)+E(f710(x15963,x15964,x15961,x15965,x15966,x15967),f710(x15963,x15964,x15962,x15965,x15966,x15967))
% 155.94/155.64 [1597]~E(x15971,x15972)+E(f710(x15973,x15974,x15975,x15971,x15976,x15977),f710(x15973,x15974,x15975,x15972,x15976,x15977))
% 155.94/155.64 [1598]~E(x15981,x15982)+E(f710(x15983,x15984,x15985,x15986,x15981,x15987),f710(x15983,x15984,x15985,x15986,x15982,x15987))
% 155.94/155.64 [1599]~E(x15991,x15992)+E(f710(x15993,x15994,x15995,x15996,x15997,x15991),f710(x15993,x15994,x15995,x15996,x15997,x15992))
% 155.94/155.64 [1600]~E(x16001,x16002)+E(f322(x16001,x16003,x16004),f322(x16002,x16003,x16004))
% 155.94/155.64 [1601]~E(x16011,x16012)+E(f322(x16013,x16011,x16014),f322(x16013,x16012,x16014))
% 155.94/155.64 [1602]~E(x16021,x16022)+E(f322(x16023,x16024,x16021),f322(x16023,x16024,x16022))
% 155.94/155.64 [1603]~E(x16031,x16032)+E(f476(x16031,x16033),f476(x16032,x16033))
% 155.94/155.64 [1604]~E(x16041,x16042)+E(f476(x16043,x16041),f476(x16043,x16042))
% 155.94/155.64 [1605]~E(x16051,x16052)+E(f604(x16051,x16053,x16054,x16055),f604(x16052,x16053,x16054,x16055))
% 155.94/155.64 [1606]~E(x16061,x16062)+E(f604(x16063,x16061,x16064,x16065),f604(x16063,x16062,x16064,x16065))
% 155.94/155.64 [1607]~E(x16071,x16072)+E(f604(x16073,x16074,x16071,x16075),f604(x16073,x16074,x16072,x16075))
% 155.94/155.64 [1608]~E(x16081,x16082)+E(f604(x16083,x16084,x16085,x16081),f604(x16083,x16084,x16085,x16082))
% 155.94/155.64 [1609]~E(x16091,x16092)+E(f469(x16091,x16093,x16094,x16095),f469(x16092,x16093,x16094,x16095))
% 155.94/155.64 [1610]~E(x16101,x16102)+E(f469(x16103,x16101,x16104,x16105),f469(x16103,x16102,x16104,x16105))
% 155.94/155.64 [1611]~E(x16111,x16112)+E(f469(x16113,x16114,x16111,x16115),f469(x16113,x16114,x16112,x16115))
% 155.94/155.64 [1612]~E(x16121,x16122)+E(f469(x16123,x16124,x16125,x16121),f469(x16123,x16124,x16125,x16122))
% 155.94/155.64 [1613]~E(x16131,x16132)+E(f812(x16131,x16133,x16134),f812(x16132,x16133,x16134))
% 155.94/155.64 [1614]~E(x16141,x16142)+E(f812(x16143,x16141,x16144),f812(x16143,x16142,x16144))
% 155.94/155.64 [1615]~E(x16151,x16152)+E(f812(x16153,x16154,x16151),f812(x16153,x16154,x16152))
% 155.94/155.64 [1616]~E(x16161,x16162)+E(f525(x16161,x16163,x16164,x16165),f525(x16162,x16163,x16164,x16165))
% 155.94/155.64 [1617]~E(x16171,x16172)+E(f525(x16173,x16171,x16174,x16175),f525(x16173,x16172,x16174,x16175))
% 155.94/155.64 [1618]~E(x16181,x16182)+E(f525(x16183,x16184,x16181,x16185),f525(x16183,x16184,x16182,x16185))
% 155.94/155.64 [1619]~E(x16191,x16192)+E(f525(x16193,x16194,x16195,x16191),f525(x16193,x16194,x16195,x16192))
% 155.94/155.64 [1620]~E(x16201,x16202)+E(f612(x16201,x16203),f612(x16202,x16203))
% 155.94/155.64 [1621]~E(x16211,x16212)+E(f612(x16213,x16211),f612(x16213,x16212))
% 155.94/155.64 [1622]~E(x16221,x16222)+E(f843(x16221,x16223,x16224),f843(x16222,x16223,x16224))
% 155.94/155.64 [1623]~E(x16231,x16232)+E(f843(x16233,x16231,x16234),f843(x16233,x16232,x16234))
% 155.94/155.64 [1624]~E(x16241,x16242)+E(f843(x16243,x16244,x16241),f843(x16243,x16244,x16242))
% 155.94/155.64 [1625]~E(x16251,x16252)+E(f494(x16251,x16253),f494(x16252,x16253))
% 155.94/155.64 [1626]~E(x16261,x16262)+E(f494(x16263,x16261),f494(x16263,x16262))
% 155.94/155.64 [1627]~E(x16271,x16272)+E(f799(x16271,x16273,x16274,x16275),f799(x16272,x16273,x16274,x16275))
% 155.94/155.64 [1628]~E(x16281,x16282)+E(f799(x16283,x16281,x16284,x16285),f799(x16283,x16282,x16284,x16285))
% 155.94/155.64 [1629]~E(x16291,x16292)+E(f799(x16293,x16294,x16291,x16295),f799(x16293,x16294,x16292,x16295))
% 155.94/155.64 [1630]~E(x16301,x16302)+E(f799(x16303,x16304,x16305,x16301),f799(x16303,x16304,x16305,x16302))
% 155.94/155.64 [1631]~E(x16311,x16312)+E(f269(x16311,x16313),f269(x16312,x16313))
% 155.94/155.64 [1632]~E(x16321,x16322)+E(f269(x16323,x16321),f269(x16323,x16322))
% 155.94/155.64 [1633]~E(x16331,x16332)+E(f231(x16331,x16333),f231(x16332,x16333))
% 155.94/155.64 [1634]~E(x16341,x16342)+E(f231(x16343,x16341),f231(x16343,x16342))
% 155.94/155.64 [1635]~E(x16351,x16352)+E(f598(x16351,x16353,x16354),f598(x16352,x16353,x16354))
% 155.94/155.64 [1636]~E(x16361,x16362)+E(f598(x16363,x16361,x16364),f598(x16363,x16362,x16364))
% 155.94/155.64 [1637]~E(x16371,x16372)+E(f598(x16373,x16374,x16371),f598(x16373,x16374,x16372))
% 155.94/155.64 [1638]~E(x16381,x16382)+E(f711(x16381,x16383,x16384),f711(x16382,x16383,x16384))
% 155.94/155.64 [1639]~E(x16391,x16392)+E(f711(x16393,x16391,x16394),f711(x16393,x16392,x16394))
% 155.94/155.64 [1640]~E(x16401,x16402)+E(f711(x16403,x16404,x16401),f711(x16403,x16404,x16402))
% 155.94/155.64 [1641]~E(x16411,x16412)+E(f749(x16411,x16413,x16414),f749(x16412,x16413,x16414))
% 155.94/155.64 [1642]~E(x16421,x16422)+E(f749(x16423,x16421,x16424),f749(x16423,x16422,x16424))
% 155.94/155.64 [1643]~E(x16431,x16432)+E(f749(x16433,x16434,x16431),f749(x16433,x16434,x16432))
% 155.94/155.64 [1644]~E(x16441,x16442)+E(f591(x16441,x16443,x16444,x16445),f591(x16442,x16443,x16444,x16445))
% 155.94/155.64 [1645]~E(x16451,x16452)+E(f591(x16453,x16451,x16454,x16455),f591(x16453,x16452,x16454,x16455))
% 155.94/155.64 [1646]~E(x16461,x16462)+E(f591(x16463,x16464,x16461,x16465),f591(x16463,x16464,x16462,x16465))
% 155.94/155.64 [1647]~E(x16471,x16472)+E(f591(x16473,x16474,x16475,x16471),f591(x16473,x16474,x16475,x16472))
% 155.94/155.64 [1648]~E(x16481,x16482)+E(f486(x16481,x16483,x16484,x16485,x16486),f486(x16482,x16483,x16484,x16485,x16486))
% 155.94/155.64 [1649]~E(x16491,x16492)+E(f486(x16493,x16491,x16494,x16495,x16496),f486(x16493,x16492,x16494,x16495,x16496))
% 155.94/155.64 [1650]~E(x16501,x16502)+E(f486(x16503,x16504,x16501,x16505,x16506),f486(x16503,x16504,x16502,x16505,x16506))
% 155.94/155.64 [1651]~E(x16511,x16512)+E(f486(x16513,x16514,x16515,x16511,x16516),f486(x16513,x16514,x16515,x16512,x16516))
% 155.94/155.64 [1652]~E(x16521,x16522)+E(f486(x16523,x16524,x16525,x16526,x16521),f486(x16523,x16524,x16525,x16526,x16522))
% 155.94/155.64 [1653]~E(x16531,x16532)+E(f629(x16531,x16533,x16534,x16535,x16536),f629(x16532,x16533,x16534,x16535,x16536))
% 155.94/155.64 [1654]~E(x16541,x16542)+E(f629(x16543,x16541,x16544,x16545,x16546),f629(x16543,x16542,x16544,x16545,x16546))
% 155.94/155.64 [1655]~E(x16551,x16552)+E(f629(x16553,x16554,x16551,x16555,x16556),f629(x16553,x16554,x16552,x16555,x16556))
% 155.94/155.64 [1656]~E(x16561,x16562)+E(f629(x16563,x16564,x16565,x16561,x16566),f629(x16563,x16564,x16565,x16562,x16566))
% 155.94/155.64 [1657]~E(x16571,x16572)+E(f629(x16573,x16574,x16575,x16576,x16571),f629(x16573,x16574,x16575,x16576,x16572))
% 155.94/155.64 [1658]~E(x16581,x16582)+E(f628(x16581,x16583,x16584,x16585),f628(x16582,x16583,x16584,x16585))
% 155.94/155.64 [1659]~E(x16591,x16592)+E(f628(x16593,x16591,x16594,x16595),f628(x16593,x16592,x16594,x16595))
% 155.94/155.64 [1660]~E(x16601,x16602)+E(f628(x16603,x16604,x16601,x16605),f628(x16603,x16604,x16602,x16605))
% 155.94/155.64 [1661]~E(x16611,x16612)+E(f628(x16613,x16614,x16615,x16611),f628(x16613,x16614,x16615,x16612))
% 155.94/155.64 [1662]~E(x16621,x16622)+E(f461(x16621,x16623,x16624,x16625),f461(x16622,x16623,x16624,x16625))
% 155.94/155.64 [1663]~E(x16631,x16632)+E(f461(x16633,x16631,x16634,x16635),f461(x16633,x16632,x16634,x16635))
% 155.94/155.64 [1664]~E(x16641,x16642)+E(f461(x16643,x16644,x16641,x16645),f461(x16643,x16644,x16642,x16645))
% 155.94/155.64 [1665]~E(x16651,x16652)+E(f461(x16653,x16654,x16655,x16651),f461(x16653,x16654,x16655,x16652))
% 155.94/155.64 [1666]~E(x16661,x16662)+E(f508(x16661,x16663,x16664,x16665,x16666),f508(x16662,x16663,x16664,x16665,x16666))
% 155.94/155.64 [1667]~E(x16671,x16672)+E(f508(x16673,x16671,x16674,x16675,x16676),f508(x16673,x16672,x16674,x16675,x16676))
% 155.94/155.64 [1668]~E(x16681,x16682)+E(f508(x16683,x16684,x16681,x16685,x16686),f508(x16683,x16684,x16682,x16685,x16686))
% 155.94/155.64 [1669]~E(x16691,x16692)+E(f508(x16693,x16694,x16695,x16691,x16696),f508(x16693,x16694,x16695,x16692,x16696))
% 155.94/155.64 [1670]~E(x16701,x16702)+E(f508(x16703,x16704,x16705,x16706,x16701),f508(x16703,x16704,x16705,x16706,x16702))
% 155.94/155.64 [1671]~E(x16711,x16712)+E(f104(x16711,x16713,x16714,x16715),f104(x16712,x16713,x16714,x16715))
% 155.94/155.64 [1672]~E(x16721,x16722)+E(f104(x16723,x16721,x16724,x16725),f104(x16723,x16722,x16724,x16725))
% 155.94/155.64 [1673]~E(x16731,x16732)+E(f104(x16733,x16734,x16731,x16735),f104(x16733,x16734,x16732,x16735))
% 155.94/155.64 [1674]~E(x16741,x16742)+E(f104(x16743,x16744,x16745,x16741),f104(x16743,x16744,x16745,x16742))
% 155.94/155.64 [1675]~E(x16751,x16752)+E(f779(x16751,x16753,x16754,x16755),f779(x16752,x16753,x16754,x16755))
% 155.94/155.64 [1676]~E(x16761,x16762)+E(f779(x16763,x16761,x16764,x16765),f779(x16763,x16762,x16764,x16765))
% 155.94/155.64 [1677]~E(x16771,x16772)+E(f779(x16773,x16774,x16771,x16775),f779(x16773,x16774,x16772,x16775))
% 155.94/155.64 [1678]~E(x16781,x16782)+E(f779(x16783,x16784,x16785,x16781),f779(x16783,x16784,x16785,x16782))
% 155.94/155.64 [1679]~E(x16791,x16792)+E(f359(x16791,x16793,x16794,x16795,x16796),f359(x16792,x16793,x16794,x16795,x16796))
% 155.94/155.64 [1680]~E(x16801,x16802)+E(f359(x16803,x16801,x16804,x16805,x16806),f359(x16803,x16802,x16804,x16805,x16806))
% 155.94/155.64 [1681]~E(x16811,x16812)+E(f359(x16813,x16814,x16811,x16815,x16816),f359(x16813,x16814,x16812,x16815,x16816))
% 155.94/155.64 [1682]~E(x16821,x16822)+E(f359(x16823,x16824,x16825,x16821,x16826),f359(x16823,x16824,x16825,x16822,x16826))
% 155.94/155.64 [1683]~E(x16831,x16832)+E(f359(x16833,x16834,x16835,x16836,x16831),f359(x16833,x16834,x16835,x16836,x16832))
% 155.94/155.64 [1684]~E(x16841,x16842)+E(f405(x16841,x16843,x16844,x16845,x16846),f405(x16842,x16843,x16844,x16845,x16846))
% 155.94/155.64 [1685]~E(x16851,x16852)+E(f405(x16853,x16851,x16854,x16855,x16856),f405(x16853,x16852,x16854,x16855,x16856))
% 155.94/155.64 [1686]~E(x16861,x16862)+E(f405(x16863,x16864,x16861,x16865,x16866),f405(x16863,x16864,x16862,x16865,x16866))
% 155.94/155.64 [1687]~E(x16871,x16872)+E(f405(x16873,x16874,x16875,x16871,x16876),f405(x16873,x16874,x16875,x16872,x16876))
% 155.94/155.64 [1688]~E(x16881,x16882)+E(f405(x16883,x16884,x16885,x16886,x16881),f405(x16883,x16884,x16885,x16886,x16882))
% 155.94/155.64 [1689]~E(x16891,x16892)+E(f403(x16891,x16893,x16894,x16895),f403(x16892,x16893,x16894,x16895))
% 155.94/155.64 [1690]~E(x16901,x16902)+E(f403(x16903,x16901,x16904,x16905),f403(x16903,x16902,x16904,x16905))
% 155.94/155.64 [1691]~E(x16911,x16912)+E(f403(x16913,x16914,x16911,x16915),f403(x16913,x16914,x16912,x16915))
% 155.94/155.64 [1692]~E(x16921,x16922)+E(f403(x16923,x16924,x16925,x16921),f403(x16923,x16924,x16925,x16922))
% 155.94/155.64 [1693]~E(x16931,x16932)+E(f637(x16931,x16933,x16934,x16935,x16936),f637(x16932,x16933,x16934,x16935,x16936))
% 155.94/155.64 [1694]~E(x16941,x16942)+E(f637(x16943,x16941,x16944,x16945,x16946),f637(x16943,x16942,x16944,x16945,x16946))
% 155.94/155.64 [1695]~E(x16951,x16952)+E(f637(x16953,x16954,x16951,x16955,x16956),f637(x16953,x16954,x16952,x16955,x16956))
% 155.94/155.64 [1696]~E(x16961,x16962)+E(f637(x16963,x16964,x16965,x16961,x16966),f637(x16963,x16964,x16965,x16962,x16966))
% 155.94/155.64 [1697]~E(x16971,x16972)+E(f637(x16973,x16974,x16975,x16976,x16971),f637(x16973,x16974,x16975,x16976,x16972))
% 155.94/155.64 [1698]~E(x16981,x16982)+E(f706(x16981,x16983,x16984,x16985),f706(x16982,x16983,x16984,x16985))
% 155.94/155.64 [1699]~E(x16991,x16992)+E(f706(x16993,x16991,x16994,x16995),f706(x16993,x16992,x16994,x16995))
% 155.94/155.64 [1700]~E(x17001,x17002)+E(f706(x17003,x17004,x17001,x17005),f706(x17003,x17004,x17002,x17005))
% 155.94/155.64 [1701]~E(x17011,x17012)+E(f706(x17013,x17014,x17015,x17011),f706(x17013,x17014,x17015,x17012))
% 155.94/155.64 [1702]~E(x17021,x17022)+E(f739(x17021,x17023,x17024,x17025),f739(x17022,x17023,x17024,x17025))
% 155.94/155.64 [1703]~E(x17031,x17032)+E(f739(x17033,x17031,x17034,x17035),f739(x17033,x17032,x17034,x17035))
% 155.94/155.64 [1704]~E(x17041,x17042)+E(f739(x17043,x17044,x17041,x17045),f739(x17043,x17044,x17042,x17045))
% 155.94/155.64 [1705]~E(x17051,x17052)+E(f739(x17053,x17054,x17055,x17051),f739(x17053,x17054,x17055,x17052))
% 155.94/155.64 [1706]~E(x17061,x17062)+E(f277(x17061,x17063,x17064,x17065),f277(x17062,x17063,x17064,x17065))
% 155.94/155.64 [1707]~E(x17071,x17072)+E(f277(x17073,x17071,x17074,x17075),f277(x17073,x17072,x17074,x17075))
% 155.94/155.64 [1708]~E(x17081,x17082)+E(f277(x17083,x17084,x17081,x17085),f277(x17083,x17084,x17082,x17085))
% 155.94/155.64 [1709]~E(x17091,x17092)+E(f277(x17093,x17094,x17095,x17091),f277(x17093,x17094,x17095,x17092))
% 155.94/155.64 [1710]~E(x17101,x17102)+E(f765(x17101,x17103,x17104),f765(x17102,x17103,x17104))
% 155.94/155.64 [1711]~E(x17111,x17112)+E(f765(x17113,x17111,x17114),f765(x17113,x17112,x17114))
% 155.94/155.64 [1712]~E(x17121,x17122)+E(f765(x17123,x17124,x17121),f765(x17123,x17124,x17122))
% 155.94/155.64 [1713]~E(x17131,x17132)+E(f332(x17131,x17133,x17134),f332(x17132,x17133,x17134))
% 155.94/155.64 [1714]~E(x17141,x17142)+E(f332(x17143,x17141,x17144),f332(x17143,x17142,x17144))
% 155.94/155.64 [1715]~E(x17151,x17152)+E(f332(x17153,x17154,x17151),f332(x17153,x17154,x17152))
% 155.94/155.64 [1716]~E(x17161,x17162)+E(f832(x17161),f832(x17162))
% 155.94/155.64 [1717]~E(x17171,x17172)+E(f597(x17171,x17173,x17174),f597(x17172,x17173,x17174))
% 155.94/155.64 [1718]~E(x17181,x17182)+E(f597(x17183,x17181,x17184),f597(x17183,x17182,x17184))
% 155.94/155.64 [1719]~E(x17191,x17192)+E(f597(x17193,x17194,x17191),f597(x17193,x17194,x17192))
% 155.94/155.64 [1720]~E(x17201,x17202)+E(f516(x17201,x17203,x17204,x17205),f516(x17202,x17203,x17204,x17205))
% 155.94/155.64 [1721]~E(x17211,x17212)+E(f516(x17213,x17211,x17214,x17215),f516(x17213,x17212,x17214,x17215))
% 155.94/155.64 [1722]~E(x17221,x17222)+E(f516(x17223,x17224,x17221,x17225),f516(x17223,x17224,x17222,x17225))
% 155.94/155.64 [1723]~E(x17231,x17232)+E(f516(x17233,x17234,x17235,x17231),f516(x17233,x17234,x17235,x17232))
% 155.94/155.64 [1724]~E(x17241,x17242)+E(f647(x17241,x17243,x17244),f647(x17242,x17243,x17244))
% 155.94/155.64 [1725]~E(x17251,x17252)+E(f647(x17253,x17251,x17254),f647(x17253,x17252,x17254))
% 155.94/155.64 [1726]~E(x17261,x17262)+E(f647(x17263,x17264,x17261),f647(x17263,x17264,x17262))
% 155.94/155.64 [1727]~E(x17271,x17272)+E(f559(x17271,x17273,x17274,x17275,x17276),f559(x17272,x17273,x17274,x17275,x17276))
% 155.94/155.64 [1728]~E(x17281,x17282)+E(f559(x17283,x17281,x17284,x17285,x17286),f559(x17283,x17282,x17284,x17285,x17286))
% 155.94/155.64 [1729]~E(x17291,x17292)+E(f559(x17293,x17294,x17291,x17295,x17296),f559(x17293,x17294,x17292,x17295,x17296))
% 155.94/155.64 [1730]~E(x17301,x17302)+E(f559(x17303,x17304,x17305,x17301,x17306),f559(x17303,x17304,x17305,x17302,x17306))
% 155.94/155.64 [1731]~E(x17311,x17312)+E(f559(x17313,x17314,x17315,x17316,x17311),f559(x17313,x17314,x17315,x17316,x17312))
% 155.94/155.64 [1732]~E(x17321,x17322)+E(f766(x17321,x17323,x17324,x17325,x17326),f766(x17322,x17323,x17324,x17325,x17326))
% 155.94/155.64 [1733]~E(x17331,x17332)+E(f766(x17333,x17331,x17334,x17335,x17336),f766(x17333,x17332,x17334,x17335,x17336))
% 155.94/155.64 [1734]~E(x17341,x17342)+E(f766(x17343,x17344,x17341,x17345,x17346),f766(x17343,x17344,x17342,x17345,x17346))
% 155.94/155.64 [1735]~E(x17351,x17352)+E(f766(x17353,x17354,x17355,x17351,x17356),f766(x17353,x17354,x17355,x17352,x17356))
% 155.94/155.64 [1736]~E(x17361,x17362)+E(f766(x17363,x17364,x17365,x17366,x17361),f766(x17363,x17364,x17365,x17366,x17362))
% 155.94/155.64 [1737]~E(x17371,x17372)+E(f262(x17371,x17373,x17374,x17375),f262(x17372,x17373,x17374,x17375))
% 155.94/155.64 [1738]~E(x17381,x17382)+E(f262(x17383,x17381,x17384,x17385),f262(x17383,x17382,x17384,x17385))
% 155.94/155.64 [1739]~E(x17391,x17392)+E(f262(x17393,x17394,x17391,x17395),f262(x17393,x17394,x17392,x17395))
% 155.94/155.64 [1740]~E(x17401,x17402)+E(f262(x17403,x17404,x17405,x17401),f262(x17403,x17404,x17405,x17402))
% 155.94/155.64 [1741]~E(x17411,x17412)+E(f782(x17411,x17413,x17414),f782(x17412,x17413,x17414))
% 155.94/155.64 [1742]~E(x17421,x17422)+E(f782(x17423,x17421,x17424),f782(x17423,x17422,x17424))
% 155.94/155.64 [1743]~E(x17431,x17432)+E(f782(x17433,x17434,x17431),f782(x17433,x17434,x17432))
% 155.94/155.64 [1744]~E(x17441,x17442)+E(f502(x17441,x17443,x17444,x17445,x17446,x17447),f502(x17442,x17443,x17444,x17445,x17446,x17447))
% 155.94/155.64 [1745]~E(x17451,x17452)+E(f502(x17453,x17451,x17454,x17455,x17456,x17457),f502(x17453,x17452,x17454,x17455,x17456,x17457))
% 155.94/155.64 [1746]~E(x17461,x17462)+E(f502(x17463,x17464,x17461,x17465,x17466,x17467),f502(x17463,x17464,x17462,x17465,x17466,x17467))
% 155.94/155.64 [1747]~E(x17471,x17472)+E(f502(x17473,x17474,x17475,x17471,x17476,x17477),f502(x17473,x17474,x17475,x17472,x17476,x17477))
% 155.94/155.64 [1748]~E(x17481,x17482)+E(f502(x17483,x17484,x17485,x17486,x17481,x17487),f502(x17483,x17484,x17485,x17486,x17482,x17487))
% 155.94/155.64 [1749]~E(x17491,x17492)+E(f502(x17493,x17494,x17495,x17496,x17497,x17491),f502(x17493,x17494,x17495,x17496,x17497,x17492))
% 155.94/155.64 [1750]~E(x17501,x17502)+E(f785(x17501,x17503),f785(x17502,x17503))
% 155.94/155.64 [1751]~E(x17511,x17512)+E(f785(x17513,x17511),f785(x17513,x17512))
% 155.94/155.64 [1752]~E(x17521,x17522)+E(f839(x17521,x17523),f839(x17522,x17523))
% 155.94/155.64 [1753]~E(x17531,x17532)+E(f839(x17533,x17531),f839(x17533,x17532))
% 155.94/155.64 [1754]~E(x17541,x17542)+E(f449(x17541,x17543,x17544,x17545),f449(x17542,x17543,x17544,x17545))
% 155.94/155.64 [1755]~E(x17551,x17552)+E(f449(x17553,x17551,x17554,x17555),f449(x17553,x17552,x17554,x17555))
% 155.94/155.64 [1756]~E(x17561,x17562)+E(f449(x17563,x17564,x17561,x17565),f449(x17563,x17564,x17562,x17565))
% 155.94/155.64 [1757]~E(x17571,x17572)+E(f449(x17573,x17574,x17575,x17571),f449(x17573,x17574,x17575,x17572))
% 155.94/155.64 [1758]~E(x17581,x17582)+E(f642(x17581,x17583,x17584,x17585,x17586,x17587,x17588),f642(x17582,x17583,x17584,x17585,x17586,x17587,x17588))
% 155.94/155.64 [1759]~E(x17591,x17592)+E(f642(x17593,x17591,x17594,x17595,x17596,x17597,x17598),f642(x17593,x17592,x17594,x17595,x17596,x17597,x17598))
% 155.94/155.64 [1760]~E(x17601,x17602)+E(f642(x17603,x17604,x17601,x17605,x17606,x17607,x17608),f642(x17603,x17604,x17602,x17605,x17606,x17607,x17608))
% 155.94/155.64 [1761]~E(x17611,x17612)+E(f642(x17613,x17614,x17615,x17611,x17616,x17617,x17618),f642(x17613,x17614,x17615,x17612,x17616,x17617,x17618))
% 155.94/155.64 [1762]~E(x17621,x17622)+E(f642(x17623,x17624,x17625,x17626,x17621,x17627,x17628),f642(x17623,x17624,x17625,x17626,x17622,x17627,x17628))
% 155.94/155.64 [1763]~E(x17631,x17632)+E(f642(x17633,x17634,x17635,x17636,x17637,x17631,x17638),f642(x17633,x17634,x17635,x17636,x17637,x17632,x17638))
% 155.94/155.64 [1764]~E(x17641,x17642)+E(f642(x17643,x17644,x17645,x17646,x17647,x17648,x17641),f642(x17643,x17644,x17645,x17646,x17647,x17648,x17642))
% 155.94/155.64 [1765]~E(x17651,x17652)+E(f534(x17651,x17653,x17654,x17655,x17656,x17657,x17658,x17659),f534(x17652,x17653,x17654,x17655,x17656,x17657,x17658,x17659))
% 155.94/155.64 [1766]~E(x17661,x17662)+E(f534(x17663,x17661,x17664,x17665,x17666,x17667,x17668,x17669),f534(x17663,x17662,x17664,x17665,x17666,x17667,x17668,x17669))
% 155.94/155.64 [1767]~E(x17671,x17672)+E(f534(x17673,x17674,x17671,x17675,x17676,x17677,x17678,x17679),f534(x17673,x17674,x17672,x17675,x17676,x17677,x17678,x17679))
% 155.94/155.64 [1768]~E(x17681,x17682)+E(f534(x17683,x17684,x17685,x17681,x17686,x17687,x17688,x17689),f534(x17683,x17684,x17685,x17682,x17686,x17687,x17688,x17689))
% 155.94/155.64 [1769]~E(x17691,x17692)+E(f534(x17693,x17694,x17695,x17696,x17691,x17697,x17698,x17699),f534(x17693,x17694,x17695,x17696,x17692,x17697,x17698,x17699))
% 155.94/155.64 [1770]~E(x17701,x17702)+E(f534(x17703,x17704,x17705,x17706,x17707,x17701,x17708,x17709),f534(x17703,x17704,x17705,x17706,x17707,x17702,x17708,x17709))
% 155.94/155.64 [1771]~E(x17711,x17712)+E(f534(x17713,x17714,x17715,x17716,x17717,x17718,x17711,x17719),f534(x17713,x17714,x17715,x17716,x17717,x17718,x17712,x17719))
% 155.94/155.64 [1772]~E(x17721,x17722)+E(f534(x17723,x17724,x17725,x17726,x17727,x17728,x17729,x17721),f534(x17723,x17724,x17725,x17726,x17727,x17728,x17729,x17722))
% 155.94/155.64 [1773]~E(x17731,x17732)+E(f394(x17731),f394(x17732))
% 155.94/155.64 [1774]~E(x17741,x17742)+E(f354(x17741,x17743,x17744),f354(x17742,x17743,x17744))
% 155.94/155.64 [1775]~E(x17751,x17752)+E(f354(x17753,x17751,x17754),f354(x17753,x17752,x17754))
% 155.94/155.64 [1776]~E(x17761,x17762)+E(f354(x17763,x17764,x17761),f354(x17763,x17764,x17762))
% 155.94/155.64 [1777]~E(x17771,x17772)+E(f734(x17771,x17773,x17774,x17775,x17776,x17777,x17778),f734(x17772,x17773,x17774,x17775,x17776,x17777,x17778))
% 155.94/155.64 [1778]~E(x17781,x17782)+E(f734(x17783,x17781,x17784,x17785,x17786,x17787,x17788),f734(x17783,x17782,x17784,x17785,x17786,x17787,x17788))
% 155.94/155.64 [1779]~E(x17791,x17792)+E(f734(x17793,x17794,x17791,x17795,x17796,x17797,x17798),f734(x17793,x17794,x17792,x17795,x17796,x17797,x17798))
% 155.94/155.64 [1780]~E(x17801,x17802)+E(f734(x17803,x17804,x17805,x17801,x17806,x17807,x17808),f734(x17803,x17804,x17805,x17802,x17806,x17807,x17808))
% 155.94/155.64 [1781]~E(x17811,x17812)+E(f734(x17813,x17814,x17815,x17816,x17811,x17817,x17818),f734(x17813,x17814,x17815,x17816,x17812,x17817,x17818))
% 155.94/155.64 [1782]~E(x17821,x17822)+E(f734(x17823,x17824,x17825,x17826,x17827,x17821,x17828),f734(x17823,x17824,x17825,x17826,x17827,x17822,x17828))
% 155.94/155.64 [1783]~E(x17831,x17832)+E(f734(x17833,x17834,x17835,x17836,x17837,x17838,x17831),f734(x17833,x17834,x17835,x17836,x17837,x17838,x17832))
% 155.94/155.64 [1784]~E(x17841,x17842)+E(f369(x17841,x17843,x17844,x17845,x17846),f369(x17842,x17843,x17844,x17845,x17846))
% 155.94/155.64 [1785]~E(x17851,x17852)+E(f369(x17853,x17851,x17854,x17855,x17856),f369(x17853,x17852,x17854,x17855,x17856))
% 155.94/155.64 [1786]~E(x17861,x17862)+E(f369(x17863,x17864,x17861,x17865,x17866),f369(x17863,x17864,x17862,x17865,x17866))
% 155.94/155.64 [1787]~E(x17871,x17872)+E(f369(x17873,x17874,x17875,x17871,x17876),f369(x17873,x17874,x17875,x17872,x17876))
% 155.94/155.64 [1788]~E(x17881,x17882)+E(f369(x17883,x17884,x17885,x17886,x17881),f369(x17883,x17884,x17885,x17886,x17882))
% 155.94/155.64 [1789]~E(x17891,x17892)+E(f528(x17891,x17893,x17894,x17895,x17896,x17897),f528(x17892,x17893,x17894,x17895,x17896,x17897))
% 155.94/155.64 [1790]~E(x17901,x17902)+E(f528(x17903,x17901,x17904,x17905,x17906,x17907),f528(x17903,x17902,x17904,x17905,x17906,x17907))
% 155.94/155.64 [1791]~E(x17911,x17912)+E(f528(x17913,x17914,x17911,x17915,x17916,x17917),f528(x17913,x17914,x17912,x17915,x17916,x17917))
% 155.94/155.64 [1792]~E(x17921,x17922)+E(f528(x17923,x17924,x17925,x17921,x17926,x17927),f528(x17923,x17924,x17925,x17922,x17926,x17927))
% 155.94/155.64 [1793]~E(x17931,x17932)+E(f528(x17933,x17934,x17935,x17936,x17931,x17937),f528(x17933,x17934,x17935,x17936,x17932,x17937))
% 155.94/155.64 [1794]~E(x17941,x17942)+E(f528(x17943,x17944,x17945,x17946,x17947,x17941),f528(x17943,x17944,x17945,x17946,x17947,x17942))
% 155.94/155.64 [1795]~E(x17951,x17952)+E(f808(x17951,x17953,x17954,x17955),f808(x17952,x17953,x17954,x17955))
% 155.94/155.64 [1796]~E(x17961,x17962)+E(f808(x17963,x17961,x17964,x17965),f808(x17963,x17962,x17964,x17965))
% 155.94/155.64 [1797]~E(x17971,x17972)+E(f808(x17973,x17974,x17971,x17975),f808(x17973,x17974,x17972,x17975))
% 155.94/155.64 [1798]~E(x17981,x17982)+E(f808(x17983,x17984,x17985,x17981),f808(x17983,x17984,x17985,x17982))
% 155.94/155.64 [1799]~E(x17991,x17992)+E(f388(x17991,x17993,x17994,x17995),f388(x17992,x17993,x17994,x17995))
% 155.94/155.64 [1800]~E(x18001,x18002)+E(f388(x18003,x18001,x18004,x18005),f388(x18003,x18002,x18004,x18005))
% 155.94/155.64 [1801]~E(x18011,x18012)+E(f388(x18013,x18014,x18011,x18015),f388(x18013,x18014,x18012,x18015))
% 155.94/155.64 [1802]~E(x18021,x18022)+E(f388(x18023,x18024,x18025,x18021),f388(x18023,x18024,x18025,x18022))
% 155.94/155.64 [1803]~E(x18031,x18032)+E(f503(x18031,x18033,x18034,x18035,x18036,x18037),f503(x18032,x18033,x18034,x18035,x18036,x18037))
% 155.94/155.64 [1804]~E(x18041,x18042)+E(f503(x18043,x18041,x18044,x18045,x18046,x18047),f503(x18043,x18042,x18044,x18045,x18046,x18047))
% 155.94/155.64 [1805]~E(x18051,x18052)+E(f503(x18053,x18054,x18051,x18055,x18056,x18057),f503(x18053,x18054,x18052,x18055,x18056,x18057))
% 155.94/155.64 [1806]~E(x18061,x18062)+E(f503(x18063,x18064,x18065,x18061,x18066,x18067),f503(x18063,x18064,x18065,x18062,x18066,x18067))
% 155.94/155.64 [1807]~E(x18071,x18072)+E(f503(x18073,x18074,x18075,x18076,x18071,x18077),f503(x18073,x18074,x18075,x18076,x18072,x18077))
% 155.94/155.64 [1808]~E(x18081,x18082)+E(f503(x18083,x18084,x18085,x18086,x18087,x18081),f503(x18083,x18084,x18085,x18086,x18087,x18082))
% 155.94/155.64 [1809]~E(x18091,x18092)+E(f374(x18091,x18093),f374(x18092,x18093))
% 155.94/155.64 [1810]~E(x18101,x18102)+E(f374(x18103,x18101),f374(x18103,x18102))
% 155.94/155.64 [1811]~E(x18111,x18112)+E(f472(x18111,x18113,x18114,x18115),f472(x18112,x18113,x18114,x18115))
% 155.94/155.64 [1812]~E(x18121,x18122)+E(f472(x18123,x18121,x18124,x18125),f472(x18123,x18122,x18124,x18125))
% 155.94/155.64 [1813]~E(x18131,x18132)+E(f472(x18133,x18134,x18131,x18135),f472(x18133,x18134,x18132,x18135))
% 155.94/155.64 [1814]~E(x18141,x18142)+E(f472(x18143,x18144,x18145,x18141),f472(x18143,x18144,x18145,x18142))
% 155.94/155.64 [1815]~E(x18151,x18152)+E(f689(x18151,x18153),f689(x18152,x18153))
% 155.94/155.64 [1816]~E(x18161,x18162)+E(f689(x18163,x18161),f689(x18163,x18162))
% 155.94/155.64 [1817]~E(x18171,x18172)+E(f496(x18171,x18173,x18174,x18175),f496(x18172,x18173,x18174,x18175))
% 155.94/155.64 [1818]~E(x18181,x18182)+E(f496(x18183,x18181,x18184,x18185),f496(x18183,x18182,x18184,x18185))
% 155.94/155.64 [1819]~E(x18191,x18192)+E(f496(x18193,x18194,x18191,x18195),f496(x18193,x18194,x18192,x18195))
% 155.94/155.64 [1820]~E(x18201,x18202)+E(f496(x18203,x18204,x18205,x18201),f496(x18203,x18204,x18205,x18202))
% 155.94/155.64 [1821]~E(x18211,x18212)+E(f695(x18211,x18213,x18214,x18215,x18216),f695(x18212,x18213,x18214,x18215,x18216))
% 155.94/155.64 [1822]~E(x18221,x18222)+E(f695(x18223,x18221,x18224,x18225,x18226),f695(x18223,x18222,x18224,x18225,x18226))
% 155.94/155.64 [1823]~E(x18231,x18232)+E(f695(x18233,x18234,x18231,x18235,x18236),f695(x18233,x18234,x18232,x18235,x18236))
% 155.94/155.64 [1824]~E(x18241,x18242)+E(f695(x18243,x18244,x18245,x18241,x18246),f695(x18243,x18244,x18245,x18242,x18246))
% 155.94/155.64 [1825]~E(x18251,x18252)+E(f695(x18253,x18254,x18255,x18256,x18251),f695(x18253,x18254,x18255,x18256,x18252))
% 155.94/155.64 [1826]~E(x18261,x18262)+E(f693(x18261,x18263,x18264),f693(x18262,x18263,x18264))
% 155.94/155.64 [1827]~E(x18271,x18272)+E(f693(x18273,x18271,x18274),f693(x18273,x18272,x18274))
% 155.94/155.64 [1828]~E(x18281,x18282)+E(f693(x18283,x18284,x18281),f693(x18283,x18284,x18282))
% 155.94/155.64 [1829]~E(x18291,x18292)+E(f813(x18291,x18293),f813(x18292,x18293))
% 155.94/155.64 [1830]~E(x18301,x18302)+E(f813(x18303,x18301),f813(x18303,x18302))
% 155.94/155.64 [1831]~E(x18311,x18312)+E(f661(x18311,x18313,x18314),f661(x18312,x18313,x18314))
% 155.94/155.64 [1832]~E(x18321,x18322)+E(f661(x18323,x18321,x18324),f661(x18323,x18322,x18324))
% 155.94/155.64 [1833]~E(x18331,x18332)+E(f661(x18333,x18334,x18331),f661(x18333,x18334,x18332))
% 155.94/155.64 [1834]~E(x18341,x18342)+E(f514(x18341,x18343,x18344,x18345,x18346),f514(x18342,x18343,x18344,x18345,x18346))
% 155.94/155.64 [1835]~E(x18351,x18352)+E(f514(x18353,x18351,x18354,x18355,x18356),f514(x18353,x18352,x18354,x18355,x18356))
% 155.94/155.64 [1836]~E(x18361,x18362)+E(f514(x18363,x18364,x18361,x18365,x18366),f514(x18363,x18364,x18362,x18365,x18366))
% 155.94/155.64 [1837]~E(x18371,x18372)+E(f514(x18373,x18374,x18375,x18371,x18376),f514(x18373,x18374,x18375,x18372,x18376))
% 155.94/155.64 [1838]~E(x18381,x18382)+E(f514(x18383,x18384,x18385,x18386,x18381),f514(x18383,x18384,x18385,x18386,x18382))
% 155.94/155.64 [1839]~E(x18391,x18392)+E(f605(x18391,x18393,x18394,x18395),f605(x18392,x18393,x18394,x18395))
% 155.94/155.64 [1840]~E(x18401,x18402)+E(f605(x18403,x18401,x18404,x18405),f605(x18403,x18402,x18404,x18405))
% 155.94/155.64 [1841]~E(x18411,x18412)+E(f605(x18413,x18414,x18411,x18415),f605(x18413,x18414,x18412,x18415))
% 155.94/155.64 [1842]~E(x18421,x18422)+E(f605(x18423,x18424,x18425,x18421),f605(x18423,x18424,x18425,x18422))
% 155.94/155.64 [1843]~E(x18431,x18432)+E(f633(x18431,x18433,x18434),f633(x18432,x18433,x18434))
% 155.94/155.64 [1844]~E(x18441,x18442)+E(f633(x18443,x18441,x18444),f633(x18443,x18442,x18444))
% 155.94/155.64 [1845]~E(x18451,x18452)+E(f633(x18453,x18454,x18451),f633(x18453,x18454,x18452))
% 155.94/155.64 [1846]~E(x18461,x18462)+E(f424(x18461,x18463,x18464,x18465,x18466,x18467,x18468),f424(x18462,x18463,x18464,x18465,x18466,x18467,x18468))
% 155.94/155.64 [1847]~E(x18471,x18472)+E(f424(x18473,x18471,x18474,x18475,x18476,x18477,x18478),f424(x18473,x18472,x18474,x18475,x18476,x18477,x18478))
% 155.94/155.64 [1848]~E(x18481,x18482)+E(f424(x18483,x18484,x18481,x18485,x18486,x18487,x18488),f424(x18483,x18484,x18482,x18485,x18486,x18487,x18488))
% 155.94/155.64 [1849]~E(x18491,x18492)+E(f424(x18493,x18494,x18495,x18491,x18496,x18497,x18498),f424(x18493,x18494,x18495,x18492,x18496,x18497,x18498))
% 155.94/155.64 [1850]~E(x18501,x18502)+E(f424(x18503,x18504,x18505,x18506,x18501,x18507,x18508),f424(x18503,x18504,x18505,x18506,x18502,x18507,x18508))
% 155.94/155.64 [1851]~E(x18511,x18512)+E(f424(x18513,x18514,x18515,x18516,x18517,x18511,x18518),f424(x18513,x18514,x18515,x18516,x18517,x18512,x18518))
% 155.94/155.64 [1852]~E(x18521,x18522)+E(f424(x18523,x18524,x18525,x18526,x18527,x18528,x18521),f424(x18523,x18524,x18525,x18526,x18527,x18528,x18522))
% 155.94/155.64 [1853]~E(x18531,x18532)+E(f659(x18531,x18533),f659(x18532,x18533))
% 155.94/155.64 [1854]~E(x18541,x18542)+E(f659(x18543,x18541),f659(x18543,x18542))
% 155.94/155.64 [1855]~E(x18551,x18552)+E(f387(x18551,x18553,x18554),f387(x18552,x18553,x18554))
% 155.94/155.64 [1856]~E(x18561,x18562)+E(f387(x18563,x18561,x18564),f387(x18563,x18562,x18564))
% 155.94/155.64 [1857]~E(x18571,x18572)+E(f387(x18573,x18574,x18571),f387(x18573,x18574,x18572))
% 155.94/155.64 [1858]~E(x18581,x18582)+E(f725(x18581,x18583),f725(x18582,x18583))
% 155.94/155.64 [1859]~E(x18591,x18592)+E(f725(x18593,x18591),f725(x18593,x18592))
% 155.94/155.64 [1860]~E(x18601,x18602)+E(f589(x18601,x18603,x18604,x18605,x18606),f589(x18602,x18603,x18604,x18605,x18606))
% 155.94/155.64 [1861]~E(x18611,x18612)+E(f589(x18613,x18611,x18614,x18615,x18616),f589(x18613,x18612,x18614,x18615,x18616))
% 155.94/155.64 [1862]~E(x18621,x18622)+E(f589(x18623,x18624,x18621,x18625,x18626),f589(x18623,x18624,x18622,x18625,x18626))
% 155.94/155.64 [1863]~E(x18631,x18632)+E(f589(x18633,x18634,x18635,x18631,x18636),f589(x18633,x18634,x18635,x18632,x18636))
% 155.94/155.64 [1864]~E(x18641,x18642)+E(f589(x18643,x18644,x18645,x18646,x18641),f589(x18643,x18644,x18645,x18646,x18642))
% 155.94/155.64 [1865]~E(x18651,x18652)+E(f717(x18651,x18653,x18654,x18655,x18656,x18657),f717(x18652,x18653,x18654,x18655,x18656,x18657))
% 155.94/155.64 [1866]~E(x18661,x18662)+E(f717(x18663,x18661,x18664,x18665,x18666,x18667),f717(x18663,x18662,x18664,x18665,x18666,x18667))
% 155.94/155.64 [1867]~E(x18671,x18672)+E(f717(x18673,x18674,x18671,x18675,x18676,x18677),f717(x18673,x18674,x18672,x18675,x18676,x18677))
% 155.94/155.64 [1868]~E(x18681,x18682)+E(f717(x18683,x18684,x18685,x18681,x18686,x18687),f717(x18683,x18684,x18685,x18682,x18686,x18687))
% 155.94/155.64 [1869]~E(x18691,x18692)+E(f717(x18693,x18694,x18695,x18696,x18691,x18697),f717(x18693,x18694,x18695,x18696,x18692,x18697))
% 155.94/155.64 [1870]~E(x18701,x18702)+E(f717(x18703,x18704,x18705,x18706,x18707,x18701),f717(x18703,x18704,x18705,x18706,x18707,x18702))
% 155.94/155.64 [1871]~E(x18711,x18712)+E(f460(x18711,x18713,x18714,x18715),f460(x18712,x18713,x18714,x18715))
% 155.94/155.64 [1872]~E(x18721,x18722)+E(f460(x18723,x18721,x18724,x18725),f460(x18723,x18722,x18724,x18725))
% 155.94/155.64 [1873]~E(x18731,x18732)+E(f460(x18733,x18734,x18731,x18735),f460(x18733,x18734,x18732,x18735))
% 155.94/155.64 [1874]~E(x18741,x18742)+E(f460(x18743,x18744,x18745,x18741),f460(x18743,x18744,x18745,x18742))
% 155.94/155.64 [1875]~E(x18751,x18752)+E(f690(x18751,x18753,x18754),f690(x18752,x18753,x18754))
% 155.94/155.64 [1876]~E(x18761,x18762)+E(f690(x18763,x18761,x18764),f690(x18763,x18762,x18764))
% 155.94/155.64 [1877]~E(x18771,x18772)+E(f690(x18773,x18774,x18771),f690(x18773,x18774,x18772))
% 155.94/155.64 [1878]~E(x18781,x18782)+E(f17(x18781,x18783,x18784,x18785),f17(x18782,x18783,x18784,x18785))
% 155.94/155.64 [1879]~E(x18791,x18792)+E(f17(x18793,x18791,x18794,x18795),f17(x18793,x18792,x18794,x18795))
% 155.94/155.64 [1880]~E(x18801,x18802)+E(f17(x18803,x18804,x18801,x18805),f17(x18803,x18804,x18802,x18805))
% 155.94/155.64 [1881]~E(x18811,x18812)+E(f17(x18813,x18814,x18815,x18811),f17(x18813,x18814,x18815,x18812))
% 155.94/155.64 [1882]~E(x18821,x18822)+E(f541(x18821),f541(x18822))
% 155.94/155.64 [1883]~E(x18831,x18832)+E(f450(x18831,x18833,x18834,x18835),f450(x18832,x18833,x18834,x18835))
% 155.94/155.64 [1884]~E(x18841,x18842)+E(f450(x18843,x18841,x18844,x18845),f450(x18843,x18842,x18844,x18845))
% 155.94/155.64 [1885]~E(x18851,x18852)+E(f450(x18853,x18854,x18851,x18855),f450(x18853,x18854,x18852,x18855))
% 155.94/155.64 [1886]~E(x18861,x18862)+E(f450(x18863,x18864,x18865,x18861),f450(x18863,x18864,x18865,x18862))
% 155.94/155.64 [1887]~E(x18871,x18872)+E(f609(x18871,x18873,x18874,x18875,x18876),f609(x18872,x18873,x18874,x18875,x18876))
% 155.94/155.64 [1888]~E(x18881,x18882)+E(f609(x18883,x18881,x18884,x18885,x18886),f609(x18883,x18882,x18884,x18885,x18886))
% 155.94/155.64 [1889]~E(x18891,x18892)+E(f609(x18893,x18894,x18891,x18895,x18896),f609(x18893,x18894,x18892,x18895,x18896))
% 155.94/155.64 [1890]~E(x18901,x18902)+E(f609(x18903,x18904,x18905,x18901,x18906),f609(x18903,x18904,x18905,x18902,x18906))
% 155.94/155.64 [1891]~E(x18911,x18912)+E(f609(x18913,x18914,x18915,x18916,x18911),f609(x18913,x18914,x18915,x18916,x18912))
% 155.94/155.64 [1892]~E(x18921,x18922)+E(f376(x18921,x18923,x18924,x18925,x18926),f376(x18922,x18923,x18924,x18925,x18926))
% 155.94/155.64 [1893]~E(x18931,x18932)+E(f376(x18933,x18931,x18934,x18935,x18936),f376(x18933,x18932,x18934,x18935,x18936))
% 155.94/155.64 [1894]~E(x18941,x18942)+E(f376(x18943,x18944,x18941,x18945,x18946),f376(x18943,x18944,x18942,x18945,x18946))
% 155.94/155.64 [1895]~E(x18951,x18952)+E(f376(x18953,x18954,x18955,x18951,x18956),f376(x18953,x18954,x18955,x18952,x18956))
% 155.94/155.64 [1896]~E(x18961,x18962)+E(f376(x18963,x18964,x18965,x18966,x18961),f376(x18963,x18964,x18965,x18966,x18962))
% 155.94/155.64 [1897]~E(x18971,x18972)+E(f142(x18971,x18973),f142(x18972,x18973))
% 155.94/155.64 [1898]~E(x18981,x18982)+E(f142(x18983,x18981),f142(x18983,x18982))
% 155.94/155.64 [1899]~E(x18991,x18992)+E(f823(x18991,x18993,x18994),f823(x18992,x18993,x18994))
% 155.94/155.64 [1900]~E(x19001,x19002)+E(f823(x19003,x19001,x19004),f823(x19003,x19002,x19004))
% 155.94/155.64 [1901]~E(x19011,x19012)+E(f823(x19013,x19014,x19011),f823(x19013,x19014,x19012))
% 155.94/155.64 [1902]~E(x19021,x19022)+E(f748(x19021,x19023,x19024),f748(x19022,x19023,x19024))
% 155.94/155.64 [1903]~E(x19031,x19032)+E(f748(x19033,x19031,x19034),f748(x19033,x19032,x19034))
% 155.94/155.64 [1904]~E(x19041,x19042)+E(f748(x19043,x19044,x19041),f748(x19043,x19044,x19042))
% 155.94/155.64 [1905]~E(x19051,x19052)+E(f482(x19051,x19053,x19054,x19055),f482(x19052,x19053,x19054,x19055))
% 155.94/155.64 [1906]~E(x19061,x19062)+E(f482(x19063,x19061,x19064,x19065),f482(x19063,x19062,x19064,x19065))
% 155.94/155.64 [1907]~E(x19071,x19072)+E(f482(x19073,x19074,x19071,x19075),f482(x19073,x19074,x19072,x19075))
% 155.94/155.64 [1908]~E(x19081,x19082)+E(f482(x19083,x19084,x19085,x19081),f482(x19083,x19084,x19085,x19082))
% 155.94/155.64 [1909]~E(x19091,x19092)+E(f654(x19091,x19093),f654(x19092,x19093))
% 155.94/155.64 [1910]~E(x19101,x19102)+E(f654(x19103,x19101),f654(x19103,x19102))
% 155.94/155.64 [1911]~E(x19111,x19112)+E(f414(x19111,x19113,x19114,x19115,x19116),f414(x19112,x19113,x19114,x19115,x19116))
% 155.94/155.64 [1912]~E(x19121,x19122)+E(f414(x19123,x19121,x19124,x19125,x19126),f414(x19123,x19122,x19124,x19125,x19126))
% 155.94/155.64 [1913]~E(x19131,x19132)+E(f414(x19133,x19134,x19131,x19135,x19136),f414(x19133,x19134,x19132,x19135,x19136))
% 155.94/155.64 [1914]~E(x19141,x19142)+E(f414(x19143,x19144,x19145,x19141,x19146),f414(x19143,x19144,x19145,x19142,x19146))
% 155.94/155.64 [1915]~E(x19151,x19152)+E(f414(x19153,x19154,x19155,x19156,x19151),f414(x19153,x19154,x19155,x19156,x19152))
% 155.94/155.64 [1916]~E(x19161,x19162)+E(f276(x19161,x19163,x19164),f276(x19162,x19163,x19164))
% 155.94/155.64 [1917]~E(x19171,x19172)+E(f276(x19173,x19171,x19174),f276(x19173,x19172,x19174))
% 155.94/155.64 [1918]~E(x19181,x19182)+E(f276(x19183,x19184,x19181),f276(x19183,x19184,x19182))
% 155.94/155.64 [1919]~E(x19191,x19192)+E(f527(x19191,x19193,x19194,x19195),f527(x19192,x19193,x19194,x19195))
% 155.94/155.64 [1920]~E(x19201,x19202)+E(f527(x19203,x19201,x19204,x19205),f527(x19203,x19202,x19204,x19205))
% 155.94/155.64 [1921]~E(x19211,x19212)+E(f527(x19213,x19214,x19211,x19215),f527(x19213,x19214,x19212,x19215))
% 155.94/155.64 [1922]~E(x19221,x19222)+E(f527(x19223,x19224,x19225,x19221),f527(x19223,x19224,x19225,x19222))
% 155.94/155.64 [1923]~E(x19231,x19232)+E(f626(x19231,x19233,x19234,x19235),f626(x19232,x19233,x19234,x19235))
% 155.94/155.64 [1924]~E(x19241,x19242)+E(f626(x19243,x19241,x19244,x19245),f626(x19243,x19242,x19244,x19245))
% 155.94/155.64 [1925]~E(x19251,x19252)+E(f626(x19253,x19254,x19251,x19255),f626(x19253,x19254,x19252,x19255))
% 155.94/155.64 [1926]~E(x19261,x19262)+E(f626(x19263,x19264,x19265,x19261),f626(x19263,x19264,x19265,x19262))
% 155.94/155.64 [1927]~E(x19271,x19272)+E(f660(x19271,x19273,x19274),f660(x19272,x19273,x19274))
% 155.94/155.64 [1928]~E(x19281,x19282)+E(f660(x19283,x19281,x19284),f660(x19283,x19282,x19284))
% 155.94/155.64 [1929]~E(x19291,x19292)+E(f660(x19293,x19294,x19291),f660(x19293,x19294,x19292))
% 155.94/155.64 [1930]~E(x19301,x19302)+E(f536(x19301,x19303,x19304),f536(x19302,x19303,x19304))
% 155.94/155.64 [1931]~E(x19311,x19312)+E(f536(x19313,x19311,x19314),f536(x19313,x19312,x19314))
% 155.94/155.64 [1932]~E(x19321,x19322)+E(f536(x19323,x19324,x19321),f536(x19323,x19324,x19322))
% 155.94/155.64 [1933]~E(x19331,x19332)+E(f384(x19331,x19333,x19334,x19335),f384(x19332,x19333,x19334,x19335))
% 155.94/155.64 [1934]~E(x19341,x19342)+E(f384(x19343,x19341,x19344,x19345),f384(x19343,x19342,x19344,x19345))
% 155.94/155.64 [1935]~E(x19351,x19352)+E(f384(x19353,x19354,x19351,x19355),f384(x19353,x19354,x19352,x19355))
% 155.94/155.64 [1936]~E(x19361,x19362)+E(f384(x19363,x19364,x19365,x19361),f384(x19363,x19364,x19365,x19362))
% 155.94/155.64 [1937]~E(x19371,x19372)+E(f736(x19371,x19373,x19374,x19375),f736(x19372,x19373,x19374,x19375))
% 155.94/155.64 [1938]~E(x19381,x19382)+E(f736(x19383,x19381,x19384,x19385),f736(x19383,x19382,x19384,x19385))
% 155.94/155.64 [1939]~E(x19391,x19392)+E(f736(x19393,x19394,x19391,x19395),f736(x19393,x19394,x19392,x19395))
% 155.94/155.64 [1940]~E(x19401,x19402)+E(f736(x19403,x19404,x19405,x19401),f736(x19403,x19404,x19405,x19402))
% 155.94/155.64 [1941]~E(x19411,x19412)+E(f320(x19411),f320(x19412))
% 155.94/155.64 [1942]~E(x19421,x19422)+E(f681(x19421,x19423,x19424),f681(x19422,x19423,x19424))
% 155.94/155.64 [1943]~E(x19431,x19432)+E(f681(x19433,x19431,x19434),f681(x19433,x19432,x19434))
% 155.94/155.64 [1944]~E(x19441,x19442)+E(f681(x19443,x19444,x19441),f681(x19443,x19444,x19442))
% 155.94/155.64 [1945]~E(x19451,x19452)+E(f759(x19451,x19453),f759(x19452,x19453))
% 155.94/155.64 [1946]~E(x19461,x19462)+E(f759(x19463,x19461),f759(x19463,x19462))
% 155.94/155.64 [1947]~E(x19471,x19472)+E(f726(x19471,x19473,x19474),f726(x19472,x19473,x19474))
% 155.94/155.64 [1948]~E(x19481,x19482)+E(f726(x19483,x19481,x19484),f726(x19483,x19482,x19484))
% 155.94/155.64 [1949]~E(x19491,x19492)+E(f726(x19493,x19494,x19491),f726(x19493,x19494,x19492))
% 155.94/155.64 [1950]~E(x19501,x19502)+E(f771(x19501,x19503,x19504,x19505,x19506),f771(x19502,x19503,x19504,x19505,x19506))
% 155.94/155.64 [1951]~E(x19511,x19512)+E(f771(x19513,x19511,x19514,x19515,x19516),f771(x19513,x19512,x19514,x19515,x19516))
% 155.94/155.64 [1952]~E(x19521,x19522)+E(f771(x19523,x19524,x19521,x19525,x19526),f771(x19523,x19524,x19522,x19525,x19526))
% 155.94/155.64 [1953]~E(x19531,x19532)+E(f771(x19533,x19534,x19535,x19531,x19536),f771(x19533,x19534,x19535,x19532,x19536))
% 155.94/155.64 [1954]~E(x19541,x19542)+E(f771(x19543,x19544,x19545,x19546,x19541),f771(x19543,x19544,x19545,x19546,x19542))
% 155.94/155.64 [1955]~E(x19551,x19552)+E(f418(x19551,x19553,x19554),f418(x19552,x19553,x19554))
% 155.94/155.64 [1956]~E(x19561,x19562)+E(f418(x19563,x19561,x19564),f418(x19563,x19562,x19564))
% 155.94/155.64 [1957]~E(x19571,x19572)+E(f418(x19573,x19574,x19571),f418(x19573,x19574,x19572))
% 155.94/155.64 [1958]~E(x19581,x19582)+E(f511(x19581,x19583,x19584,x19585),f511(x19582,x19583,x19584,x19585))
% 155.94/155.64 [1959]~E(x19591,x19592)+E(f511(x19593,x19591,x19594,x19595),f511(x19593,x19592,x19594,x19595))
% 155.94/155.64 [1960]~E(x19601,x19602)+E(f511(x19603,x19604,x19601,x19605),f511(x19603,x19604,x19602,x19605))
% 155.94/155.64 [1961]~E(x19611,x19612)+E(f511(x19613,x19614,x19615,x19611),f511(x19613,x19614,x19615,x19612))
% 155.94/155.64 [1962]~E(x19621,x19622)+E(f364(x19621,x19623),f364(x19622,x19623))
% 155.94/155.64 [1963]~E(x19631,x19632)+E(f364(x19633,x19631),f364(x19633,x19632))
% 155.94/155.64 [1964]~E(x19641,x19642)+E(f487(x19641,x19643,x19644,x19645,x19646),f487(x19642,x19643,x19644,x19645,x19646))
% 155.94/155.64 [1965]~E(x19651,x19652)+E(f487(x19653,x19651,x19654,x19655,x19656),f487(x19653,x19652,x19654,x19655,x19656))
% 155.94/155.64 [1966]~E(x19661,x19662)+E(f487(x19663,x19664,x19661,x19665,x19666),f487(x19663,x19664,x19662,x19665,x19666))
% 155.94/155.64 [1967]~E(x19671,x19672)+E(f487(x19673,x19674,x19675,x19671,x19676),f487(x19673,x19674,x19675,x19672,x19676))
% 155.94/155.64 [1968]~E(x19681,x19682)+E(f487(x19683,x19684,x19685,x19686,x19681),f487(x19683,x19684,x19685,x19686,x19682))
% 155.94/155.64 [1969]~E(x19691,x19692)+E(f107(x19691,x19693,x19694,x19695),f107(x19692,x19693,x19694,x19695))
% 155.94/155.64 [1970]~E(x19701,x19702)+E(f107(x19703,x19701,x19704,x19705),f107(x19703,x19702,x19704,x19705))
% 155.94/155.64 [1971]~E(x19711,x19712)+E(f107(x19713,x19714,x19711,x19715),f107(x19713,x19714,x19712,x19715))
% 155.94/155.64 [1972]~E(x19721,x19722)+E(f107(x19723,x19724,x19725,x19721),f107(x19723,x19724,x19725,x19722))
% 155.94/155.64 [1973]~E(x19731,x19732)+E(f318(x19731),f318(x19732))
% 155.94/155.64 [1974]~E(x19741,x19742)+E(f361(x19741,x19743,x19744,x19745,x19746),f361(x19742,x19743,x19744,x19745,x19746))
% 155.94/155.64 [1975]~E(x19751,x19752)+E(f361(x19753,x19751,x19754,x19755,x19756),f361(x19753,x19752,x19754,x19755,x19756))
% 155.94/155.64 [1976]~E(x19761,x19762)+E(f361(x19763,x19764,x19761,x19765,x19766),f361(x19763,x19764,x19762,x19765,x19766))
% 155.94/155.64 [1977]~E(x19771,x19772)+E(f361(x19773,x19774,x19775,x19771,x19776),f361(x19773,x19774,x19775,x19772,x19776))
% 155.94/155.64 [1978]~E(x19781,x19782)+E(f361(x19783,x19784,x19785,x19786,x19781),f361(x19783,x19784,x19785,x19786,x19782))
% 155.94/155.64 [1979]~E(x19791,x19792)+E(f786(x19791),f786(x19792))
% 155.94/155.64 [1980]~E(x19801,x19802)+E(f390(x19801,x19803),f390(x19802,x19803))
% 155.94/155.64 [1981]~E(x19811,x19812)+E(f390(x19813,x19811),f390(x19813,x19812))
% 155.94/155.64 [1982]~E(x19821,x19822)+E(f271(x19821,x19823,x19824),f271(x19822,x19823,x19824))
% 155.94/155.64 [1983]~E(x19831,x19832)+E(f271(x19833,x19831,x19834),f271(x19833,x19832,x19834))
% 155.94/155.64 [1984]~E(x19841,x19842)+E(f271(x19843,x19844,x19841),f271(x19843,x19844,x19842))
% 155.94/155.64 [1985]~E(x19851,x19852)+E(f346(x19851,x19853,x19854),f346(x19852,x19853,x19854))
% 155.94/155.64 [1986]~E(x19861,x19862)+E(f346(x19863,x19861,x19864),f346(x19863,x19862,x19864))
% 155.94/155.64 [1987]~E(x19871,x19872)+E(f346(x19873,x19874,x19871),f346(x19873,x19874,x19872))
% 155.94/155.64 [1988]~E(x19881,x19882)+E(f822(x19881,x19883),f822(x19882,x19883))
% 155.94/155.64 [1989]~E(x19891,x19892)+E(f822(x19893,x19891),f822(x19893,x19892))
% 155.94/155.64 [1990]~E(x19901,x19902)+E(f684(x19901,x19903,x19904,x19905),f684(x19902,x19903,x19904,x19905))
% 155.94/155.64 [1991]~E(x19911,x19912)+E(f684(x19913,x19911,x19914,x19915),f684(x19913,x19912,x19914,x19915))
% 155.94/155.64 [1992]~E(x19921,x19922)+E(f684(x19923,x19924,x19921,x19925),f684(x19923,x19924,x19922,x19925))
% 155.94/155.64 [1993]~E(x19931,x19932)+E(f684(x19933,x19934,x19935,x19931),f684(x19933,x19934,x19935,x19932))
% 155.94/155.64 [1994]~E(x19941,x19942)+E(f526(x19941,x19943,x19944),f526(x19942,x19943,x19944))
% 155.94/155.64 [1995]~E(x19951,x19952)+E(f526(x19953,x19951,x19954),f526(x19953,x19952,x19954))
% 155.94/155.64 [1996]~E(x19961,x19962)+E(f526(x19963,x19964,x19961),f526(x19963,x19964,x19962))
% 155.94/155.64 [1997]~E(x19971,x19972)+E(f545(x19971,x19973),f545(x19972,x19973))
% 155.94/155.64 [1998]~E(x19981,x19982)+E(f545(x19983,x19981),f545(x19983,x19982))
% 155.94/155.64 [1999]~E(x19991,x19992)+E(f272(x19991,x19993,x19994),f272(x19992,x19993,x19994))
% 155.94/155.64 [2000]~E(x20001,x20002)+E(f272(x20003,x20001,x20004),f272(x20003,x20002,x20004))
% 155.94/155.64 [2001]~E(x20011,x20012)+E(f272(x20013,x20014,x20011),f272(x20013,x20014,x20012))
% 155.94/155.64 [2002]~E(x20021,x20022)+E(f258(x20021,x20023),f258(x20022,x20023))
% 155.94/155.64 [2003]~E(x20031,x20032)+E(f258(x20033,x20031),f258(x20033,x20032))
% 155.94/155.64 [2004]~E(x20041,x20042)+E(f794(x20041,x20043,x20044),f794(x20042,x20043,x20044))
% 155.94/155.64 [2005]~E(x20051,x20052)+E(f794(x20053,x20051,x20054),f794(x20053,x20052,x20054))
% 155.94/155.64 [2006]~E(x20061,x20062)+E(f794(x20063,x20064,x20061),f794(x20063,x20064,x20062))
% 155.94/155.64 [2007]~E(x20071,x20072)+E(f270(x20071,x20073),f270(x20072,x20073))
% 155.94/155.64 [2008]~E(x20081,x20082)+E(f270(x20083,x20081),f270(x20083,x20082))
% 155.94/155.64 [2009]~E(x20091,x20092)+E(f838(x20091,x20093,x20094),f838(x20092,x20093,x20094))
% 155.94/155.64 [2010]~E(x20101,x20102)+E(f838(x20103,x20101,x20104),f838(x20103,x20102,x20104))
% 155.94/155.64 [2011]~E(x20111,x20112)+E(f838(x20113,x20114,x20111),f838(x20113,x20114,x20112))
% 155.94/155.64 [2012]~E(x20121,x20122)+E(f634(x20121,x20123,x20124,x20125),f634(x20122,x20123,x20124,x20125))
% 155.94/155.64 [2013]~E(x20131,x20132)+E(f634(x20133,x20131,x20134,x20135),f634(x20133,x20132,x20134,x20135))
% 155.94/155.64 [2014]~E(x20141,x20142)+E(f634(x20143,x20144,x20141,x20145),f634(x20143,x20144,x20142,x20145))
% 155.94/155.64 [2015]~E(x20151,x20152)+E(f634(x20153,x20154,x20155,x20151),f634(x20153,x20154,x20155,x20152))
% 155.94/155.64 [2016]~E(x20161,x20162)+E(f330(x20161,x20163,x20164),f330(x20162,x20163,x20164))
% 155.94/155.64 [2017]~E(x20171,x20172)+E(f330(x20173,x20171,x20174),f330(x20173,x20172,x20174))
% 155.94/155.64 [2018]~E(x20181,x20182)+E(f330(x20183,x20184,x20181),f330(x20183,x20184,x20182))
% 155.94/155.64 [2019]~E(x20191,x20192)+E(f825(x20191,x20193,x20194,x20195),f825(x20192,x20193,x20194,x20195))
% 155.94/155.64 [2020]~E(x20201,x20202)+E(f825(x20203,x20201,x20204,x20205),f825(x20203,x20202,x20204,x20205))
% 155.94/155.64 [2021]~E(x20211,x20212)+E(f825(x20213,x20214,x20211,x20215),f825(x20213,x20214,x20212,x20215))
% 155.94/155.64 [2022]~E(x20221,x20222)+E(f825(x20223,x20224,x20225,x20221),f825(x20223,x20224,x20225,x20222))
% 155.94/155.64 [2023]~E(x20231,x20232)+E(f573(x20231,x20233),f573(x20232,x20233))
% 155.94/155.64 [2024]~E(x20241,x20242)+E(f573(x20243,x20241),f573(x20243,x20242))
% 155.94/155.64 [2025]~E(x20251,x20252)+E(f327(x20251,x20253),f327(x20252,x20253))
% 155.94/155.64 [2026]~E(x20261,x20262)+E(f327(x20263,x20261),f327(x20263,x20262))
% 155.94/155.64 [2027]~E(x20271,x20272)+E(f437(x20271,x20273,x20274),f437(x20272,x20273,x20274))
% 155.94/155.64 [2028]~E(x20281,x20282)+E(f437(x20283,x20281,x20284),f437(x20283,x20282,x20284))
% 155.94/155.64 [2029]~E(x20291,x20292)+E(f437(x20293,x20294,x20291),f437(x20293,x20294,x20292))
% 155.94/155.64 [2030]~E(x20301,x20302)+E(f447(x20301,x20303,x20304,x20305),f447(x20302,x20303,x20304,x20305))
% 155.94/155.64 [2031]~E(x20311,x20312)+E(f447(x20313,x20311,x20314,x20315),f447(x20313,x20312,x20314,x20315))
% 155.94/155.64 [2032]~E(x20321,x20322)+E(f447(x20323,x20324,x20321,x20325),f447(x20323,x20324,x20322,x20325))
% 155.94/155.64 [2033]~E(x20331,x20332)+E(f447(x20333,x20334,x20335,x20331),f447(x20333,x20334,x20335,x20332))
% 155.94/155.64 [2034]~E(x20341,x20342)+E(f833(x20341,x20343),f833(x20342,x20343))
% 155.94/155.64 [2035]~E(x20351,x20352)+E(f833(x20353,x20351),f833(x20353,x20352))
% 155.94/155.64 [2036]~E(x20361,x20362)+E(f471(x20361,x20363,x20364,x20365),f471(x20362,x20363,x20364,x20365))
% 155.94/155.64 [2037]~E(x20371,x20372)+E(f471(x20373,x20371,x20374,x20375),f471(x20373,x20372,x20374,x20375))
% 155.94/155.64 [2038]~E(x20381,x20382)+E(f471(x20383,x20384,x20381,x20385),f471(x20383,x20384,x20382,x20385))
% 155.94/155.64 [2039]~E(x20391,x20392)+E(f471(x20393,x20394,x20395,x20391),f471(x20393,x20394,x20395,x20392))
% 155.94/155.64 [2040]~E(x20401,x20402)+E(f783(x20401,x20403,x20404),f783(x20402,x20403,x20404))
% 155.94/155.64 [2041]~E(x20411,x20412)+E(f783(x20413,x20411,x20414),f783(x20413,x20412,x20414))
% 155.94/155.64 [2042]~E(x20421,x20422)+E(f783(x20423,x20424,x20421),f783(x20423,x20424,x20422))
% 155.94/155.64 [2043]~E(x20431,x20432)+E(f694(x20431,x20433,x20434,x20435),f694(x20432,x20433,x20434,x20435))
% 155.94/155.64 [2044]~E(x20441,x20442)+E(f694(x20443,x20441,x20444,x20445),f694(x20443,x20442,x20444,x20445))
% 155.94/155.64 [2045]~E(x20451,x20452)+E(f694(x20453,x20454,x20451,x20455),f694(x20453,x20454,x20452,x20455))
% 155.94/155.64 [2046]~E(x20461,x20462)+E(f694(x20463,x20464,x20465,x20461),f694(x20463,x20464,x20465,x20462))
% 155.94/155.64 [2047]~E(x20471,x20472)+E(f621(x20471,x20473,x20474,x20475,x20476),f621(x20472,x20473,x20474,x20475,x20476))
% 155.94/155.64 [2048]~E(x20481,x20482)+E(f621(x20483,x20481,x20484,x20485,x20486),f621(x20483,x20482,x20484,x20485,x20486))
% 155.94/155.64 [2049]~E(x20491,x20492)+E(f621(x20493,x20494,x20491,x20495,x20496),f621(x20493,x20494,x20492,x20495,x20496))
% 155.94/155.64 [2050]~E(x20501,x20502)+E(f621(x20503,x20504,x20505,x20501,x20506),f621(x20503,x20504,x20505,x20502,x20506))
% 155.94/155.64 [2051]~E(x20511,x20512)+E(f621(x20513,x20514,x20515,x20516,x20511),f621(x20513,x20514,x20515,x20516,x20512))
% 155.94/155.64 [2052]~E(x20521,x20522)+E(f515(x20521,x20523,x20524),f515(x20522,x20523,x20524))
% 155.94/155.64 [2053]~E(x20531,x20532)+E(f515(x20533,x20531,x20534),f515(x20533,x20532,x20534))
% 155.94/155.64 [2054]~E(x20541,x20542)+E(f515(x20543,x20544,x20541),f515(x20543,x20544,x20542))
% 155.94/155.64 [2055]~E(x20551,x20552)+E(f365(x20551,x20553,x20554),f365(x20552,x20553,x20554))
% 155.94/155.64 [2056]~E(x20561,x20562)+E(f365(x20563,x20561,x20564),f365(x20563,x20562,x20564))
% 155.94/155.64 [2057]~E(x20571,x20572)+E(f365(x20573,x20574,x20571),f365(x20573,x20574,x20572))
% 155.94/155.64 [2058]~E(x20581,x20582)+E(f640(x20581,x20583,x20584,x20585,x20586),f640(x20582,x20583,x20584,x20585,x20586))
% 155.94/155.64 [2059]~E(x20591,x20592)+E(f640(x20593,x20591,x20594,x20595,x20596),f640(x20593,x20592,x20594,x20595,x20596))
% 155.94/155.64 [2060]~E(x20601,x20602)+E(f640(x20603,x20604,x20601,x20605,x20606),f640(x20603,x20604,x20602,x20605,x20606))
% 155.94/155.64 [2061]~E(x20611,x20612)+E(f640(x20613,x20614,x20615,x20611,x20616),f640(x20613,x20614,x20615,x20612,x20616))
% 155.94/155.64 [2062]~E(x20621,x20622)+E(f640(x20623,x20624,x20625,x20626,x20621),f640(x20623,x20624,x20625,x20626,x20622))
% 155.94/155.64 [2063]~E(x20631,x20632)+E(f658(x20631,x20633),f658(x20632,x20633))
% 155.94/155.64 [2064]~E(x20641,x20642)+E(f658(x20643,x20641),f658(x20643,x20642))
% 155.94/155.64 [2065]~E(x20651,x20652)+E(f764(x20651,x20653,x20654),f764(x20652,x20653,x20654))
% 155.94/155.64 [2066]~E(x20661,x20662)+E(f764(x20663,x20661,x20664),f764(x20663,x20662,x20664))
% 155.94/155.64 [2067]~E(x20671,x20672)+E(f764(x20673,x20674,x20671),f764(x20673,x20674,x20672))
% 155.94/155.64 [2068]~E(x20681,x20682)+E(f807(x20681,x20683,x20684,x20685),f807(x20682,x20683,x20684,x20685))
% 155.94/155.64 [2069]~E(x20691,x20692)+E(f807(x20693,x20691,x20694,x20695),f807(x20693,x20692,x20694,x20695))
% 155.94/155.64 [2070]~E(x20701,x20702)+E(f807(x20703,x20704,x20701,x20705),f807(x20703,x20704,x20702,x20705))
% 155.94/155.64 [2071]~E(x20711,x20712)+E(f807(x20713,x20714,x20715,x20711),f807(x20713,x20714,x20715,x20712))
% 155.94/155.64 [2072]~E(x20721,x20722)+E(f208(x20721,x20723),f208(x20722,x20723))
% 155.94/155.64 [2073]~E(x20731,x20732)+E(f208(x20733,x20731),f208(x20733,x20732))
% 155.94/155.64 [2074]~E(x20741,x20742)+E(f407(x20741,x20743,x20744,x20745,x20746),f407(x20742,x20743,x20744,x20745,x20746))
% 155.94/155.64 [2075]~E(x20751,x20752)+E(f407(x20753,x20751,x20754,x20755,x20756),f407(x20753,x20752,x20754,x20755,x20756))
% 155.94/155.64 [2076]~E(x20761,x20762)+E(f407(x20763,x20764,x20761,x20765,x20766),f407(x20763,x20764,x20762,x20765,x20766))
% 155.94/155.64 [2077]~E(x20771,x20772)+E(f407(x20773,x20774,x20775,x20771,x20776),f407(x20773,x20774,x20775,x20772,x20776))
% 155.94/155.64 [2078]~E(x20781,x20782)+E(f407(x20783,x20784,x20785,x20786,x20781),f407(x20783,x20784,x20785,x20786,x20782))
% 155.94/155.64 [2079]~E(x20791,x20792)+E(f581(x20791),f581(x20792))
% 155.94/155.64 [2080]~E(x20801,x20802)+E(f795(x20801,x20803,x20804),f795(x20802,x20803,x20804))
% 155.94/155.64 [2081]~E(x20811,x20812)+E(f795(x20813,x20811,x20814),f795(x20813,x20812,x20814))
% 155.94/155.64 [2082]~E(x20821,x20822)+E(f795(x20823,x20824,x20821),f795(x20823,x20824,x20822))
% 155.94/155.64 [2083]~E(x20831,x20832)+E(f648(x20831,x20833,x20834),f648(x20832,x20833,x20834))
% 155.94/155.64 [2084]~E(x20841,x20842)+E(f648(x20843,x20841,x20844),f648(x20843,x20842,x20844))
% 155.94/155.64 [2085]~E(x20851,x20852)+E(f648(x20853,x20854,x20851),f648(x20853,x20854,x20852))
% 155.94/155.64 [2086]~E(x20861,x20862)+E(f564(x20861,x20863,x20864,x20865,x20866,x20867),f564(x20862,x20863,x20864,x20865,x20866,x20867))
% 155.94/155.64 [2087]~E(x20871,x20872)+E(f564(x20873,x20871,x20874,x20875,x20876,x20877),f564(x20873,x20872,x20874,x20875,x20876,x20877))
% 155.94/155.64 [2088]~E(x20881,x20882)+E(f564(x20883,x20884,x20881,x20885,x20886,x20887),f564(x20883,x20884,x20882,x20885,x20886,x20887))
% 155.94/155.64 [2089]~E(x20891,x20892)+E(f564(x20893,x20894,x20895,x20891,x20896,x20897),f564(x20893,x20894,x20895,x20892,x20896,x20897))
% 155.94/155.64 [2090]~E(x20901,x20902)+E(f564(x20903,x20904,x20905,x20906,x20901,x20907),f564(x20903,x20904,x20905,x20906,x20902,x20907))
% 155.94/155.64 [2091]~E(x20911,x20912)+E(f564(x20913,x20914,x20915,x20916,x20917,x20911),f564(x20913,x20914,x20915,x20916,x20917,x20912))
% 155.94/155.64 [2092]~E(x20921,x20922)+E(f489(x20921,x20923,x20924),f489(x20922,x20923,x20924))
% 155.94/155.64 [2093]~E(x20931,x20932)+E(f489(x20933,x20931,x20934),f489(x20933,x20932,x20934))
% 155.94/155.64 [2094]~E(x20941,x20942)+E(f489(x20943,x20944,x20941),f489(x20943,x20944,x20942))
% 155.94/155.64 [2095]~E(x20951,x20952)+E(f160(x20951,x20953,x20954,x20955),f160(x20952,x20953,x20954,x20955))
% 155.94/155.64 [2096]~E(x20961,x20962)+E(f160(x20963,x20961,x20964,x20965),f160(x20963,x20962,x20964,x20965))
% 155.94/155.64 [2097]~E(x20971,x20972)+E(f160(x20973,x20974,x20971,x20975),f160(x20973,x20974,x20972,x20975))
% 155.94/155.64 [2098]~E(x20981,x20982)+E(f160(x20983,x20984,x20985,x20981),f160(x20983,x20984,x20985,x20982))
% 155.94/155.64 [2099]~E(x20991,x20992)+E(f257(x20991,x20993),f257(x20992,x20993))
% 155.94/155.64 [2100]~E(x21001,x21002)+E(f257(x21003,x21001),f257(x21003,x21002))
% 155.94/155.64 [2101]~E(x21011,x21012)+E(f774(x21011,x21013),f774(x21012,x21013))
% 155.94/155.64 [2102]~E(x21021,x21022)+E(f774(x21023,x21021),f774(x21023,x21022))
% 155.94/155.64 [2103]~E(x21031,x21032)+E(f651(x21031,x21033),f651(x21032,x21033))
% 155.94/155.64 [2104]~E(x21041,x21042)+E(f651(x21043,x21041),f651(x21043,x21042))
% 155.94/155.64 [2105]~E(x21051,x21052)+E(f780(x21051,x21053,x21054),f780(x21052,x21053,x21054))
% 155.94/155.64 [2106]~E(x21061,x21062)+E(f780(x21063,x21061,x21064),f780(x21063,x21062,x21064))
% 155.94/155.64 [2107]~E(x21071,x21072)+E(f780(x21073,x21074,x21071),f780(x21073,x21074,x21072))
% 155.94/155.64 [2108]~E(x21081,x21082)+E(f698(x21081,x21083,x21084),f698(x21082,x21083,x21084))
% 155.94/155.64 [2109]~E(x21091,x21092)+E(f698(x21093,x21091,x21094),f698(x21093,x21092,x21094))
% 155.94/155.64 [2110]~E(x21101,x21102)+E(f698(x21103,x21104,x21101),f698(x21103,x21104,x21102))
% 155.94/155.64 [2111]~E(x21111,x21112)+E(f431(x21111,x21113,x21114),f431(x21112,x21113,x21114))
% 155.94/155.64 [2112]~E(x21121,x21122)+E(f431(x21123,x21121,x21124),f431(x21123,x21122,x21124))
% 155.94/155.64 [2113]~E(x21131,x21132)+E(f431(x21133,x21134,x21131),f431(x21133,x21134,x21132))
% 155.94/155.64 [2114]~E(x21141,x21142)+E(f712(x21141,x21143,x21144,x21145),f712(x21142,x21143,x21144,x21145))
% 155.94/155.64 [2115]~E(x21151,x21152)+E(f712(x21153,x21151,x21154,x21155),f712(x21153,x21152,x21154,x21155))
% 155.94/155.64 [2116]~E(x21161,x21162)+E(f712(x21163,x21164,x21161,x21165),f712(x21163,x21164,x21162,x21165))
% 155.94/155.64 [2117]~E(x21171,x21172)+E(f712(x21173,x21174,x21175,x21171),f712(x21173,x21174,x21175,x21172))
% 155.94/155.64 [2118]~E(x21181,x21182)+E(f481(x21181,x21183,x21184,x21185),f481(x21182,x21183,x21184,x21185))
% 155.94/155.64 [2119]~E(x21191,x21192)+E(f481(x21193,x21191,x21194,x21195),f481(x21193,x21192,x21194,x21195))
% 155.94/155.64 [2120]~E(x21201,x21202)+E(f481(x21203,x21204,x21201,x21205),f481(x21203,x21204,x21202,x21205))
% 155.94/155.64 [2121]~E(x21211,x21212)+E(f481(x21213,x21214,x21215,x21211),f481(x21213,x21214,x21215,x21212))
% 155.94/155.64 [2122]~E(x21221,x21222)+E(f836(x21221),f836(x21222))
% 155.94/155.64 [2123]~E(x21231,x21232)+E(f776(x21231,x21233,x21234,x21235,x21236),f776(x21232,x21233,x21234,x21235,x21236))
% 155.94/155.64 [2124]~E(x21241,x21242)+E(f776(x21243,x21241,x21244,x21245,x21246),f776(x21243,x21242,x21244,x21245,x21246))
% 155.94/155.64 [2125]~E(x21251,x21252)+E(f776(x21253,x21254,x21251,x21255,x21256),f776(x21253,x21254,x21252,x21255,x21256))
% 155.94/155.64 [2126]~E(x21261,x21262)+E(f776(x21263,x21264,x21265,x21261,x21266),f776(x21263,x21264,x21265,x21262,x21266))
% 155.94/155.64 [2127]~E(x21271,x21272)+E(f776(x21273,x21274,x21275,x21276,x21271),f776(x21273,x21274,x21275,x21276,x21272))
% 155.94/155.64 [2128]~E(x21281,x21282)+E(f459(x21281,x21283,x21284,x21285),f459(x21282,x21283,x21284,x21285))
% 155.94/155.64 [2129]~E(x21291,x21292)+E(f459(x21293,x21291,x21294,x21295),f459(x21293,x21292,x21294,x21295))
% 155.94/155.64 [2130]~E(x21301,x21302)+E(f459(x21303,x21304,x21301,x21305),f459(x21303,x21304,x21302,x21305))
% 155.94/155.64 [2131]~E(x21311,x21312)+E(f459(x21313,x21314,x21315,x21311),f459(x21313,x21314,x21315,x21312))
% 155.94/155.64 [2132]~E(x21321,x21322)+E(f438(x21321,x21323,x21324),f438(x21322,x21323,x21324))
% 155.94/155.64 [2133]~E(x21331,x21332)+E(f438(x21333,x21331,x21334),f438(x21333,x21332,x21334))
% 155.94/155.64 [2134]~E(x21341,x21342)+E(f438(x21343,x21344,x21341),f438(x21343,x21344,x21342))
% 155.94/155.64 [2135]~E(x21351,x21352)+E(f663(x21351,x21353,x21354),f663(x21352,x21353,x21354))
% 155.94/155.64 [2136]~E(x21361,x21362)+E(f663(x21363,x21361,x21364),f663(x21363,x21362,x21364))
% 155.94/155.64 [2137]~E(x21371,x21372)+E(f663(x21373,x21374,x21371),f663(x21373,x21374,x21372))
% 155.94/155.64 [2138]~E(x21381,x21382)+E(f828(x21381,x21383,x21384,x21385),f828(x21382,x21383,x21384,x21385))
% 155.94/155.64 [2139]~E(x21391,x21392)+E(f828(x21393,x21391,x21394,x21395),f828(x21393,x21392,x21394,x21395))
% 155.94/155.64 [2140]~E(x21401,x21402)+E(f828(x21403,x21404,x21401,x21405),f828(x21403,x21404,x21402,x21405))
% 155.94/155.64 [2141]~E(x21411,x21412)+E(f828(x21413,x21414,x21415,x21411),f828(x21413,x21414,x21415,x21412))
% 155.94/155.64 [2142]~E(x21421,x21422)+E(f479(x21421,x21423,x21424,x21425),f479(x21422,x21423,x21424,x21425))
% 155.94/155.64 [2143]~E(x21431,x21432)+E(f479(x21433,x21431,x21434,x21435),f479(x21433,x21432,x21434,x21435))
% 155.94/155.64 [2144]~E(x21441,x21442)+E(f479(x21443,x21444,x21441,x21445),f479(x21443,x21444,x21442,x21445))
% 155.94/155.64 [2145]~E(x21451,x21452)+E(f479(x21453,x21454,x21455,x21451),f479(x21453,x21454,x21455,x21452))
% 155.94/155.64 [2146]~E(x21461,x21462)+E(f824(x21461),f824(x21462))
% 155.94/155.64 [2147]~E(x21471,x21472)+E(f436(x21471,x21473,x21474),f436(x21472,x21473,x21474))
% 155.94/155.64 [2148]~E(x21481,x21482)+E(f436(x21483,x21481,x21484),f436(x21483,x21482,x21484))
% 155.94/155.64 [2149]~E(x21491,x21492)+E(f436(x21493,x21494,x21491),f436(x21493,x21494,x21492))
% 155.94/155.64 [2150]~E(x21501,x21502)+E(f345(x21501,x21503,x21504),f345(x21502,x21503,x21504))
% 155.94/155.64 [2151]~E(x21511,x21512)+E(f345(x21513,x21511,x21514),f345(x21513,x21512,x21514))
% 155.94/155.64 [2152]~E(x21521,x21522)+E(f345(x21523,x21524,x21521),f345(x21523,x21524,x21522))
% 155.94/155.64 [2153]~E(x21531,x21532)+E(f465(x21531,x21533,x21534),f465(x21532,x21533,x21534))
% 155.94/155.64 [2154]~E(x21541,x21542)+E(f465(x21543,x21541,x21544),f465(x21543,x21542,x21544))
% 155.94/155.64 [2155]~E(x21551,x21552)+E(f465(x21553,x21554,x21551),f465(x21553,x21554,x21552))
% 155.94/155.64 [2156]~E(x21561,x21562)+E(f454(x21561,x21563),f454(x21562,x21563))
% 155.94/155.64 [2157]~E(x21571,x21572)+E(f454(x21573,x21571),f454(x21573,x21572))
% 155.94/155.64 [2158]~E(x21581,x21582)+E(f552(x21581,x21583,x21584,x21585,x21586,x21587,x21588),f552(x21582,x21583,x21584,x21585,x21586,x21587,x21588))
% 155.94/155.64 [2159]~E(x21591,x21592)+E(f552(x21593,x21591,x21594,x21595,x21596,x21597,x21598),f552(x21593,x21592,x21594,x21595,x21596,x21597,x21598))
% 155.94/155.64 [2160]~E(x21601,x21602)+E(f552(x21603,x21604,x21601,x21605,x21606,x21607,x21608),f552(x21603,x21604,x21602,x21605,x21606,x21607,x21608))
% 155.94/155.64 [2161]~E(x21611,x21612)+E(f552(x21613,x21614,x21615,x21611,x21616,x21617,x21618),f552(x21613,x21614,x21615,x21612,x21616,x21617,x21618))
% 155.94/155.64 [2162]~E(x21621,x21622)+E(f552(x21623,x21624,x21625,x21626,x21621,x21627,x21628),f552(x21623,x21624,x21625,x21626,x21622,x21627,x21628))
% 155.94/155.64 [2163]~E(x21631,x21632)+E(f552(x21633,x21634,x21635,x21636,x21637,x21631,x21638),f552(x21633,x21634,x21635,x21636,x21637,x21632,x21638))
% 155.94/155.64 [2164]~E(x21641,x21642)+E(f552(x21643,x21644,x21645,x21646,x21647,x21648,x21641),f552(x21643,x21644,x21645,x21646,x21647,x21648,x21642))
% 155.94/155.64 [2165]~E(x21651,x21652)+E(f542(x21651,x21653,x21654),f542(x21652,x21653,x21654))
% 155.94/155.64 [2166]~E(x21661,x21662)+E(f542(x21663,x21661,x21664),f542(x21663,x21662,x21664))
% 155.94/155.64 [2167]~E(x21671,x21672)+E(f542(x21673,x21674,x21671),f542(x21673,x21674,x21672))
% 155.94/155.64 [2168]~E(x21681,x21682)+E(f206(x21681),f206(x21682))
% 155.94/155.64 [2169]~E(x21691,x21692)+E(f625(x21691,x21693,x21694,x21695),f625(x21692,x21693,x21694,x21695))
% 155.94/155.64 [2170]~E(x21701,x21702)+E(f625(x21703,x21701,x21704,x21705),f625(x21703,x21702,x21704,x21705))
% 155.94/155.64 [2171]~E(x21711,x21712)+E(f625(x21713,x21714,x21711,x21715),f625(x21713,x21714,x21712,x21715))
% 155.94/155.64 [2172]~E(x21721,x21722)+E(f625(x21723,x21724,x21725,x21721),f625(x21723,x21724,x21725,x21722))
% 155.94/155.64 [2173]~E(x21731,x21732)+E(f707(x21731,x21733,x21734,x21735),f707(x21732,x21733,x21734,x21735))
% 155.94/155.64 [2174]~E(x21741,x21742)+E(f707(x21743,x21741,x21744,x21745),f707(x21743,x21742,x21744,x21745))
% 155.94/155.64 [2175]~E(x21751,x21752)+E(f707(x21753,x21754,x21751,x21755),f707(x21753,x21754,x21752,x21755))
% 155.94/155.64 [2176]~E(x21761,x21762)+E(f707(x21763,x21764,x21765,x21761),f707(x21763,x21764,x21765,x21762))
% 155.94/155.64 [2177]~E(x21771,x21772)+E(f216(x21771,x21773,x21774,x21775),f216(x21772,x21773,x21774,x21775))
% 155.94/155.64 [2178]~E(x21781,x21782)+E(f216(x21783,x21781,x21784,x21785),f216(x21783,x21782,x21784,x21785))
% 155.94/155.64 [2179]~E(x21791,x21792)+E(f216(x21793,x21794,x21791,x21795),f216(x21793,x21794,x21792,x21795))
% 155.94/155.64 [2180]~E(x21801,x21802)+E(f216(x21803,x21804,x21805,x21801),f216(x21803,x21804,x21805,x21802))
% 155.94/155.64 [2181]~E(x21811,x21812)+E(f816(x21811,x21813,x21814,x21815,x21816),f816(x21812,x21813,x21814,x21815,x21816))
% 155.94/155.64 [2182]~E(x21821,x21822)+E(f816(x21823,x21821,x21824,x21825,x21826),f816(x21823,x21822,x21824,x21825,x21826))
% 155.94/155.64 [2183]~E(x21831,x21832)+E(f816(x21833,x21834,x21831,x21835,x21836),f816(x21833,x21834,x21832,x21835,x21836))
% 155.94/155.64 [2184]~E(x21841,x21842)+E(f816(x21843,x21844,x21845,x21841,x21846),f816(x21843,x21844,x21845,x21842,x21846))
% 155.94/155.64 [2185]~E(x21851,x21852)+E(f816(x21853,x21854,x21855,x21856,x21851),f816(x21853,x21854,x21855,x21856,x21852))
% 155.94/155.64 [2186]~E(x21861,x21862)+E(f363(x21861,x21863),f363(x21862,x21863))
% 155.94/155.64 [2187]~E(x21871,x21872)+E(f363(x21873,x21871),f363(x21873,x21872))
% 155.94/155.64 [2188]~E(x21881,x21882)+E(f373(x21881,x21883,x21884,x21885),f373(x21882,x21883,x21884,x21885))
% 155.94/155.64 [2189]~E(x21891,x21892)+E(f373(x21893,x21891,x21894,x21895),f373(x21893,x21892,x21894,x21895))
% 155.94/155.64 [2190]~E(x21901,x21902)+E(f373(x21903,x21904,x21901,x21905),f373(x21903,x21904,x21902,x21905))
% 155.94/155.64 [2191]~E(x21911,x21912)+E(f373(x21913,x21914,x21915,x21911),f373(x21913,x21914,x21915,x21912))
% 155.94/155.64 [2192]~E(x21921,x21922)+E(f627(x21921,x21923,x21924,x21925),f627(x21922,x21923,x21924,x21925))
% 155.94/155.64 [2193]~E(x21931,x21932)+E(f627(x21933,x21931,x21934,x21935),f627(x21933,x21932,x21934,x21935))
% 155.94/155.64 [2194]~E(x21941,x21942)+E(f627(x21943,x21944,x21941,x21945),f627(x21943,x21944,x21942,x21945))
% 155.94/155.64 [2195]~E(x21951,x21952)+E(f627(x21953,x21954,x21955,x21951),f627(x21953,x21954,x21955,x21952))
% 155.94/155.64 [2196]~E(x21961,x21962)+E(f615(x21961,x21963),f615(x21962,x21963))
% 155.94/155.64 [2197]~E(x21971,x21972)+E(f615(x21973,x21971),f615(x21973,x21972))
% 155.94/155.64 [2198]~E(x21981,x21982)+E(f492(x21981,x21983,x21984),f492(x21982,x21983,x21984))
% 155.94/155.64 [2199]~E(x21991,x21992)+E(f492(x21993,x21991,x21994),f492(x21993,x21992,x21994))
% 155.94/155.64 [2200]~E(x22001,x22002)+E(f492(x22003,x22004,x22001),f492(x22003,x22004,x22002))
% 155.94/155.64 [2201]~E(x22011,x22012)+E(f755(x22011,x22013,x22014,x22015,x22016),f755(x22012,x22013,x22014,x22015,x22016))
% 155.94/155.64 [2202]~E(x22021,x22022)+E(f755(x22023,x22021,x22024,x22025,x22026),f755(x22023,x22022,x22024,x22025,x22026))
% 155.94/155.64 [2203]~E(x22031,x22032)+E(f755(x22033,x22034,x22031,x22035,x22036),f755(x22033,x22034,x22032,x22035,x22036))
% 155.94/155.64 [2204]~E(x22041,x22042)+E(f755(x22043,x22044,x22045,x22041,x22046),f755(x22043,x22044,x22045,x22042,x22046))
% 155.94/155.64 [2205]~E(x22051,x22052)+E(f755(x22053,x22054,x22055,x22056,x22051),f755(x22053,x22054,x22055,x22056,x22052))
% 155.94/155.64 [2206]~E(x22061,x22062)+E(f379(x22061,x22063),f379(x22062,x22063))
% 155.94/155.64 [2207]~E(x22071,x22072)+E(f379(x22073,x22071),f379(x22073,x22072))
% 155.94/155.64 [2208]~E(x22081,x22082)+E(f102(x22081),f102(x22082))
% 155.94/155.64 [2209]~E(x22091,x22092)+E(f599(x22091,x22093),f599(x22092,x22093))
% 155.94/155.64 [2210]~E(x22101,x22102)+E(f599(x22103,x22101),f599(x22103,x22102))
% 155.94/155.64 [2211]~E(x22111,x22112)+E(f426(x22111,x22113,x22114),f426(x22112,x22113,x22114))
% 155.94/155.64 [2212]~E(x22121,x22122)+E(f426(x22123,x22121,x22124),f426(x22123,x22122,x22124))
% 155.94/155.64 [2213]~E(x22131,x22132)+E(f426(x22133,x22134,x22131),f426(x22133,x22134,x22132))
% 155.94/155.64 [2214]~E(x22141,x22142)+E(f535(x22141,x22143,x22144,x22145,x22146,x22147,x22148,x22149),f535(x22142,x22143,x22144,x22145,x22146,x22147,x22148,x22149))
% 155.94/155.64 [2215]~E(x22151,x22152)+E(f535(x22153,x22151,x22154,x22155,x22156,x22157,x22158,x22159),f535(x22153,x22152,x22154,x22155,x22156,x22157,x22158,x22159))
% 155.94/155.64 [2216]~E(x22161,x22162)+E(f535(x22163,x22164,x22161,x22165,x22166,x22167,x22168,x22169),f535(x22163,x22164,x22162,x22165,x22166,x22167,x22168,x22169))
% 155.94/155.64 [2217]~E(x22171,x22172)+E(f535(x22173,x22174,x22175,x22171,x22176,x22177,x22178,x22179),f535(x22173,x22174,x22175,x22172,x22176,x22177,x22178,x22179))
% 155.94/155.64 [2218]~E(x22181,x22182)+E(f535(x22183,x22184,x22185,x22186,x22181,x22187,x22188,x22189),f535(x22183,x22184,x22185,x22186,x22182,x22187,x22188,x22189))
% 155.94/155.64 [2219]~E(x22191,x22192)+E(f535(x22193,x22194,x22195,x22196,x22197,x22191,x22198,x22199),f535(x22193,x22194,x22195,x22196,x22197,x22192,x22198,x22199))
% 155.94/155.64 [2220]~E(x22201,x22202)+E(f535(x22203,x22204,x22205,x22206,x22207,x22208,x22201,x22209),f535(x22203,x22204,x22205,x22206,x22207,x22208,x22202,x22209))
% 155.94/155.64 [2221]~E(x22211,x22212)+E(f535(x22213,x22214,x22215,x22216,x22217,x22218,x22219,x22211),f535(x22213,x22214,x22215,x22216,x22217,x22218,x22219,x22212))
% 155.94/155.64 [2222]~E(x22221,x22222)+E(f360(x22221,x22223),f360(x22222,x22223))
% 155.94/155.64 [2223]~E(x22231,x22232)+E(f360(x22233,x22231),f360(x22233,x22232))
% 155.94/155.64 [2224]~E(x22241,x22242)+E(f714(x22241,x22243,x22244,x22245,x22246,x22247),f714(x22242,x22243,x22244,x22245,x22246,x22247))
% 155.94/155.64 [2225]~E(x22251,x22252)+E(f714(x22253,x22251,x22254,x22255,x22256,x22257),f714(x22253,x22252,x22254,x22255,x22256,x22257))
% 155.94/155.64 [2226]~E(x22261,x22262)+E(f714(x22263,x22264,x22261,x22265,x22266,x22267),f714(x22263,x22264,x22262,x22265,x22266,x22267))
% 155.94/155.64 [2227]~E(x22271,x22272)+E(f714(x22273,x22274,x22275,x22271,x22276,x22277),f714(x22273,x22274,x22275,x22272,x22276,x22277))
% 155.94/155.64 [2228]~E(x22281,x22282)+E(f714(x22283,x22284,x22285,x22286,x22281,x22287),f714(x22283,x22284,x22285,x22286,x22282,x22287))
% 155.94/155.64 [2229]~E(x22291,x22292)+E(f714(x22293,x22294,x22295,x22296,x22297,x22291),f714(x22293,x22294,x22295,x22296,x22297,x22292))
% 155.94/155.64 [2230]~E(x22301,x22302)+E(f539(x22301),f539(x22302))
% 155.94/155.64 [2231]~E(x22311,x22312)+E(f452(x22311,x22313,x22314,x22315),f452(x22312,x22313,x22314,x22315))
% 155.94/155.64 [2232]~E(x22321,x22322)+E(f452(x22323,x22321,x22324,x22325),f452(x22323,x22322,x22324,x22325))
% 155.94/155.64 [2233]~E(x22331,x22332)+E(f452(x22333,x22334,x22331,x22335),f452(x22333,x22334,x22332,x22335))
% 155.94/155.64 [2234]~E(x22341,x22342)+E(f452(x22343,x22344,x22345,x22341),f452(x22343,x22344,x22345,x22342))
% 155.94/155.64 [2235]~E(x22351,x22352)+E(f565(x22351,x22353,x22354,x22355,x22356,x22357),f565(x22352,x22353,x22354,x22355,x22356,x22357))
% 155.94/155.64 [2236]~E(x22361,x22362)+E(f565(x22363,x22361,x22364,x22365,x22366,x22367),f565(x22363,x22362,x22364,x22365,x22366,x22367))
% 155.94/155.64 [2237]~E(x22371,x22372)+E(f565(x22373,x22374,x22371,x22375,x22376,x22377),f565(x22373,x22374,x22372,x22375,x22376,x22377))
% 155.94/155.64 [2238]~E(x22381,x22382)+E(f565(x22383,x22384,x22385,x22381,x22386,x22387),f565(x22383,x22384,x22385,x22382,x22386,x22387))
% 155.94/155.64 [2239]~E(x22391,x22392)+E(f565(x22393,x22394,x22395,x22396,x22391,x22397),f565(x22393,x22394,x22395,x22396,x22392,x22397))
% 155.94/155.64 [2240]~E(x22401,x22402)+E(f565(x22403,x22404,x22405,x22406,x22407,x22401),f565(x22403,x22404,x22405,x22406,x22407,x22402))
% 155.94/155.64 [2241]~E(x22411,x22412)+E(f372(x22411),f372(x22412))
% 155.94/155.64 [2242]~E(x22421,x22422)+E(f453(x22421,x22423,x22424,x22425,x22426,x22427),f453(x22422,x22423,x22424,x22425,x22426,x22427))
% 155.94/155.64 [2243]~E(x22431,x22432)+E(f453(x22433,x22431,x22434,x22435,x22436,x22437),f453(x22433,x22432,x22434,x22435,x22436,x22437))
% 155.94/155.64 [2244]~E(x22441,x22442)+E(f453(x22443,x22444,x22441,x22445,x22446,x22447),f453(x22443,x22444,x22442,x22445,x22446,x22447))
% 155.94/155.64 [2245]~E(x22451,x22452)+E(f453(x22453,x22454,x22455,x22451,x22456,x22457),f453(x22453,x22454,x22455,x22452,x22456,x22457))
% 155.94/155.64 [2246]~E(x22461,x22462)+E(f453(x22463,x22464,x22465,x22466,x22461,x22467),f453(x22463,x22464,x22465,x22466,x22462,x22467))
% 155.94/155.64 [2247]~E(x22471,x22472)+E(f453(x22473,x22474,x22475,x22476,x22477,x22471),f453(x22473,x22474,x22475,x22476,x22477,x22472))
% 155.94/155.64 [2248]~E(x22481,x22482)+E(f325(x22481,x22483),f325(x22482,x22483))
% 155.94/155.64 [2249]~E(x22491,x22492)+E(f325(x22493,x22491),f325(x22493,x22492))
% 155.94/155.64 [2250]~E(x22501,x22502)+E(f729(x22501,x22503,x22504,x22505,x22506),f729(x22502,x22503,x22504,x22505,x22506))
% 155.94/155.64 [2251]~E(x22511,x22512)+E(f729(x22513,x22511,x22514,x22515,x22516),f729(x22513,x22512,x22514,x22515,x22516))
% 155.94/155.64 [2252]~E(x22521,x22522)+E(f729(x22523,x22524,x22521,x22525,x22526),f729(x22523,x22524,x22522,x22525,x22526))
% 155.94/155.64 [2253]~E(x22531,x22532)+E(f729(x22533,x22534,x22535,x22531,x22536),f729(x22533,x22534,x22535,x22532,x22536))
% 155.94/155.64 [2254]~E(x22541,x22542)+E(f729(x22543,x22544,x22545,x22546,x22541),f729(x22543,x22544,x22545,x22546,x22542))
% 155.94/155.64 [2255]~E(x22551,x22552)+E(f820(x22551),f820(x22552))
% 155.94/155.64 [2256]~E(x22561,x22562)+E(f463(x22561,x22563),f463(x22562,x22563))
% 155.94/155.64 [2257]~E(x22571,x22572)+E(f463(x22573,x22571),f463(x22573,x22572))
% 155.94/155.64 [2258]~E(x22581,x22582)+E(f488(x22581,x22583,x22584,x22585,x22586),f488(x22582,x22583,x22584,x22585,x22586))
% 155.94/155.64 [2259]~E(x22591,x22592)+E(f488(x22593,x22591,x22594,x22595,x22596),f488(x22593,x22592,x22594,x22595,x22596))
% 155.94/155.64 [2260]~E(x22601,x22602)+E(f488(x22603,x22604,x22601,x22605,x22606),f488(x22603,x22604,x22602,x22605,x22606))
% 155.94/155.64 [2261]~E(x22611,x22612)+E(f488(x22613,x22614,x22615,x22611,x22616),f488(x22613,x22614,x22615,x22612,x22616))
% 155.94/155.64 [2262]~E(x22621,x22622)+E(f488(x22623,x22624,x22625,x22626,x22621),f488(x22623,x22624,x22625,x22626,x22622))
% 155.94/155.64 [2263]~E(x22631,x22632)+E(f362(x22631),f362(x22632))
% 155.94/155.64 [2264]~E(x22641,x22642)+E(f576(x22641,x22643,x22644,x22645),f576(x22642,x22643,x22644,x22645))
% 155.94/155.64 [2265]~E(x22651,x22652)+E(f576(x22653,x22651,x22654,x22655),f576(x22653,x22652,x22654,x22655))
% 155.94/155.64 [2266]~E(x22661,x22662)+E(f576(x22663,x22664,x22661,x22665),f576(x22663,x22664,x22662,x22665))
% 155.94/155.64 [2267]~E(x22671,x22672)+E(f576(x22673,x22674,x22675,x22671),f576(x22673,x22674,x22675,x22672))
% 155.94/155.64 [2268]~E(x22681,x22682)+E(f340(x22681,x22683,x22684),f340(x22682,x22683,x22684))
% 155.94/155.64 [2269]~E(x22691,x22692)+E(f340(x22693,x22691,x22694),f340(x22693,x22692,x22694))
% 155.94/155.64 [2270]~E(x22701,x22702)+E(f340(x22703,x22704,x22701),f340(x22703,x22704,x22702))
% 155.94/155.64 [2271]~E(x22711,x22712)+E(f635(x22711,x22713,x22714,x22715),f635(x22712,x22713,x22714,x22715))
% 155.94/155.64 [2272]~E(x22721,x22722)+E(f635(x22723,x22721,x22724,x22725),f635(x22723,x22722,x22724,x22725))
% 155.94/155.64 [2273]~E(x22731,x22732)+E(f635(x22733,x22734,x22731,x22735),f635(x22733,x22734,x22732,x22735))
% 155.94/155.64 [2274]~E(x22741,x22742)+E(f635(x22743,x22744,x22745,x22741),f635(x22743,x22744,x22745,x22742))
% 155.94/155.64 [2275]~E(x22751,x22752)+E(f555(x22751,x22753),f555(x22752,x22753))
% 155.94/155.64 [2276]~E(x22761,x22762)+E(f555(x22763,x22761),f555(x22763,x22762))
% 155.94/155.64 [2277]~E(x22771,x22772)+E(f380(x22771,x22773),f380(x22772,x22773))
% 155.94/155.64 [2278]~E(x22781,x22782)+E(f380(x22783,x22781),f380(x22783,x22782))
% 155.94/155.64 [2279]~E(x22791,x22792)+E(f397(x22791,x22793,x22794),f397(x22792,x22793,x22794))
% 155.94/155.64 [2280]~E(x22801,x22802)+E(f397(x22803,x22801,x22804),f397(x22803,x22802,x22804))
% 155.94/155.64 [2281]~E(x22811,x22812)+E(f397(x22813,x22814,x22811),f397(x22813,x22814,x22812))
% 155.94/155.64 [2282]~E(x22821,x22822)+E(f829(x22821,x22823,x22824,x22825),f829(x22822,x22823,x22824,x22825))
% 155.94/155.64 [2283]~E(x22831,x22832)+E(f829(x22833,x22831,x22834,x22835),f829(x22833,x22832,x22834,x22835))
% 155.94/155.64 [2284]~E(x22841,x22842)+E(f829(x22843,x22844,x22841,x22845),f829(x22843,x22844,x22842,x22845))
% 155.94/155.64 [2285]~E(x22851,x22852)+E(f829(x22853,x22854,x22855,x22851),f829(x22853,x22854,x22855,x22852))
% 155.94/155.64 [2286]~E(x22861,x22862)+E(f524(x22861,x22863,x22864),f524(x22862,x22863,x22864))
% 155.94/155.64 [2287]~E(x22871,x22872)+E(f524(x22873,x22871,x22874),f524(x22873,x22872,x22874))
% 155.94/155.64 [2288]~E(x22881,x22882)+E(f524(x22883,x22884,x22881),f524(x22883,x22884,x22882))
% 155.94/155.64 [2289]~E(x22891,x22892)+E(f430(x22891,x22893),f430(x22892,x22893))
% 155.94/155.64 [2290]~E(x22901,x22902)+E(f430(x22903,x22901),f430(x22903,x22902))
% 155.94/155.64 [2291]~E(x22911,x22912)+E(f533(x22911,x22913,x22914,x22915,x22916),f533(x22912,x22913,x22914,x22915,x22916))
% 155.94/155.64 [2292]~E(x22921,x22922)+E(f533(x22923,x22921,x22924,x22925,x22926),f533(x22923,x22922,x22924,x22925,x22926))
% 155.94/155.64 [2293]~E(x22931,x22932)+E(f533(x22933,x22934,x22931,x22935,x22936),f533(x22933,x22934,x22932,x22935,x22936))
% 155.94/155.64 [2294]~E(x22941,x22942)+E(f533(x22943,x22944,x22945,x22941,x22946),f533(x22943,x22944,x22945,x22942,x22946))
% 155.94/155.64 [2295]~E(x22951,x22952)+E(f533(x22953,x22954,x22955,x22956,x22951),f533(x22953,x22954,x22955,x22956,x22952))
% 155.94/155.64 [2296]~E(x22961,x22962)+E(f699(x22961,x22963,x22964,x22965),f699(x22962,x22963,x22964,x22965))
% 155.94/155.64 [2297]~E(x22971,x22972)+E(f699(x22973,x22971,x22974,x22975),f699(x22973,x22972,x22974,x22975))
% 155.94/155.64 [2298]~E(x22981,x22982)+E(f699(x22983,x22984,x22981,x22985),f699(x22983,x22984,x22982,x22985))
% 155.94/155.64 [2299]~E(x22991,x22992)+E(f699(x22993,x22994,x22995,x22991),f699(x22993,x22994,x22995,x22992))
% 155.94/155.64 [2300]~E(x23001,x23002)+E(f130(x23001),f130(x23002))
% 155.94/155.64 [2301]~E(x23011,x23012)+E(f572(x23011,x23013,x23014),f572(x23012,x23013,x23014))
% 155.94/155.64 [2302]~E(x23021,x23022)+E(f572(x23023,x23021,x23024),f572(x23023,x23022,x23024))
% 155.94/155.64 [2303]~E(x23031,x23032)+E(f572(x23033,x23034,x23031),f572(x23033,x23034,x23032))
% 155.94/155.64 [2304]~E(x23041,x23042)+E(f329(x23041,x23043,x23044),f329(x23042,x23043,x23044))
% 155.94/155.64 [2305]~E(x23051,x23052)+E(f329(x23053,x23051,x23054),f329(x23053,x23052,x23054))
% 155.94/155.64 [2306]~E(x23061,x23062)+E(f329(x23063,x23064,x23061),f329(x23063,x23064,x23062))
% 155.94/155.64 [2307]~E(x23071,x23072)+E(f631(x23071,x23073,x23074),f631(x23072,x23073,x23074))
% 155.94/155.64 [2308]~E(x23081,x23082)+E(f631(x23083,x23081,x23084),f631(x23083,x23082,x23084))
% 155.94/155.64 [2309]~E(x23091,x23092)+E(f631(x23093,x23094,x23091),f631(x23093,x23094,x23092))
% 155.94/155.64 [2310]~E(x23101,x23102)+E(f485(x23101,x23103,x23104,x23105,x23106,x23107),f485(x23102,x23103,x23104,x23105,x23106,x23107))
% 155.94/155.64 [2311]~E(x23111,x23112)+E(f485(x23113,x23111,x23114,x23115,x23116,x23117),f485(x23113,x23112,x23114,x23115,x23116,x23117))
% 155.94/155.64 [2312]~E(x23121,x23122)+E(f485(x23123,x23124,x23121,x23125,x23126,x23127),f485(x23123,x23124,x23122,x23125,x23126,x23127))
% 155.94/155.64 [2313]~E(x23131,x23132)+E(f485(x23133,x23134,x23135,x23131,x23136,x23137),f485(x23133,x23134,x23135,x23132,x23136,x23137))
% 155.94/155.64 [2314]~E(x23141,x23142)+E(f485(x23143,x23144,x23145,x23146,x23141,x23147),f485(x23143,x23144,x23145,x23146,x23142,x23147))
% 155.94/155.64 [2315]~E(x23151,x23152)+E(f485(x23153,x23154,x23155,x23156,x23157,x23151),f485(x23153,x23154,x23155,x23156,x23157,x23152))
% 155.94/155.64 [2316]~E(x23161,x23162)+E(f532(x23161,x23163,x23164,x23165,x23166),f532(x23162,x23163,x23164,x23165,x23166))
% 155.94/155.64 [2317]~E(x23171,x23172)+E(f532(x23173,x23171,x23174,x23175,x23176),f532(x23173,x23172,x23174,x23175,x23176))
% 155.94/155.64 [2318]~E(x23181,x23182)+E(f532(x23183,x23184,x23181,x23185,x23186),f532(x23183,x23184,x23182,x23185,x23186))
% 155.94/155.64 [2319]~E(x23191,x23192)+E(f532(x23193,x23194,x23195,x23191,x23196),f532(x23193,x23194,x23195,x23192,x23196))
% 155.94/155.64 [2320]~E(x23201,x23202)+E(f532(x23203,x23204,x23205,x23206,x23201),f532(x23203,x23204,x23205,x23206,x23202))
% 155.94/155.64 [2321]~E(x23211,x23212)+E(f513(x23211,x23213,x23214,x23215,x23216),f513(x23212,x23213,x23214,x23215,x23216))
% 155.94/155.64 [2322]~E(x23221,x23222)+E(f513(x23223,x23221,x23224,x23225,x23226),f513(x23223,x23222,x23224,x23225,x23226))
% 155.94/155.64 [2323]~E(x23231,x23232)+E(f513(x23233,x23234,x23231,x23235,x23236),f513(x23233,x23234,x23232,x23235,x23236))
% 155.94/155.64 [2324]~E(x23241,x23242)+E(f513(x23243,x23244,x23245,x23241,x23246),f513(x23243,x23244,x23245,x23242,x23246))
% 155.94/155.64 [2325]~E(x23251,x23252)+E(f513(x23253,x23254,x23255,x23256,x23251),f513(x23253,x23254,x23255,x23256,x23252))
% 155.94/155.64 [2326]~E(x23261,x23262)+E(f439(x23261,x23263,x23264),f439(x23262,x23263,x23264))
% 155.94/155.64 [2327]~E(x23271,x23272)+E(f439(x23273,x23271,x23274),f439(x23273,x23272,x23274))
% 155.94/155.64 [2328]~E(x23281,x23282)+E(f439(x23283,x23284,x23281),f439(x23283,x23284,x23282))
% 155.94/155.64 [2329]~E(x23291,x23292)+E(f798(x23291,x23293,x23294,x23295),f798(x23292,x23293,x23294,x23295))
% 155.94/155.64 [2330]~E(x23301,x23302)+E(f798(x23303,x23301,x23304,x23305),f798(x23303,x23302,x23304,x23305))
% 155.94/155.64 [2331]~E(x23311,x23312)+E(f798(x23313,x23314,x23311,x23315),f798(x23313,x23314,x23312,x23315))
% 155.94/155.64 [2332]~E(x23321,x23322)+E(f798(x23323,x23324,x23325,x23321),f798(x23323,x23324,x23325,x23322))
% 155.94/155.64 [2333]~E(x23331,x23332)+E(f649(x23331),f649(x23332))
% 155.94/155.64 [2334]~E(x23341,x23342)+E(f326(x23341,x23343),f326(x23342,x23343))
% 155.94/155.64 [2335]~E(x23351,x23352)+E(f326(x23353,x23351),f326(x23353,x23352))
% 155.94/155.64 [2336]~E(x23361,x23362)+E(f429(x23361),f429(x23362))
% 155.94/155.64 [2337]~E(x23371,x23372)+E(f401(x23371,x23373,x23374,x23375,x23376),f401(x23372,x23373,x23374,x23375,x23376))
% 155.94/155.64 [2338]~E(x23381,x23382)+E(f401(x23383,x23381,x23384,x23385,x23386),f401(x23383,x23382,x23384,x23385,x23386))
% 155.94/155.64 [2339]~E(x23391,x23392)+E(f401(x23393,x23394,x23391,x23395,x23396),f401(x23393,x23394,x23392,x23395,x23396))
% 155.94/155.64 [2340]~E(x23401,x23402)+E(f401(x23403,x23404,x23405,x23401,x23406),f401(x23403,x23404,x23405,x23402,x23406))
% 155.94/155.64 [2341]~E(x23411,x23412)+E(f401(x23413,x23414,x23415,x23416,x23411),f401(x23413,x23414,x23415,x23416,x23412))
% 155.94/155.64 [2342]~E(x23421,x23422)+E(f214(x23421,x23423,x23424,x23425,x23426),f214(x23422,x23423,x23424,x23425,x23426))
% 155.94/155.64 [2343]~E(x23431,x23432)+E(f214(x23433,x23431,x23434,x23435,x23436),f214(x23433,x23432,x23434,x23435,x23436))
% 155.94/155.64 [2344]~E(x23441,x23442)+E(f214(x23443,x23444,x23441,x23445,x23446),f214(x23443,x23444,x23442,x23445,x23446))
% 155.94/155.64 [2345]~E(x23451,x23452)+E(f214(x23453,x23454,x23455,x23451,x23456),f214(x23453,x23454,x23455,x23452,x23456))
% 155.94/155.64 [2346]~E(x23461,x23462)+E(f214(x23463,x23464,x23465,x23466,x23461),f214(x23463,x23464,x23465,x23466,x23462))
% 155.94/155.64 [2347]~E(x23471,x23472)+E(f402(x23471,x23473,x23474,x23475,x23476),f402(x23472,x23473,x23474,x23475,x23476))
% 155.94/155.64 [2348]~E(x23481,x23482)+E(f402(x23483,x23481,x23484,x23485,x23486),f402(x23483,x23482,x23484,x23485,x23486))
% 155.94/155.64 [2349]~E(x23491,x23492)+E(f402(x23493,x23494,x23491,x23495,x23496),f402(x23493,x23494,x23492,x23495,x23496))
% 155.94/155.64 [2350]~E(x23501,x23502)+E(f402(x23503,x23504,x23505,x23501,x23506),f402(x23503,x23504,x23505,x23502,x23506))
% 155.94/155.64 [2351]~E(x23511,x23512)+E(f402(x23513,x23514,x23515,x23516,x23511),f402(x23513,x23514,x23515,x23516,x23512))
% 155.94/155.64 [2352]~E(x23521,x23522)+E(f457(x23521,x23523,x23524),f457(x23522,x23523,x23524))
% 155.94/155.64 [2353]~E(x23531,x23532)+E(f457(x23533,x23531,x23534),f457(x23533,x23532,x23534))
% 155.94/155.64 [2354]~E(x23541,x23542)+E(f457(x23543,x23544,x23541),f457(x23543,x23544,x23542))
% 155.94/155.64 [2355]~E(x23551,x23552)+E(f700(x23551,x23553,x23554,x23555),f700(x23552,x23553,x23554,x23555))
% 155.94/155.64 [2356]~E(x23561,x23562)+E(f700(x23563,x23561,x23564,x23565),f700(x23563,x23562,x23564,x23565))
% 155.94/155.64 [2357]~E(x23571,x23572)+E(f700(x23573,x23574,x23571,x23575),f700(x23573,x23574,x23572,x23575))
% 155.94/155.64 [2358]~E(x23581,x23582)+E(f700(x23583,x23584,x23585,x23581),f700(x23583,x23584,x23585,x23582))
% 155.94/155.64 [2359]~E(x23591,x23592)+E(f618(x23591,x23593,x23594,x23595),f618(x23592,x23593,x23594,x23595))
% 155.94/155.64 [2360]~E(x23601,x23602)+E(f618(x23603,x23601,x23604,x23605),f618(x23603,x23602,x23604,x23605))
% 155.94/155.64 [2361]~E(x23611,x23612)+E(f618(x23613,x23614,x23611,x23615),f618(x23613,x23614,x23612,x23615))
% 155.94/155.64 [2362]~E(x23621,x23622)+E(f618(x23623,x23624,x23625,x23621),f618(x23623,x23624,x23625,x23622))
% 155.94/155.64 [2363]~E(x23631,x23632)+E(f548(x23631,x23633,x23634,x23635,x23636),f548(x23632,x23633,x23634,x23635,x23636))
% 155.94/155.64 [2364]~E(x23641,x23642)+E(f548(x23643,x23641,x23644,x23645,x23646),f548(x23643,x23642,x23644,x23645,x23646))
% 155.94/155.64 [2365]~E(x23651,x23652)+E(f548(x23653,x23654,x23651,x23655,x23656),f548(x23653,x23654,x23652,x23655,x23656))
% 155.94/155.64 [2366]~E(x23661,x23662)+E(f548(x23663,x23664,x23665,x23661,x23666),f548(x23663,x23664,x23665,x23662,x23666))
% 155.94/155.64 [2367]~E(x23671,x23672)+E(f548(x23673,x23674,x23675,x23676,x23671),f548(x23673,x23674,x23675,x23676,x23672))
% 155.94/155.64 [2368]~E(x23681,x23682)+E(f762(x23681,x23683,x23684),f762(x23682,x23683,x23684))
% 155.94/155.64 [2369]~E(x23691,x23692)+E(f762(x23693,x23691,x23694),f762(x23693,x23692,x23694))
% 155.94/155.64 [2370]~E(x23701,x23702)+E(f762(x23703,x23704,x23701),f762(x23703,x23704,x23702))
% 155.94/155.64 [2371]~E(x23711,x23712)+E(f607(x23711,x23713,x23714,x23715),f607(x23712,x23713,x23714,x23715))
% 155.94/155.64 [2372]~E(x23721,x23722)+E(f607(x23723,x23721,x23724,x23725),f607(x23723,x23722,x23724,x23725))
% 155.94/155.64 [2373]~E(x23731,x23732)+E(f607(x23733,x23734,x23731,x23735),f607(x23733,x23734,x23732,x23735))
% 155.94/155.64 [2374]~E(x23741,x23742)+E(f607(x23743,x23744,x23745,x23741),f607(x23743,x23744,x23745,x23742))
% 155.94/155.64 [2375]~E(x23751,x23752)+E(f835(x23751),f835(x23752))
% 155.94/155.64 [2376]~E(x23761,x23762)+E(f427(x23761,x23763,x23764,x23765,x23766),f427(x23762,x23763,x23764,x23765,x23766))
% 155.94/155.64 [2377]~E(x23771,x23772)+E(f427(x23773,x23771,x23774,x23775,x23776),f427(x23773,x23772,x23774,x23775,x23776))
% 155.94/155.64 [2378]~E(x23781,x23782)+E(f427(x23783,x23784,x23781,x23785,x23786),f427(x23783,x23784,x23782,x23785,x23786))
% 155.94/155.64 [2379]~E(x23791,x23792)+E(f427(x23793,x23794,x23795,x23791,x23796),f427(x23793,x23794,x23795,x23792,x23796))
% 155.94/155.64 [2380]~E(x23801,x23802)+E(f427(x23803,x23804,x23805,x23806,x23801),f427(x23803,x23804,x23805,x23806,x23802))
% 155.94/155.64 [2381]~E(x23811,x23812)+E(f368(x23811),f368(x23812))
% 155.94/155.64 [2382]~E(x23821,x23822)+E(f668(x23821,x23823,x23824),f668(x23822,x23823,x23824))
% 155.94/155.64 [2383]~E(x23831,x23832)+E(f668(x23833,x23831,x23834),f668(x23833,x23832,x23834))
% 155.94/155.64 [2384]~E(x23841,x23842)+E(f668(x23843,x23844,x23841),f668(x23843,x23844,x23842))
% 155.94/155.64 [2385]~E(x23851,x23852)+E(f585(x23851,x23853,x23854,x23855),f585(x23852,x23853,x23854,x23855))
% 155.94/155.64 [2386]~E(x23861,x23862)+E(f585(x23863,x23861,x23864,x23865),f585(x23863,x23862,x23864,x23865))
% 155.94/155.64 [2387]~E(x23871,x23872)+E(f585(x23873,x23874,x23871,x23875),f585(x23873,x23874,x23872,x23875))
% 155.94/155.64 [2388]~E(x23881,x23882)+E(f585(x23883,x23884,x23885,x23881),f585(x23883,x23884,x23885,x23882))
% 155.94/155.64 [2389]~E(x23891,x23892)+E(f821(x23891,x23893),f821(x23892,x23893))
% 155.94/155.64 [2390]~E(x23901,x23902)+E(f821(x23903,x23901),f821(x23903,x23902))
% 155.94/155.64 [2391]~E(x23911,x23912)+E(f596(x23911,x23913,x23914,x23915,x23916,x23917,x23918),f596(x23912,x23913,x23914,x23915,x23916,x23917,x23918))
% 155.94/155.64 [2392]~E(x23921,x23922)+E(f596(x23923,x23921,x23924,x23925,x23926,x23927,x23928),f596(x23923,x23922,x23924,x23925,x23926,x23927,x23928))
% 155.94/155.64 [2393]~E(x23931,x23932)+E(f596(x23933,x23934,x23931,x23935,x23936,x23937,x23938),f596(x23933,x23934,x23932,x23935,x23936,x23937,x23938))
% 155.94/155.64 [2394]~E(x23941,x23942)+E(f596(x23943,x23944,x23945,x23941,x23946,x23947,x23948),f596(x23943,x23944,x23945,x23942,x23946,x23947,x23948))
% 155.94/155.64 [2395]~E(x23951,x23952)+E(f596(x23953,x23954,x23955,x23956,x23951,x23957,x23958),f596(x23953,x23954,x23955,x23956,x23952,x23957,x23958))
% 155.94/155.64 [2396]~E(x23961,x23962)+E(f596(x23963,x23964,x23965,x23966,x23967,x23961,x23968),f596(x23963,x23964,x23965,x23966,x23967,x23962,x23968))
% 155.94/155.64 [2397]~E(x23971,x23972)+E(f596(x23973,x23974,x23975,x23976,x23977,x23978,x23971),f596(x23973,x23974,x23975,x23976,x23977,x23978,x23972))
% 155.94/155.64 [2398]~E(x23981,x23982)+E(f655(x23981,x23983,x23984),f655(x23982,x23983,x23984))
% 155.94/155.64 [2399]~E(x23991,x23992)+E(f655(x23993,x23991,x23994),f655(x23993,x23992,x23994))
% 155.94/155.64 [2400]~E(x24001,x24002)+E(f655(x24003,x24004,x24001),f655(x24003,x24004,x24002))
% 155.94/155.64 [2401]~E(x24011,x24012)+E(f464(x24011,x24013),f464(x24012,x24013))
% 155.94/155.64 [2402]~E(x24021,x24022)+E(f464(x24023,x24021),f464(x24023,x24022))
% 155.94/155.64 [2403]~E(x24031,x24032)+E(f675(x24031,x24033),f675(x24032,x24033))
% 155.94/155.64 [2404]~E(x24041,x24042)+E(f675(x24043,x24041),f675(x24043,x24042))
% 155.94/155.64 [2405]~E(x24051,x24052)+E(f753(x24051,x24053,x24054,x24055,x24056,x24057,x24058,x24059),f753(x24052,x24053,x24054,x24055,x24056,x24057,x24058,x24059))
% 155.94/155.64 [2406]~E(x24061,x24062)+E(f753(x24063,x24061,x24064,x24065,x24066,x24067,x24068,x24069),f753(x24063,x24062,x24064,x24065,x24066,x24067,x24068,x24069))
% 155.94/155.64 [2407]~E(x24071,x24072)+E(f753(x24073,x24074,x24071,x24075,x24076,x24077,x24078,x24079),f753(x24073,x24074,x24072,x24075,x24076,x24077,x24078,x24079))
% 155.94/155.64 [2408]~E(x24081,x24082)+E(f753(x24083,x24084,x24085,x24081,x24086,x24087,x24088,x24089),f753(x24083,x24084,x24085,x24082,x24086,x24087,x24088,x24089))
% 155.94/155.64 [2409]~E(x24091,x24092)+E(f753(x24093,x24094,x24095,x24096,x24091,x24097,x24098,x24099),f753(x24093,x24094,x24095,x24096,x24092,x24097,x24098,x24099))
% 155.94/155.64 [2410]~E(x24101,x24102)+E(f753(x24103,x24104,x24105,x24106,x24107,x24101,x24108,x24109),f753(x24103,x24104,x24105,x24106,x24107,x24102,x24108,x24109))
% 155.94/155.64 [2411]~E(x24111,x24112)+E(f753(x24113,x24114,x24115,x24116,x24117,x24118,x24111,x24119),f753(x24113,x24114,x24115,x24116,x24117,x24118,x24112,x24119))
% 155.94/155.64 [2412]~E(x24121,x24122)+E(f753(x24123,x24124,x24125,x24126,x24127,x24128,x24129,x24121),f753(x24123,x24124,x24125,x24126,x24127,x24128,x24129,x24122))
% 155.94/155.64 [2413]~E(x24131,x24132)+E(f456(x24131,x24133),f456(x24132,x24133))
% 155.94/155.64 [2414]~E(x24141,x24142)+E(f456(x24143,x24141),f456(x24143,x24142))
% 155.94/155.64 [2415]~E(x24151,x24152)+E(f344(x24151,x24153,x24154),f344(x24152,x24153,x24154))
% 155.94/155.64 [2416]~E(x24161,x24162)+E(f344(x24163,x24161,x24164),f344(x24163,x24162,x24164))
% 155.94/155.64 [2417]~E(x24171,x24172)+E(f344(x24173,x24174,x24171),f344(x24173,x24174,x24172))
% 155.94/155.64 [2418]~E(x24181,x24182)+E(f758(x24181,x24183,x24184,x24185),f758(x24182,x24183,x24184,x24185))
% 155.94/155.64 [2419]~E(x24191,x24192)+E(f758(x24193,x24191,x24194,x24195),f758(x24193,x24192,x24194,x24195))
% 155.94/155.64 [2420]~E(x24201,x24202)+E(f758(x24203,x24204,x24201,x24205),f758(x24203,x24204,x24202,x24205))
% 155.94/155.64 [2421]~E(x24211,x24212)+E(f758(x24213,x24214,x24215,x24211),f758(x24213,x24214,x24215,x24212))
% 155.94/155.64 [2422]~E(x24221,x24222)+E(f504(x24221,x24223,x24224,x24225,x24226,x24227),f504(x24222,x24223,x24224,x24225,x24226,x24227))
% 155.94/155.64 [2423]~E(x24231,x24232)+E(f504(x24233,x24231,x24234,x24235,x24236,x24237),f504(x24233,x24232,x24234,x24235,x24236,x24237))
% 155.94/155.64 [2424]~E(x24241,x24242)+E(f504(x24243,x24244,x24241,x24245,x24246,x24247),f504(x24243,x24244,x24242,x24245,x24246,x24247))
% 155.94/155.64 [2425]~E(x24251,x24252)+E(f504(x24253,x24254,x24255,x24251,x24256,x24257),f504(x24253,x24254,x24255,x24252,x24256,x24257))
% 155.94/155.64 [2426]~E(x24261,x24262)+E(f504(x24263,x24264,x24265,x24266,x24261,x24267),f504(x24263,x24264,x24265,x24266,x24262,x24267))
% 155.94/155.64 [2427]~E(x24271,x24272)+E(f504(x24273,x24274,x24275,x24276,x24277,x24271),f504(x24273,x24274,x24275,x24276,x24277,x24272))
% 155.94/155.64 [2428]~E(x24281,x24282)+E(f412(x24281,x24283,x24284,x24285),f412(x24282,x24283,x24284,x24285))
% 155.94/155.64 [2429]~E(x24291,x24292)+E(f412(x24293,x24291,x24294,x24295),f412(x24293,x24292,x24294,x24295))
% 155.94/155.64 [2430]~E(x24301,x24302)+E(f412(x24303,x24304,x24301,x24305),f412(x24303,x24304,x24302,x24305))
% 155.94/155.64 [2431]~E(x24311,x24312)+E(f412(x24313,x24314,x24315,x24311),f412(x24313,x24314,x24315,x24312))
% 155.94/155.64 [2432]~E(x24321,x24322)+E(f530(x24321,x24323,x24324,x24325,x24326,x24327),f530(x24322,x24323,x24324,x24325,x24326,x24327))
% 155.94/155.64 [2433]~E(x24331,x24332)+E(f530(x24333,x24331,x24334,x24335,x24336,x24337),f530(x24333,x24332,x24334,x24335,x24336,x24337))
% 155.94/155.64 [2434]~E(x24341,x24342)+E(f530(x24343,x24344,x24341,x24345,x24346,x24347),f530(x24343,x24344,x24342,x24345,x24346,x24347))
% 155.94/155.64 [2435]~E(x24351,x24352)+E(f530(x24353,x24354,x24355,x24351,x24356,x24357),f530(x24353,x24354,x24355,x24352,x24356,x24357))
% 155.94/155.64 [2436]~E(x24361,x24362)+E(f530(x24363,x24364,x24365,x24366,x24361,x24367),f530(x24363,x24364,x24365,x24366,x24362,x24367))
% 155.94/155.64 [2437]~E(x24371,x24372)+E(f530(x24373,x24374,x24375,x24376,x24377,x24371),f530(x24373,x24374,x24375,x24376,x24377,x24372))
% 155.94/155.64 [2438]~E(x24381,x24382)+E(f409(x24381,x24383,x24384,x24385,x24386),f409(x24382,x24383,x24384,x24385,x24386))
% 155.94/155.64 [2439]~E(x24391,x24392)+E(f409(x24393,x24391,x24394,x24395,x24396),f409(x24393,x24392,x24394,x24395,x24396))
% 155.94/155.64 [2440]~E(x24401,x24402)+E(f409(x24403,x24404,x24401,x24405,x24406),f409(x24403,x24404,x24402,x24405,x24406))
% 155.94/155.64 [2441]~E(x24411,x24412)+E(f409(x24413,x24414,x24415,x24411,x24416),f409(x24413,x24414,x24415,x24412,x24416))
% 155.94/155.64 [2442]~E(x24421,x24422)+E(f409(x24423,x24424,x24425,x24426,x24421),f409(x24423,x24424,x24425,x24426,x24422))
% 155.94/155.64 [2443]~E(x24431,x24432)+E(f715(x24431,x24433,x24434,x24435,x24436,x24437),f715(x24432,x24433,x24434,x24435,x24436,x24437))
% 155.94/155.64 [2444]~E(x24441,x24442)+E(f715(x24443,x24441,x24444,x24445,x24446,x24447),f715(x24443,x24442,x24444,x24445,x24446,x24447))
% 155.94/155.64 [2445]~E(x24451,x24452)+E(f715(x24453,x24454,x24451,x24455,x24456,x24457),f715(x24453,x24454,x24452,x24455,x24456,x24457))
% 155.94/155.64 [2446]~E(x24461,x24462)+E(f715(x24463,x24464,x24465,x24461,x24466,x24467),f715(x24463,x24464,x24465,x24462,x24466,x24467))
% 155.94/155.64 [2447]~E(x24471,x24472)+E(f715(x24473,x24474,x24475,x24476,x24471,x24477),f715(x24473,x24474,x24475,x24476,x24472,x24477))
% 155.94/155.64 [2448]~E(x24481,x24482)+E(f715(x24483,x24484,x24485,x24486,x24487,x24481),f715(x24483,x24484,x24485,x24486,x24487,x24482))
% 155.94/155.64 [2449]~E(x24491,x24492)+E(f632(x24491,x24493,x24494),f632(x24492,x24493,x24494))
% 155.94/155.64 [2450]~E(x24501,x24502)+E(f632(x24503,x24501,x24504),f632(x24503,x24502,x24504))
% 155.94/155.64 [2451]~E(x24511,x24512)+E(f632(x24513,x24514,x24511),f632(x24513,x24514,x24512))
% 155.94/155.64 [2452]~E(x24521,x24522)+E(f399(x24521,x24523,x24524,x24525),f399(x24522,x24523,x24524,x24525))
% 155.94/155.64 [2453]~E(x24531,x24532)+E(f399(x24533,x24531,x24534,x24535),f399(x24533,x24532,x24534,x24535))
% 155.94/155.64 [2454]~E(x24541,x24542)+E(f399(x24543,x24544,x24541,x24545),f399(x24543,x24544,x24542,x24545))
% 155.94/155.64 [2455]~E(x24551,x24552)+E(f399(x24553,x24554,x24555,x24551),f399(x24553,x24554,x24555,x24552))
% 155.94/155.64 [2456]~E(x24561,x24562)+E(f864(x24561,x24563),f864(x24562,x24563))
% 155.94/155.64 [2457]~E(x24571,x24572)+E(f864(x24573,x24571),f864(x24573,x24572))
% 155.94/155.64 [2458]~E(x24581,x24582)+E(f540(x24581,x24583,x24584),f540(x24582,x24583,x24584))
% 155.94/155.64 [2459]~E(x24591,x24592)+E(f540(x24593,x24591,x24594),f540(x24593,x24592,x24594))
% 155.94/155.64 [2460]~E(x24601,x24602)+E(f540(x24603,x24604,x24601),f540(x24603,x24604,x24602))
% 155.94/155.64 [2461]~E(x24611,x24612)+E(f443(x24611,x24613,x24614,x24615,x24616),f443(x24612,x24613,x24614,x24615,x24616))
% 155.94/155.64 [2462]~E(x24621,x24622)+E(f443(x24623,x24621,x24624,x24625,x24626),f443(x24623,x24622,x24624,x24625,x24626))
% 155.94/155.64 [2463]~E(x24631,x24632)+E(f443(x24633,x24634,x24631,x24635,x24636),f443(x24633,x24634,x24632,x24635,x24636))
% 155.94/155.64 [2464]~E(x24641,x24642)+E(f443(x24643,x24644,x24645,x24641,x24646),f443(x24643,x24644,x24645,x24642,x24646))
% 155.94/155.64 [2465]~E(x24651,x24652)+E(f443(x24653,x24654,x24655,x24656,x24651),f443(x24653,x24654,x24655,x24656,x24652))
% 155.94/155.64 [2466]~E(x24661,x24662)+E(f215(x24661,x24663,x24664,x24665,x24666),f215(x24662,x24663,x24664,x24665,x24666))
% 155.94/155.64 [2467]~E(x24671,x24672)+E(f215(x24673,x24671,x24674,x24675,x24676),f215(x24673,x24672,x24674,x24675,x24676))
% 155.94/155.64 [2468]~E(x24681,x24682)+E(f215(x24683,x24684,x24681,x24685,x24686),f215(x24683,x24684,x24682,x24685,x24686))
% 155.94/155.64 [2469]~E(x24691,x24692)+E(f215(x24693,x24694,x24695,x24691,x24696),f215(x24693,x24694,x24695,x24692,x24696))
% 155.94/155.64 [2470]~E(x24701,x24702)+E(f215(x24703,x24704,x24705,x24706,x24701),f215(x24703,x24704,x24705,x24706,x24702))
% 155.94/155.64 [2471]~E(x24711,x24712)+E(f217(x24711,x24713,x24714,x24715),f217(x24712,x24713,x24714,x24715))
% 155.94/155.64 [2472]~E(x24721,x24722)+E(f217(x24723,x24721,x24724,x24725),f217(x24723,x24722,x24724,x24725))
% 155.94/155.64 [2473]~E(x24731,x24732)+E(f217(x24733,x24734,x24731,x24735),f217(x24733,x24734,x24732,x24735))
% 155.94/155.64 [2474]~E(x24741,x24742)+E(f217(x24743,x24744,x24745,x24741),f217(x24743,x24744,x24745,x24742))
% 155.94/155.64 [2475]~E(x24751,x24752)+E(f466(x24751,x24753,x24754),f466(x24752,x24753,x24754))
% 155.94/155.64 [2476]~E(x24761,x24762)+E(f466(x24763,x24761,x24764),f466(x24763,x24762,x24764))
% 155.94/155.64 [2477]~E(x24771,x24772)+E(f466(x24773,x24774,x24771),f466(x24773,x24774,x24772))
% 155.94/155.64 [2478]~E(x24781,x24782)+E(f664(x24781,x24783,x24784),f664(x24782,x24783,x24784))
% 155.94/155.64 [2479]~E(x24791,x24792)+E(f664(x24793,x24791,x24794),f664(x24793,x24792,x24794))
% 155.94/155.64 [2480]~E(x24801,x24802)+E(f664(x24803,x24804,x24801),f664(x24803,x24804,x24802))
% 155.94/155.64 [2481]~E(x24811,x24812)+E(f462(x24811,x24813),f462(x24812,x24813))
% 155.94/155.64 [2482]~E(x24821,x24822)+E(f462(x24823,x24821),f462(x24823,x24822))
% 155.94/155.64 [2483]~E(x24831,x24832)+E(f719(x24831,x24833,x24834),f719(x24832,x24833,x24834))
% 155.94/155.64 [2484]~E(x24841,x24842)+E(f719(x24843,x24841,x24844),f719(x24843,x24842,x24844))
% 155.94/155.64 [2485]~E(x24851,x24852)+E(f719(x24853,x24854,x24851),f719(x24853,x24854,x24852))
% 155.94/155.64 [2486]~E(x24861,x24862)+E(f105(x24861,x24863,x24864),f105(x24862,x24863,x24864))
% 155.94/155.64 [2487]~E(x24871,x24872)+E(f105(x24873,x24871,x24874),f105(x24873,x24872,x24874))
% 155.94/155.64 [2488]~E(x24881,x24882)+E(f105(x24883,x24884,x24881),f105(x24883,x24884,x24882))
% 155.94/155.64 [2489]~E(x24891,x24892)+E(f592(x24891,x24893,x24894,x24895,x24896),f592(x24892,x24893,x24894,x24895,x24896))
% 155.94/155.64 [2490]~E(x24901,x24902)+E(f592(x24903,x24901,x24904,x24905,x24906),f592(x24903,x24902,x24904,x24905,x24906))
% 155.94/155.64 [2491]~E(x24911,x24912)+E(f592(x24913,x24914,x24911,x24915,x24916),f592(x24913,x24914,x24912,x24915,x24916))
% 155.94/155.64 [2492]~E(x24921,x24922)+E(f592(x24923,x24924,x24925,x24921,x24926),f592(x24923,x24924,x24925,x24922,x24926))
% 155.94/155.64 [2493]~E(x24931,x24932)+E(f592(x24933,x24934,x24935,x24936,x24931),f592(x24933,x24934,x24935,x24936,x24932))
% 155.94/155.64 [2494]~E(x24941,x24942)+E(f375(x24941,x24943),f375(x24942,x24943))
% 155.94/155.64 [2495]~E(x24951,x24952)+E(f375(x24953,x24951),f375(x24953,x24952))
% 155.94/155.64 [2496]~E(x24961,x24962)+E(f550(x24961,x24963),f550(x24962,x24963))
% 155.94/155.64 [2497]~E(x24971,x24972)+E(f550(x24973,x24971),f550(x24973,x24972))
% 155.94/155.64 [2498]~E(x24981,x24982)+E(f444(x24981,x24983,x24984,x24985,x24986),f444(x24982,x24983,x24984,x24985,x24986))
% 155.94/155.64 [2499]~E(x24991,x24992)+E(f444(x24993,x24991,x24994,x24995,x24996),f444(x24993,x24992,x24994,x24995,x24996))
% 155.94/155.64 [2500]~E(x25001,x25002)+E(f444(x25003,x25004,x25001,x25005,x25006),f444(x25003,x25004,x25002,x25005,x25006))
% 155.94/155.64 [2501]~E(x25011,x25012)+E(f444(x25013,x25014,x25015,x25011,x25016),f444(x25013,x25014,x25015,x25012,x25016))
% 155.94/155.64 [2502]~E(x25021,x25022)+E(f444(x25023,x25024,x25025,x25026,x25021),f444(x25023,x25024,x25025,x25026,x25022))
% 155.94/155.64 [2503]~E(x25031,x25032)+E(f213(x25031,x25033,x25034,x25035,x25036),f213(x25032,x25033,x25034,x25035,x25036))
% 155.94/155.64 [2504]~E(x25041,x25042)+E(f213(x25043,x25041,x25044,x25045,x25046),f213(x25043,x25042,x25044,x25045,x25046))
% 155.94/155.64 [2505]~E(x25051,x25052)+E(f213(x25053,x25054,x25051,x25055,x25056),f213(x25053,x25054,x25052,x25055,x25056))
% 155.94/155.64 [2506]~E(x25061,x25062)+E(f213(x25063,x25064,x25065,x25061,x25066),f213(x25063,x25064,x25065,x25062,x25066))
% 155.94/155.64 [2507]~E(x25071,x25072)+E(f213(x25073,x25074,x25075,x25076,x25071),f213(x25073,x25074,x25075,x25076,x25072))
% 155.94/155.64 [2508]~E(x25081,x25082)+E(f546(x25081,x25083),f546(x25082,x25083))
% 155.94/155.64 [2509]~E(x25091,x25092)+E(f546(x25093,x25091),f546(x25093,x25092))
% 155.94/155.64 [2510]~E(x25101,x25102)+E(f538(x25101),f538(x25102))
% 155.94/155.64 [2511]~E(x25111,x25112)+E(f735(x25111,x25113,x25114),f735(x25112,x25113,x25114))
% 155.94/155.64 [2512]~E(x25121,x25122)+E(f735(x25123,x25121,x25124),f735(x25123,x25122,x25124))
% 155.94/155.64 [2513]~E(x25131,x25132)+E(f735(x25133,x25134,x25131),f735(x25133,x25134,x25132))
% 155.94/155.64 [2514]~E(x25141,x25142)+E(f678(x25141,x25143,x25144),f678(x25142,x25143,x25144))
% 155.94/155.64 [2515]~E(x25151,x25152)+E(f678(x25153,x25151,x25154),f678(x25153,x25152,x25154))
% 155.94/155.64 [2516]~E(x25161,x25162)+E(f678(x25163,x25164,x25161),f678(x25163,x25164,x25162))
% 155.94/155.64 [2517]~E(x25171,x25172)+E(f343(x25171,x25173,x25174),f343(x25172,x25173,x25174))
% 155.94/155.64 [2518]~E(x25181,x25182)+E(f343(x25183,x25181,x25184),f343(x25183,x25182,x25184))
% 155.94/155.64 [2519]~E(x25191,x25192)+E(f343(x25193,x25194,x25191),f343(x25193,x25194,x25192))
% 155.94/155.64 [2520]~E(x25201,x25202)+E(f602(x25201,x25203,x25204,x25205),f602(x25202,x25203,x25204,x25205))
% 155.94/155.64 [2521]~E(x25211,x25212)+E(f602(x25213,x25211,x25214,x25215),f602(x25213,x25212,x25214,x25215))
% 155.94/155.64 [2522]~E(x25221,x25222)+E(f602(x25223,x25224,x25221,x25225),f602(x25223,x25224,x25222,x25225))
% 155.94/155.64 [2523]~E(x25231,x25232)+E(f602(x25233,x25234,x25235,x25231),f602(x25233,x25234,x25235,x25232))
% 155.94/155.64 [2524]~E(x25241,x25242)+E(f718(x25241,x25243,x25244,x25245,x25246,x25247),f718(x25242,x25243,x25244,x25245,x25246,x25247))
% 155.94/155.64 [2525]~E(x25251,x25252)+E(f718(x25253,x25251,x25254,x25255,x25256,x25257),f718(x25253,x25252,x25254,x25255,x25256,x25257))
% 155.94/155.64 [2526]~E(x25261,x25262)+E(f718(x25263,x25264,x25261,x25265,x25266,x25267),f718(x25263,x25264,x25262,x25265,x25266,x25267))
% 155.94/155.64 [2527]~E(x25271,x25272)+E(f718(x25273,x25274,x25275,x25271,x25276,x25277),f718(x25273,x25274,x25275,x25272,x25276,x25277))
% 155.94/155.64 [2528]~E(x25281,x25282)+E(f718(x25283,x25284,x25285,x25286,x25281,x25287),f718(x25283,x25284,x25285,x25286,x25282,x25287))
% 155.94/155.64 [2529]~E(x25291,x25292)+E(f718(x25293,x25294,x25295,x25296,x25297,x25291),f718(x25293,x25294,x25295,x25296,x25297,x25292))
% 155.94/155.64 [2530]~E(x25301,x25302)+E(f590(x25301,x25303,x25304,x25305,x25306),f590(x25302,x25303,x25304,x25305,x25306))
% 155.94/155.64 [2531]~E(x25311,x25312)+E(f590(x25313,x25311,x25314,x25315,x25316),f590(x25313,x25312,x25314,x25315,x25316))
% 155.94/155.64 [2532]~E(x25321,x25322)+E(f590(x25323,x25324,x25321,x25325,x25326),f590(x25323,x25324,x25322,x25325,x25326))
% 155.94/155.64 [2533]~E(x25331,x25332)+E(f590(x25333,x25334,x25335,x25331,x25336),f590(x25333,x25334,x25335,x25332,x25336))
% 155.94/155.64 [2534]~E(x25341,x25342)+E(f590(x25343,x25344,x25345,x25346,x25341),f590(x25343,x25344,x25345,x25346,x25342))
% 155.94/155.64 [2535]~E(x25351,x25352)+E(f554(x25351,x25353),f554(x25352,x25353))
% 155.94/155.64 [2536]~E(x25361,x25362)+E(f554(x25363,x25361),f554(x25363,x25362))
% 155.94/155.64 [2537]~E(x25371,x25372)+E(f557(x25371,x25373),f557(x25372,x25373))
% 155.94/155.64 [2538]~E(x25381,x25382)+E(f557(x25383,x25381),f557(x25383,x25382))
% 155.94/155.64 [2539]~E(x25391,x25392)+E(f737(x25391,x25393,x25394),f737(x25392,x25393,x25394))
% 155.94/155.64 [2540]~E(x25401,x25402)+E(f737(x25403,x25401,x25404),f737(x25403,x25402,x25404))
% 155.94/155.64 [2541]~E(x25411,x25412)+E(f737(x25413,x25414,x25411),f737(x25413,x25414,x25412))
% 155.94/155.64 [2542]~E(x25421,x25422)+E(f553(x25421,x25423),f553(x25422,x25423))
% 155.94/155.64 [2543]~E(x25431,x25432)+E(f553(x25433,x25431),f553(x25433,x25432))
% 155.94/155.64 [2544]~E(x25441,x25442)+E(f523(x25441,x25443),f523(x25442,x25443))
% 155.94/155.64 [2545]~E(x25451,x25452)+E(f523(x25453,x25451),f523(x25453,x25452))
% 155.94/155.64 [2546]~E(x25461,x25462)+E(f428(x25461,x25463,x25464),f428(x25462,x25463,x25464))
% 155.94/155.64 [2547]~E(x25471,x25472)+E(f428(x25473,x25471,x25474),f428(x25473,x25472,x25474))
% 155.94/155.64 [2548]~E(x25481,x25482)+E(f428(x25483,x25484,x25481),f428(x25483,x25484,x25482))
% 155.94/155.64 [2549]~E(x25491,x25492)+E(f787(x25491,x25493),f787(x25492,x25493))
% 155.94/155.64 [2550]~E(x25501,x25502)+E(f787(x25503,x25501),f787(x25503,x25502))
% 155.94/155.64 [2551]~E(x25511,x25512)+E(f568(x25511,x25513,x25514,x25515),f568(x25512,x25513,x25514,x25515))
% 155.94/155.64 [2552]~E(x25521,x25522)+E(f568(x25523,x25521,x25524,x25525),f568(x25523,x25522,x25524,x25525))
% 155.94/155.64 [2553]~E(x25531,x25532)+E(f568(x25533,x25534,x25531,x25535),f568(x25533,x25534,x25532,x25535))
% 155.94/155.64 [2554]~E(x25541,x25542)+E(f568(x25543,x25544,x25545,x25541),f568(x25543,x25544,x25545,x25542))
% 155.94/155.64 [2555]~E(x25551,x25552)+E(f781(x25551,x25553,x25554),f781(x25552,x25553,x25554))
% 155.94/155.64 [2556]~E(x25561,x25562)+E(f781(x25563,x25561,x25564),f781(x25563,x25562,x25564))
% 155.94/155.64 [2557]~E(x25571,x25572)+E(f781(x25573,x25574,x25571),f781(x25573,x25574,x25572))
% 155.94/155.64 [2558]~E(x25581,x25582)+E(f317(x25581),f317(x25582))
% 155.94/155.64 [2559]~P1(x25591)+P1(x25592)+~E(x25591,x25592)
% 155.94/155.64 [2560]~P22(x25601)+P22(x25602)+~E(x25601,x25602)
% 155.94/155.64 [2561]~P23(x25611)+P23(x25612)+~E(x25611,x25612)
% 155.94/155.64 [2562]P33(x25622,x25623)+~E(x25621,x25622)+~P33(x25621,x25623)
% 155.94/155.64 [2563]P33(x25633,x25632)+~E(x25631,x25632)+~P33(x25633,x25631)
% 155.94/155.64 [2564]~P103(x25641)+P103(x25642)+~E(x25641,x25642)
% 155.94/155.64 [2565]~P24(x25651)+P24(x25652)+~E(x25651,x25652)
% 155.94/155.64 [2566]~P112(x25661)+P112(x25662)+~E(x25661,x25662)
% 155.94/155.64 [2567]~P101(x25671)+P101(x25672)+~E(x25671,x25672)
% 155.94/155.64 [2568]~P25(x25681)+P25(x25682)+~E(x25681,x25682)
% 155.94/155.64 [2569]~P26(x25691)+P26(x25692)+~E(x25691,x25692)
% 155.94/155.64 [2570]P19(x25702,x25703,x25704,x25705)+~E(x25701,x25702)+~P19(x25701,x25703,x25704,x25705)
% 155.94/155.64 [2571]P19(x25713,x25712,x25714,x25715)+~E(x25711,x25712)+~P19(x25713,x25711,x25714,x25715)
% 155.94/155.64 [2572]P19(x25723,x25724,x25722,x25725)+~E(x25721,x25722)+~P19(x25723,x25724,x25721,x25725)
% 155.94/155.64 [2573]P19(x25733,x25734,x25735,x25732)+~E(x25731,x25732)+~P19(x25733,x25734,x25735,x25731)
% 155.94/155.64 [2574]~P107(x25741)+P107(x25742)+~E(x25741,x25742)
% 155.94/155.64 [2575]~P130(x25751)+P130(x25752)+~E(x25751,x25752)
% 155.94/155.64 [2576]~P117(x25761)+P117(x25762)+~E(x25761,x25762)
% 155.94/155.64 [2577]~P31(x25771)+P31(x25772)+~E(x25771,x25772)
% 155.94/155.64 [2578]~P72(x25781)+P72(x25782)+~E(x25781,x25782)
% 155.94/155.64 [2579]~P98(x25791)+P98(x25792)+~E(x25791,x25792)
% 155.94/155.64 [2580]~P70(x25801)+P70(x25802)+~E(x25801,x25802)
% 155.94/155.64 [2581]~P136(x25811)+P136(x25812)+~E(x25811,x25812)
% 155.94/155.64 [2582]P11(x25822,x25823,x25824)+~E(x25821,x25822)+~P11(x25821,x25823,x25824)
% 155.94/155.64 [2583]P11(x25833,x25832,x25834)+~E(x25831,x25832)+~P11(x25833,x25831,x25834)
% 155.94/155.64 [2584]P11(x25843,x25844,x25842)+~E(x25841,x25842)+~P11(x25843,x25844,x25841)
% 155.94/155.64 [2585]~P75(x25851)+P75(x25852)+~E(x25851,x25852)
% 155.94/155.64 [2586]~P30(x25861)+P30(x25862)+~E(x25861,x25862)
% 155.94/155.64 [2587]P139(x25872,x25873,x25874)+~E(x25871,x25872)+~P139(x25871,x25873,x25874)
% 155.94/155.64 [2588]P139(x25883,x25882,x25884)+~E(x25881,x25882)+~P139(x25883,x25881,x25884)
% 155.94/155.64 [2589]P139(x25893,x25894,x25892)+~E(x25891,x25892)+~P139(x25893,x25894,x25891)
% 155.94/155.64 [2590]~P27(x25901)+P27(x25902)+~E(x25901,x25902)
% 155.94/155.64 [2591]~P91(x25911)+P91(x25912)+~E(x25911,x25912)
% 155.94/155.64 [2592]~P43(x25921)+P43(x25922)+~E(x25921,x25922)
% 155.94/155.64 [2593]~P28(x25931)+P28(x25932)+~E(x25931,x25932)
% 155.94/155.64 [2594]P36(x25942,x25943,x25944,x25945)+~E(x25941,x25942)+~P36(x25941,x25943,x25944,x25945)
% 155.94/155.64 [2595]P36(x25953,x25952,x25954,x25955)+~E(x25951,x25952)+~P36(x25953,x25951,x25954,x25955)
% 155.94/155.64 [2596]P36(x25963,x25964,x25962,x25965)+~E(x25961,x25962)+~P36(x25963,x25964,x25961,x25965)
% 155.94/155.64 [2597]P36(x25973,x25974,x25975,x25972)+~E(x25971,x25972)+~P36(x25973,x25974,x25975,x25971)
% 155.94/155.64 [2598]~P135(x25981)+P135(x25982)+~E(x25981,x25982)
% 155.94/155.64 [2599]~P29(x25991)+P29(x25992)+~E(x25991,x25992)
% 155.94/155.64 [2600]~P66(x26001)+P66(x26002)+~E(x26001,x26002)
% 155.94/155.64 [2601]~P99(x26011)+P99(x26012)+~E(x26011,x26012)
% 155.94/155.64 [2602]~P111(x26021)+P111(x26022)+~E(x26021,x26022)
% 155.94/155.64 [2603]~P71(x26031)+P71(x26032)+~E(x26031,x26032)
% 155.94/155.64 [2604]~P73(x26041)+P73(x26042)+~E(x26041,x26042)
% 155.94/155.64 [2605]~P87(x26051)+P87(x26052)+~E(x26051,x26052)
% 155.94/155.64 [2606]P140(x26062,x26063,x26064)+~E(x26061,x26062)+~P140(x26061,x26063,x26064)
% 155.94/155.64 [2607]P140(x26073,x26072,x26074)+~E(x26071,x26072)+~P140(x26073,x26071,x26074)
% 155.94/155.64 [2608]P140(x26083,x26084,x26082)+~E(x26081,x26082)+~P140(x26083,x26084,x26081)
% 155.94/155.64 [2609]P58(x26092,x26093,x26094,x26095)+~E(x26091,x26092)+~P58(x26091,x26093,x26094,x26095)
% 155.94/155.64 [2610]P58(x26103,x26102,x26104,x26105)+~E(x26101,x26102)+~P58(x26103,x26101,x26104,x26105)
% 155.94/155.64 [2611]P58(x26113,x26114,x26112,x26115)+~E(x26111,x26112)+~P58(x26113,x26114,x26111,x26115)
% 155.94/155.64 [2612]P58(x26123,x26124,x26125,x26122)+~E(x26121,x26122)+~P58(x26123,x26124,x26125,x26121)
% 155.94/155.64 [2613]~P76(x26131)+P76(x26132)+~E(x26131,x26132)
% 155.94/155.64 [2614]~P79(x26141)+P79(x26142)+~E(x26141,x26142)
% 155.94/155.64 [2615]P18(x26152,x26153,x26154)+~E(x26151,x26152)+~P18(x26151,x26153,x26154)
% 155.94/155.64 [2616]P18(x26163,x26162,x26164)+~E(x26161,x26162)+~P18(x26163,x26161,x26164)
% 155.94/155.64 [2617]P18(x26173,x26174,x26172)+~E(x26171,x26172)+~P18(x26173,x26174,x26171)
% 155.94/155.64 [2618]~P127(x26181)+P127(x26182)+~E(x26181,x26182)
% 155.94/155.64 [2619]P3(x26192,x26193,x26194)+~E(x26191,x26192)+~P3(x26191,x26193,x26194)
% 155.94/155.64 [2620]P3(x26203,x26202,x26204)+~E(x26201,x26202)+~P3(x26203,x26201,x26204)
% 155.94/155.64 [2621]P3(x26213,x26214,x26212)+~E(x26211,x26212)+~P3(x26213,x26214,x26211)
% 155.94/155.64 [2622]~P104(x26221)+P104(x26222)+~E(x26221,x26222)
% 155.94/155.64 [2623]~P88(x26231)+P88(x26232)+~E(x26231,x26232)
% 155.94/155.64 [2624]P39(x26242,x26243,x26244,x26245,x26246)+~E(x26241,x26242)+~P39(x26241,x26243,x26244,x26245,x26246)
% 155.94/155.64 [2625]P39(x26253,x26252,x26254,x26255,x26256)+~E(x26251,x26252)+~P39(x26253,x26251,x26254,x26255,x26256)
% 155.94/155.64 [2626]P39(x26263,x26264,x26262,x26265,x26266)+~E(x26261,x26262)+~P39(x26263,x26264,x26261,x26265,x26266)
% 155.94/155.64 [2627]P39(x26273,x26274,x26275,x26272,x26276)+~E(x26271,x26272)+~P39(x26273,x26274,x26275,x26271,x26276)
% 155.94/155.64 [2628]P39(x26283,x26284,x26285,x26286,x26282)+~E(x26281,x26282)+~P39(x26283,x26284,x26285,x26286,x26281)
% 155.94/155.64 [2629]~P128(x26291)+P128(x26292)+~E(x26291,x26292)
% 155.94/155.64 [2630]P41(x26302,x26303)+~E(x26301,x26302)+~P41(x26301,x26303)
% 155.94/155.64 [2631]P41(x26313,x26312)+~E(x26311,x26312)+~P41(x26313,x26311)
% 155.94/155.64 [2632]~P94(x26321)+P94(x26322)+~E(x26321,x26322)
% 155.94/155.64 [2633]~P108(x26331)+P108(x26332)+~E(x26331,x26332)
% 155.94/155.64 [2634]~P89(x26341)+P89(x26342)+~E(x26341,x26342)
% 155.94/155.64 [2635]~P77(x26351)+P77(x26352)+~E(x26351,x26352)
% 155.94/155.64 [2636]~P84(x26361)+P84(x26362)+~E(x26361,x26362)
% 155.94/155.64 [2637]P35(x26372,x26373)+~E(x26371,x26372)+~P35(x26371,x26373)
% 155.94/155.64 [2638]P35(x26383,x26382)+~E(x26381,x26382)+~P35(x26383,x26381)
% 155.94/155.64 [2639]~P90(x26391)+P90(x26392)+~E(x26391,x26392)
% 155.94/155.64 [2640]P16(x26402,x26403,x26404,x26405,x26406)+~E(x26401,x26402)+~P16(x26401,x26403,x26404,x26405,x26406)
% 155.94/155.64 [2641]P16(x26413,x26412,x26414,x26415,x26416)+~E(x26411,x26412)+~P16(x26413,x26411,x26414,x26415,x26416)
% 155.94/155.64 [2642]P16(x26423,x26424,x26422,x26425,x26426)+~E(x26421,x26422)+~P16(x26423,x26424,x26421,x26425,x26426)
% 155.94/155.64 [2643]P16(x26433,x26434,x26435,x26432,x26436)+~E(x26431,x26432)+~P16(x26433,x26434,x26435,x26431,x26436)
% 155.94/155.64 [2644]P16(x26443,x26444,x26445,x26446,x26442)+~E(x26441,x26442)+~P16(x26443,x26444,x26445,x26446,x26441)
% 155.94/155.64 [2645]~P118(x26451)+P118(x26452)+~E(x26451,x26452)
% 155.94/155.64 [2646]~P100(x26461)+P100(x26462)+~E(x26461,x26462)
% 155.94/155.64 [2647]~P96(x26471)+P96(x26472)+~E(x26471,x26472)
% 155.94/155.64 [2648]~P64(x26481)+P64(x26482)+~E(x26481,x26482)
% 155.94/155.64 [2649]P14(x26492,x26493,x26494,x26495)+~E(x26491,x26492)+~P14(x26491,x26493,x26494,x26495)
% 155.94/155.64 [2650]P14(x26503,x26502,x26504,x26505)+~E(x26501,x26502)+~P14(x26503,x26501,x26504,x26505)
% 155.94/155.64 [2651]P14(x26513,x26514,x26512,x26515)+~E(x26511,x26512)+~P14(x26513,x26514,x26511,x26515)
% 155.94/155.64 [2652]P14(x26523,x26524,x26525,x26522)+~E(x26521,x26522)+~P14(x26523,x26524,x26525,x26521)
% 155.94/155.64 [2653]~P137(x26531)+P137(x26532)+~E(x26531,x26532)
% 155.94/155.64 [2654]P49(x26542,x26543,x26544)+~E(x26541,x26542)+~P49(x26541,x26543,x26544)
% 155.94/155.64 [2655]P49(x26553,x26552,x26554)+~E(x26551,x26552)+~P49(x26553,x26551,x26554)
% 155.94/155.64 [2656]P49(x26563,x26564,x26562)+~E(x26561,x26562)+~P49(x26563,x26564,x26561)
% 155.94/155.64 [2657]P57(x26572,x26573)+~E(x26571,x26572)+~P57(x26571,x26573)
% 155.94/155.64 [2658]P57(x26583,x26582)+~E(x26581,x26582)+~P57(x26583,x26581)
% 155.94/155.64 [2659]~P67(x26591)+P67(x26592)+~E(x26591,x26592)
% 155.94/155.64 [2660]~P102(x26601)+P102(x26602)+~E(x26601,x26602)
% 155.94/155.64 [2661]~P63(x26611)+P63(x26612)+~E(x26611,x26612)
% 155.94/155.64 [2662]P48(x26622,x26623)+~E(x26621,x26622)+~P48(x26621,x26623)
% 155.94/155.64 [2663]P48(x26633,x26632)+~E(x26631,x26632)+~P48(x26633,x26631)
% 155.94/155.64 [2664]~P92(x26641)+P92(x26642)+~E(x26641,x26642)
% 155.94/155.64 [2665]P21(x26652,x26653,x26654)+~E(x26651,x26652)+~P21(x26651,x26653,x26654)
% 155.94/155.64 [2666]P21(x26663,x26662,x26664)+~E(x26661,x26662)+~P21(x26663,x26661,x26664)
% 155.94/155.64 [2667]P21(x26673,x26674,x26672)+~E(x26671,x26672)+~P21(x26673,x26674,x26671)
% 155.94/155.64 [2668]P38(x26682,x26683,x26684)+~E(x26681,x26682)+~P38(x26681,x26683,x26684)
% 155.94/155.64 [2669]P38(x26693,x26692,x26694)+~E(x26691,x26692)+~P38(x26693,x26691,x26694)
% 155.94/155.64 [2670]P38(x26703,x26704,x26702)+~E(x26701,x26702)+~P38(x26703,x26704,x26701)
% 155.94/155.64 [2671]~P105(x26711)+P105(x26712)+~E(x26711,x26712)
% 155.94/155.64 [2672]~P110(x26721)+P110(x26722)+~E(x26721,x26722)
% 155.94/155.64 [2673]P55(x26732,x26733,x26734)+~E(x26731,x26732)+~P55(x26731,x26733,x26734)
% 155.94/155.64 [2674]P55(x26743,x26742,x26744)+~E(x26741,x26742)+~P55(x26743,x26741,x26744)
% 155.94/155.64 [2675]P55(x26753,x26754,x26752)+~E(x26751,x26752)+~P55(x26753,x26754,x26751)
% 155.94/155.64 [2676]~P60(x26761)+P60(x26762)+~E(x26761,x26762)
% 155.94/155.64 [2677]~P132(x26771)+P132(x26772)+~E(x26771,x26772)
% 155.94/155.64 [2678]~P80(x26781)+P80(x26782)+~E(x26781,x26782)
% 155.94/155.64 [2679]~P61(x26791)+P61(x26792)+~E(x26791,x26792)
% 155.94/155.64 [2680]~P120(x26801)+P120(x26802)+~E(x26801,x26802)
% 155.94/155.64 [2681]~P113(x26811)+P113(x26812)+~E(x26811,x26812)
% 155.94/155.64 [2682]~P106(x26821)+P106(x26822)+~E(x26821,x26822)
% 155.94/155.64 [2683]P12(x26832,x26833,x26834)+~E(x26831,x26832)+~P12(x26831,x26833,x26834)
% 155.94/155.64 [2684]P12(x26843,x26842,x26844)+~E(x26841,x26842)+~P12(x26843,x26841,x26844)
% 155.94/155.64 [2685]P12(x26853,x26854,x26852)+~E(x26851,x26852)+~P12(x26853,x26854,x26851)
% 155.94/155.64 [2686]P50(x26862,x26863,x26864)+~E(x26861,x26862)+~P50(x26861,x26863,x26864)
% 155.94/155.64 [2687]P50(x26873,x26872,x26874)+~E(x26871,x26872)+~P50(x26873,x26871,x26874)
% 155.94/155.64 [2688]P50(x26883,x26884,x26882)+~E(x26881,x26882)+~P50(x26883,x26884,x26881)
% 155.94/155.64 [2689]~P131(x26891)+P131(x26892)+~E(x26891,x26892)
% 155.94/155.64 [2690]P6(x26902,x26903,x26904,x26905,x26906)+~E(x26901,x26902)+~P6(x26901,x26903,x26904,x26905,x26906)
% 155.94/155.64 [2691]P6(x26913,x26912,x26914,x26915,x26916)+~E(x26911,x26912)+~P6(x26913,x26911,x26914,x26915,x26916)
% 155.94/155.64 [2692]P6(x26923,x26924,x26922,x26925,x26926)+~E(x26921,x26922)+~P6(x26923,x26924,x26921,x26925,x26926)
% 155.94/155.64 [2693]P6(x26933,x26934,x26935,x26932,x26936)+~E(x26931,x26932)+~P6(x26933,x26934,x26935,x26931,x26936)
% 155.94/155.64 [2694]P6(x26943,x26944,x26945,x26946,x26942)+~E(x26941,x26942)+~P6(x26943,x26944,x26945,x26946,x26941)
% 155.94/155.64 [2695]~P115(x26951)+P115(x26952)+~E(x26951,x26952)
% 155.94/155.64 [2696]~P81(x26961)+P81(x26962)+~E(x26961,x26962)
% 155.94/155.64 [2697]P34(x26972,x26973,x26974)+~E(x26971,x26972)+~P34(x26971,x26973,x26974)
% 155.94/155.64 [2698]P34(x26983,x26982,x26984)+~E(x26981,x26982)+~P34(x26983,x26981,x26984)
% 155.94/155.64 [2699]P34(x26993,x26994,x26992)+~E(x26991,x26992)+~P34(x26993,x26994,x26991)
% 155.94/155.64 [2700]P8(x27002,x27003,x27004)+~E(x27001,x27002)+~P8(x27001,x27003,x27004)
% 155.94/155.64 [2701]P8(x27013,x27012,x27014)+~E(x27011,x27012)+~P8(x27013,x27011,x27014)
% 155.94/155.64 [2702]P8(x27023,x27024,x27022)+~E(x27021,x27022)+~P8(x27023,x27024,x27021)
% 155.94/155.64 [2703]~P109(x27031)+P109(x27032)+~E(x27031,x27032)
% 155.94/155.64 [2704]P17(x27042,x27043,x27044,x27045,x27046,x27047)+~E(x27041,x27042)+~P17(x27041,x27043,x27044,x27045,x27046,x27047)
% 155.94/155.64 [2705]P17(x27053,x27052,x27054,x27055,x27056,x27057)+~E(x27051,x27052)+~P17(x27053,x27051,x27054,x27055,x27056,x27057)
% 155.94/155.64 [2706]P17(x27063,x27064,x27062,x27065,x27066,x27067)+~E(x27061,x27062)+~P17(x27063,x27064,x27061,x27065,x27066,x27067)
% 155.94/155.64 [2707]P17(x27073,x27074,x27075,x27072,x27076,x27077)+~E(x27071,x27072)+~P17(x27073,x27074,x27075,x27071,x27076,x27077)
% 155.94/155.64 [2708]P17(x27083,x27084,x27085,x27086,x27082,x27087)+~E(x27081,x27082)+~P17(x27083,x27084,x27085,x27086,x27081,x27087)
% 155.94/155.64 [2709]P17(x27093,x27094,x27095,x27096,x27097,x27092)+~E(x27091,x27092)+~P17(x27093,x27094,x27095,x27096,x27097,x27091)
% 155.94/155.64 [2710]~P32(x27101)+P32(x27102)+~E(x27101,x27102)
% 155.94/155.64 [2711]~P40(x27111)+P40(x27112)+~E(x27111,x27112)
% 155.94/155.64 [2712]P13(x27122,x27123,x27124)+~E(x27121,x27122)+~P13(x27121,x27123,x27124)
% 155.94/155.64 [2713]P13(x27133,x27132,x27134)+~E(x27131,x27132)+~P13(x27133,x27131,x27134)
% 155.94/155.64 [2714]P13(x27143,x27144,x27142)+~E(x27141,x27142)+~P13(x27143,x27144,x27141)
% 155.94/155.64 [2715]P10(x27152,x27153,x27154,x27155,x27156,x27157)+~E(x27151,x27152)+~P10(x27151,x27153,x27154,x27155,x27156,x27157)
% 155.94/155.64 [2716]P10(x27163,x27162,x27164,x27165,x27166,x27167)+~E(x27161,x27162)+~P10(x27163,x27161,x27164,x27165,x27166,x27167)
% 155.94/155.64 [2717]P10(x27173,x27174,x27172,x27175,x27176,x27177)+~E(x27171,x27172)+~P10(x27173,x27174,x27171,x27175,x27176,x27177)
% 155.94/155.64 [2718]P10(x27183,x27184,x27185,x27182,x27186,x27187)+~E(x27181,x27182)+~P10(x27183,x27184,x27185,x27181,x27186,x27187)
% 155.94/155.64 [2719]P10(x27193,x27194,x27195,x27196,x27192,x27197)+~E(x27191,x27192)+~P10(x27193,x27194,x27195,x27196,x27191,x27197)
% 155.94/155.64 [2720]P10(x27203,x27204,x27205,x27206,x27207,x27202)+~E(x27201,x27202)+~P10(x27203,x27204,x27205,x27206,x27207,x27201)
% 155.94/155.64 [2721]~P121(x27211)+P121(x27212)+~E(x27211,x27212)
% 155.94/155.64 [2722]~P122(x27221)+P122(x27222)+~E(x27221,x27222)
% 155.94/155.64 [2723]P2(x27232,x27233)+~E(x27231,x27232)+~P2(x27231,x27233)
% 155.94/155.64 [2724]P2(x27243,x27242)+~E(x27241,x27242)+~P2(x27243,x27241)
% 155.94/155.64 [2725]P56(x27252,x27253,x27254,x27255,x27256)+~E(x27251,x27252)+~P56(x27251,x27253,x27254,x27255,x27256)
% 155.94/155.64 [2726]P56(x27263,x27262,x27264,x27265,x27266)+~E(x27261,x27262)+~P56(x27263,x27261,x27264,x27265,x27266)
% 155.94/155.64 [2727]P56(x27273,x27274,x27272,x27275,x27276)+~E(x27271,x27272)+~P56(x27273,x27274,x27271,x27275,x27276)
% 155.94/155.64 [2728]P56(x27283,x27284,x27285,x27282,x27286)+~E(x27281,x27282)+~P56(x27283,x27284,x27285,x27281,x27286)
% 155.94/155.64 [2729]P56(x27293,x27294,x27295,x27296,x27292)+~E(x27291,x27292)+~P56(x27293,x27294,x27295,x27296,x27291)
% 155.94/155.64 [2730]~P85(x27301)+P85(x27302)+~E(x27301,x27302)
% 155.94/155.64 [2731]~P93(x27311)+P93(x27312)+~E(x27311,x27312)
% 155.94/155.64 [2732]~P134(x27321)+P134(x27322)+~E(x27321,x27322)
% 155.94/155.64 [2733]~P123(x27331)+P123(x27332)+~E(x27331,x27332)
% 155.94/155.64 [2734]~P62(x27341)+P62(x27342)+~E(x27341,x27342)
% 155.94/155.64 [2735]P54(x27352,x27353,x27354)+~E(x27351,x27352)+~P54(x27351,x27353,x27354)
% 155.94/155.64 [2736]P54(x27363,x27362,x27364)+~E(x27361,x27362)+~P54(x27363,x27361,x27364)
% 155.94/155.64 [2737]P54(x27373,x27374,x27372)+~E(x27371,x27372)+~P54(x27373,x27374,x27371)
% 155.94/155.64 [2738]P7(x27382,x27383,x27384)+~E(x27381,x27382)+~P7(x27381,x27383,x27384)
% 155.94/155.64 [2739]P7(x27393,x27392,x27394)+~E(x27391,x27392)+~P7(x27393,x27391,x27394)
% 155.94/155.64 [2740]P7(x27403,x27404,x27402)+~E(x27401,x27402)+~P7(x27403,x27404,x27401)
% 155.94/155.64 [2741]P46(x27412,x27413)+~E(x27411,x27412)+~P46(x27411,x27413)
% 155.94/155.64 [2742]P46(x27423,x27422)+~E(x27421,x27422)+~P46(x27423,x27421)
% 155.94/155.64 [2743]~P97(x27431)+P97(x27432)+~E(x27431,x27432)
% 155.94/155.64 [2744]~P83(x27441)+P83(x27442)+~E(x27441,x27442)
% 155.94/155.64 [2745]~P129(x27451)+P129(x27452)+~E(x27451,x27452)
% 155.94/155.64 [2746]P9(x27462,x27463,x27464,x27465)+~E(x27461,x27462)+~P9(x27461,x27463,x27464,x27465)
% 155.94/155.64 [2747]P9(x27473,x27472,x27474,x27475)+~E(x27471,x27472)+~P9(x27473,x27471,x27474,x27475)
% 155.94/155.64 [2748]P9(x27483,x27484,x27482,x27485)+~E(x27481,x27482)+~P9(x27483,x27484,x27481,x27485)
% 155.94/155.64 [2749]P9(x27493,x27494,x27495,x27492)+~E(x27491,x27492)+~P9(x27493,x27494,x27495,x27491)
% 155.94/155.64 [2750]P45(x27502,x27503,x27504,x27505,x27506,x27507)+~E(x27501,x27502)+~P45(x27501,x27503,x27504,x27505,x27506,x27507)
% 155.94/155.64 [2751]P45(x27513,x27512,x27514,x27515,x27516,x27517)+~E(x27511,x27512)+~P45(x27513,x27511,x27514,x27515,x27516,x27517)
% 155.94/155.64 [2752]P45(x27523,x27524,x27522,x27525,x27526,x27527)+~E(x27521,x27522)+~P45(x27523,x27524,x27521,x27525,x27526,x27527)
% 155.94/155.64 [2753]P45(x27533,x27534,x27535,x27532,x27536,x27537)+~E(x27531,x27532)+~P45(x27533,x27534,x27535,x27531,x27536,x27537)
% 155.94/155.64 [2754]P45(x27543,x27544,x27545,x27546,x27542,x27547)+~E(x27541,x27542)+~P45(x27543,x27544,x27545,x27546,x27541,x27547)
% 155.94/155.64 [2755]P45(x27553,x27554,x27555,x27556,x27557,x27552)+~E(x27551,x27552)+~P45(x27553,x27554,x27555,x27556,x27557,x27551)
% 155.94/155.64 [2756]~P116(x27561)+P116(x27562)+~E(x27561,x27562)
% 155.94/155.64 [2757]~P119(x27571)+P119(x27572)+~E(x27571,x27572)
% 155.94/155.64 [2758]~P74(x27581)+P74(x27582)+~E(x27581,x27582)
% 155.94/155.64 [2759]P37(x27592,x27593,x27594,x27595)+~E(x27591,x27592)+~P37(x27591,x27593,x27594,x27595)
% 155.94/155.64 [2760]P37(x27603,x27602,x27604,x27605)+~E(x27601,x27602)+~P37(x27603,x27601,x27604,x27605)
% 155.94/155.64 [2761]P37(x27613,x27614,x27612,x27615)+~E(x27611,x27612)+~P37(x27613,x27614,x27611,x27615)
% 155.94/155.64 [2762]P37(x27623,x27624,x27625,x27622)+~E(x27621,x27622)+~P37(x27623,x27624,x27625,x27621)
% 155.94/155.64 [2763]~P68(x27631)+P68(x27632)+~E(x27631,x27632)
% 155.94/155.64 [2764]P59(x27642,x27643)+~E(x27641,x27642)+~P59(x27641,x27643)
% 155.94/155.64 [2765]P59(x27653,x27652)+~E(x27651,x27652)+~P59(x27653,x27651)
% 155.94/155.64 [2766]~P114(x27661)+P114(x27662)+~E(x27661,x27662)
% 155.94/155.64 [2767]~P65(x27671)+P65(x27672)+~E(x27671,x27672)
% 155.94/155.64 [2768]~P133(x27681)+P133(x27682)+~E(x27681,x27682)
% 155.94/155.64 [2769]P42(x27692,x27693)+~E(x27691,x27692)+~P42(x27691,x27693)
% 155.94/155.64 [2770]P42(x27703,x27702)+~E(x27701,x27702)+~P42(x27703,x27701)
% 155.94/155.64 [2771]~P126(x27711)+P126(x27712)+~E(x27711,x27712)
% 155.94/155.64 [2772]P20(x27722,x27723)+~E(x27721,x27722)+~P20(x27721,x27723)
% 155.94/155.64 [2773]P20(x27733,x27732)+~E(x27731,x27732)+~P20(x27733,x27731)
% 155.94/155.64 [2774]P44(x27742,x27743,x27744,x27745)+~E(x27741,x27742)+~P44(x27741,x27743,x27744,x27745)
% 155.94/155.64 [2775]P44(x27753,x27752,x27754,x27755)+~E(x27751,x27752)+~P44(x27753,x27751,x27754,x27755)
% 155.94/155.64 [2776]P44(x27763,x27764,x27762,x27765)+~E(x27761,x27762)+~P44(x27763,x27764,x27761,x27765)
% 155.94/155.64 [2777]P44(x27773,x27774,x27775,x27772)+~E(x27771,x27772)+~P44(x27773,x27774,x27775,x27771)
% 155.94/155.64 [2778]~P78(x27781)+P78(x27782)+~E(x27781,x27782)
% 155.94/155.64 [2779]~P138(x27791)+P138(x27792)+~E(x27791,x27792)
% 155.94/155.64 [2780]P53(x27802,x27803,x27804,x27805,x27806,x27807,x27808)+~E(x27801,x27802)+~P53(x27801,x27803,x27804,x27805,x27806,x27807,x27808)
% 155.94/155.64 [2781]P53(x27813,x27812,x27814,x27815,x27816,x27817,x27818)+~E(x27811,x27812)+~P53(x27813,x27811,x27814,x27815,x27816,x27817,x27818)
% 155.94/155.64 [2782]P53(x27823,x27824,x27822,x27825,x27826,x27827,x27828)+~E(x27821,x27822)+~P53(x27823,x27824,x27821,x27825,x27826,x27827,x27828)
% 155.94/155.64 [2783]P53(x27833,x27834,x27835,x27832,x27836,x27837,x27838)+~E(x27831,x27832)+~P53(x27833,x27834,x27835,x27831,x27836,x27837,x27838)
% 155.94/155.64 [2784]P53(x27843,x27844,x27845,x27846,x27842,x27847,x27848)+~E(x27841,x27842)+~P53(x27843,x27844,x27845,x27846,x27841,x27847,x27848)
% 155.94/155.64 [2785]P53(x27853,x27854,x27855,x27856,x27857,x27852,x27858)+~E(x27851,x27852)+~P53(x27853,x27854,x27855,x27856,x27857,x27851,x27858)
% 155.94/155.64 [2786]P53(x27863,x27864,x27865,x27866,x27867,x27868,x27862)+~E(x27861,x27862)+~P53(x27863,x27864,x27865,x27866,x27867,x27868,x27861)
% 155.94/155.64 [2787]P52(x27872,x27873)+~E(x27871,x27872)+~P52(x27871,x27873)
% 155.94/155.64 [2788]P52(x27883,x27882)+~E(x27881,x27882)+~P52(x27883,x27881)
% 155.94/155.64 [2789]~P124(x27891)+P124(x27892)+~E(x27891,x27892)
% 155.94/155.64 [2790]P51(x27902,x27903)+~E(x27901,x27902)+~P51(x27901,x27903)
% 155.94/155.64 [2791]P51(x27913,x27912)+~E(x27911,x27912)+~P51(x27913,x27911)
% 155.94/155.64 [2792]~P4(x27921)+P4(x27922)+~E(x27921,x27922)
% 155.94/155.64 [2793]P15(x27932,x27933,x27934,x27935)+~E(x27931,x27932)+~P15(x27931,x27933,x27934,x27935)
% 155.94/155.64 [2794]P15(x27943,x27942,x27944,x27945)+~E(x27941,x27942)+~P15(x27943,x27941,x27944,x27945)
% 155.94/155.64 [2795]P15(x27953,x27954,x27952,x27955)+~E(x27951,x27952)+~P15(x27953,x27954,x27951,x27955)
% 155.94/155.64 [2796]P15(x27963,x27964,x27965,x27962)+~E(x27961,x27962)+~P15(x27963,x27964,x27965,x27961)
% 155.94/155.64 [2797]~P125(x27971)+P125(x27972)+~E(x27971,x27972)
% 155.94/155.64 [2798]~P82(x27981)+P82(x27982)+~E(x27981,x27982)
% 155.94/155.64 [2799]~P86(x27991)+P86(x27992)+~E(x27991,x27992)
% 155.94/155.64 [2800]~P47(x28001)+P47(x28002)+~E(x28001,x28002)
% 155.94/155.64 [2801]~P95(x28011)+P95(x28012)+~E(x28011,x28012)
% 155.94/155.64 [2802]~P69(x28021)+P69(x28022)+~E(x28021,x28022)
% 155.94/155.64 [2803]P5(x28032,x28033,x28034)+~E(x28031,x28032)+~P5(x28031,x28033,x28034)
% 155.94/155.64 [2804]P5(x28043,x28042,x28044)+~E(x28041,x28042)+~P5(x28043,x28041,x28044)
% 155.94/155.64 [2805]P5(x28053,x28054,x28052)+~E(x28051,x28052)+~P5(x28053,x28054,x28051)
% 155.94/155.64
% 155.94/155.64 %-------------------------------------------
% 155.94/155.67 cnf(10102,plain,
% 155.94/155.67 (~E(f312(a126,x101021),x101021)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10105,plain,
% 155.94/155.67 (E(f37(x101051,x101052,x101053,x101054,x101055,x101056,x101057,x101058,x101059,a23),x101052)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(10108,plain,
% 155.94/155.67 (E(f37(x101081,x101082,x101083,x101084,x101085,x101086,x101087,x101088,x101089,a23),x101082)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(10111,plain,
% 155.94/155.67 (~E(f312(a126,x101111),x101111)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10114,plain,
% 155.94/155.67 (~E(f312(a126,x101141),x101141)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10117,plain,
% 155.94/155.67 (E(f37(x101171,x101172,x101173,x101174,x101175,x101176,x101177,x101178,x101179,a23),x101172)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(10124,plain,
% 155.94/155.67 (~E(f312(a126,x101241),x101241)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10135,plain,
% 155.94/155.67 (~E(f312(a126,x101351),x101351)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10140,plain,
% 155.94/155.67 (~P22(f312(f71(x101401,x101402,f189(f861(x101401,a846))),x101403))),
% 155.94/155.67 inference(rename_variables,[],[4498])).
% 155.94/155.67 cnf(10143,plain,
% 155.94/155.67 (~P22(f312(f71(x101431,x101432,f189(f861(x101431,a846))),x101433))),
% 155.94/155.67 inference(rename_variables,[],[4498])).
% 155.94/155.67 cnf(10146,plain,
% 155.94/155.67 (~E(f312(a126,x101461),x101461)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10149,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x101491),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(10152,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x101521),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(10165,plain,
% 155.94/155.67 (~P22(f312(f189(f861(x101651,a846)),x101652))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,4389,10102,10111,10114,10124,10135,2806,3040,3108,3048,3189,4475,10149,4472,4417,4483,3182,4467,4498,10140,4501,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968])).
% 155.94/155.67 cnf(10169,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x101691)),x101691))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(10172,plain,
% 155.94/155.67 (~E(f312(f312(f147(x101721),x101722),x101723),x101723)),
% 155.94/155.67 inference(rename_variables,[],[4423])).
% 155.94/155.67 cnf(10175,plain,
% 155.94/155.67 (E(f312(f117(a1),x101751),f312(f116(a1),x101751))),
% 155.94/155.67 inference(rename_variables,[],[3069])).
% 155.94/155.67 cnf(10178,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x101781),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(10180,plain,
% 155.94/155.67 (E(f54(a853,f37(x101801,f312(f312(f90(a853),x101802),x101803),x101804,x101805,x101806,x101807,x101808,x101809,x1018010,a23),x101802),f2(a853))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,10117,4389,10102,10111,10114,10124,10135,2806,3040,3108,3069,3048,4423,3189,4475,10149,10152,4472,4417,4484,4483,3182,4467,4498,10140,4501,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995])).
% 155.94/155.67 cnf(10181,plain,
% 155.94/155.67 (E(f37(x101811,x101812,x101813,x101814,x101815,x101816,x101817,x101818,x101819,a23),x101812)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(10184,plain,
% 155.94/155.67 (E(f37(x101841,x101842,x101843,x101844,x101845,x101846,x101847,x101848,x101849,a23),x101842)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(10188,plain,
% 155.94/155.67 (~P22(f312(a194,a92))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,10117,10181,4389,10102,10111,10114,10124,10135,2806,3040,3108,3069,3048,4423,3189,4475,10149,10152,4472,4417,4484,4483,3182,4467,4498,10140,4501,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045])).
% 155.94/155.67 cnf(10191,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),f312(f312(f89(a853),x101911),x101912)),x101912))),
% 155.94/155.67 inference(rename_variables,[],[4499])).
% 155.94/155.67 cnf(10194,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),f312(f312(f89(a853),x101941),x101942)),x101942))),
% 155.94/155.67 inference(rename_variables,[],[4499])).
% 155.94/155.67 cnf(10201,plain,
% 155.94/155.67 (~E(x102011,f312(a126,x102011))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,10117,10181,4389,10102,10111,10114,10124,10135,2806,3040,3108,3069,3048,4423,3274,3189,4475,10149,10152,4472,4417,4484,4031,4483,3182,4467,4498,10140,4501,4499,10191,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114])).
% 155.94/155.67 cnf(10215,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x102151),x102151))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(10218,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f54(a853,x102181,x102182)),x102181))),
% 155.94/155.67 inference(rename_variables,[],[3661])).
% 155.94/155.67 cnf(10237,plain,
% 155.94/155.67 (E(f312(f53(a853),f312(f279(a853),x102371)),x102371)),
% 155.94/155.67 inference(rename_variables,[],[3104])).
% 155.94/155.67 cnf(10245,plain,
% 155.94/155.67 (~E(f312(a126,x102451),x102451)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10248,plain,
% 155.94/155.67 (~E(f312(a126,x102481),x102481)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10251,plain,
% 155.94/155.67 (~E(f312(a126,x102511),x102511)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10253,plain,
% 155.94/155.67 (P22(f312(a194,a111))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,10117,10181,4389,10102,10111,10114,10124,10135,10146,10245,10248,2806,3040,3108,3069,3048,3137,4423,3104,4504,3121,3274,3189,4475,10149,10152,3793,3207,4472,4417,4471,10215,3299,3721,3661,4484,10169,4031,4483,4462,3182,4467,4498,10140,4501,4499,10191,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251])).
% 155.94/155.67 cnf(10256,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x102561),f312(a126,x102561)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(10267,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x102671),x102671))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(10274,plain,
% 155.94/155.67 (E(f37(x102741,x102742,x102743,x102744,x102745,x102746,x102747,x102748,x102749,a23),x102742)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(10277,plain,
% 155.94/155.67 (E(f37(x102771,x102772,x102773,x102774,x102775,x102776,x102777,x102778,x102779,a23),x102772)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(10300,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x103001),x103001))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(10307,plain,
% 155.94/155.67 (~E(f312(f312(f312(f81(x103071,f857(x103072)),x103073),x103074),f312(f219(x103072),x103075)),f312(f16(f857(x103072),x103071),f192(x103072)))),
% 155.94/155.67 inference(rename_variables,[],[4495])).
% 155.94/155.67 cnf(10332,plain,
% 155.94/155.67 (~E(f312(f312(f147(x103321),x103322),x103323),x103323)),
% 155.94/155.67 inference(rename_variables,[],[4423])).
% 155.94/155.67 cnf(10335,plain,
% 155.94/155.67 (~E(f312(a27,x103351),f36(x103352,x103353))),
% 155.94/155.67 inference(rename_variables,[],[4407])).
% 155.94/155.67 cnf(10348,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x103481),x103481))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(10351,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x103511),x103511))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(10354,plain,
% 155.94/155.67 (~E(f312(a126,x103541),x103541)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10361,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x103611),x103611))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(10372,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x103721),f312(a126,x103721)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(10379,plain,
% 155.94/155.67 (E(f312(f312(f129(x103791),f127(x103791)),x103792),x103792)),
% 155.94/155.67 inference(rename_variables,[],[3157])).
% 155.94/155.67 cnf(10397,plain,
% 155.94/155.67 (~P22(f312(f71(x103971,x103972,f189(f861(x103971,a846))),x103973))),
% 155.94/155.67 inference(rename_variables,[],[4498])).
% 155.94/155.67 cnf(10426,plain,
% 155.94/155.67 (~E(f312(a27,x104261),f36(x104262,x104263))),
% 155.94/155.67 inference(rename_variables,[],[4407])).
% 155.94/155.67 cnf(10432,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),f2(a853)),f312(a118,f87(a1))))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,10117,10181,10184,10274,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,4407,10335,2806,3040,3108,3069,3048,3137,3157,10379,4495,4423,10172,3104,3987,4504,3121,3571,3274,10256,10372,3189,4475,10149,10152,10178,4491,3643,3793,3232,3234,3207,4472,4417,3910,3204,10267,3205,3206,4471,10215,10300,3299,3721,3661,10218,4484,10169,4031,4483,4462,3182,3183,4464,4467,4498,10140,10143,4501,3682,4499,10191,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806])).
% 155.94/155.67 cnf(10435,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x104351),x104351))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(10440,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x104401),x104401))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(10443,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x104431),f312(a126,x104431)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(10446,plain,
% 155.94/155.67 (~P22(f312(f71(x104461,x104462,f189(f861(x104461,a846))),x104463))),
% 155.94/155.67 inference(rename_variables,[],[4498])).
% 155.94/155.67 cnf(10451,plain,
% 155.94/155.67 (~P22(f312(f71(x104511,x104512,f189(f861(x104511,a846))),x104513))),
% 155.94/155.67 inference(rename_variables,[],[4498])).
% 155.94/155.67 cnf(10463,plain,
% 155.94/155.67 (~E(f312(f165(x104631),f312(a126,f312(f312(f129(x104631),f312(f165(x104631),x104632)),f312(f312(f147(x104631),x104633),f127(x104631))))),f312(f312(f147(x104631),x104633),x104632))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,10117,10181,10184,10274,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,4407,10335,2806,3040,3108,3069,3048,3137,3157,10379,4495,4423,10172,3104,3987,4504,3121,3571,3274,10256,10372,10443,3189,4475,10149,10152,10178,4491,3643,3793,3232,3234,3207,4472,4417,3910,3204,10267,10361,3205,3206,4471,10215,10300,10351,3299,3721,3661,10218,4484,10169,4031,4483,4462,3182,3183,4464,4467,4498,10140,10143,10397,10446,4501,3682,4499,10191,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927])).
% 155.94/155.67 cnf(10464,plain,
% 155.94/155.67 (~E(f312(a126,x104641),x104641)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10478,plain,
% 155.94/155.67 (P22(f312(f312(f228(a113),f312(a3,x104781)),f312(a3,f312(a126,x104781))))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,10117,10181,10184,10274,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,4407,10335,2806,3040,3108,3069,3048,3137,3157,10379,4495,4423,10172,3104,3987,4504,3121,3571,3274,10256,10372,10443,3656,3189,4475,10149,10152,10178,4491,3643,3793,3232,3234,3207,4472,4417,3910,3204,10267,10361,3205,3206,4471,10215,10300,10351,3299,3721,3661,10218,4484,10169,4031,4483,4462,3182,3183,4464,4467,4498,10140,10143,10397,10446,4501,3682,4499,10191,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999])).
% 155.94/155.67 cnf(10487,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x104871),f312(a126,x104871)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(10490,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x104901),f312(a126,x104901)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(10493,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x104931),f312(a126,f312(f312(f89(a853),x104932),x104931))))),
% 155.94/155.67 inference(rename_variables,[],[3654])).
% 155.94/155.67 cnf(10496,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x104961),f312(f312(f90(a853),x104961),x104961)))),
% 155.94/155.67 inference(rename_variables,[],[3481])).
% 155.94/155.67 cnf(10499,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x104991),f312(f312(f90(a853),x104991),x104991)))),
% 155.94/155.67 inference(rename_variables,[],[3481])).
% 155.94/155.67 cnf(10504,plain,
% 155.94/155.67 (P22(f312(f312(f314(x105041),x105042),f235(f861(x105041,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3364])).
% 155.94/155.67 cnf(10519,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),f312(f312(f89(a853),x105191),x105192)),x105192))),
% 155.94/155.67 inference(rename_variables,[],[4499])).
% 155.94/155.67 cnf(10522,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),f312(f312(f89(a853),x105221),x105222)),x105222))),
% 155.94/155.67 inference(rename_variables,[],[4499])).
% 155.94/155.67 cnf(10525,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x105251)),x105251))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(10528,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x105281)),x105281))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(10531,plain,
% 155.94/155.67 (P22(f312(f235(f861(x105311,a846)),x105312))),
% 155.94/155.67 inference(rename_variables,[],[3268])).
% 155.94/155.67 cnf(10534,plain,
% 155.94/155.67 (E(f312(f53(a853),f312(f279(a853),x105341)),x105341)),
% 155.94/155.67 inference(rename_variables,[],[3104])).
% 155.94/155.67 cnf(10537,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x105371),f312(a126,x105371)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(10544,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x105441),x105441))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(10549,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x105491),x105491))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(10558,plain,
% 155.94/155.67 (E(f37(x105581,x105582,x105583,x105584,x105585,x105586,x105587,x105588,x105589,a23),x105582)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(10561,plain,
% 155.94/155.67 (P22(f312(f235(f861(x105611,a846)),x105612))),
% 155.94/155.67 inference(rename_variables,[],[3268])).
% 155.94/155.67 cnf(10563,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(f312(f90(a853),f312(a126,x105631)),f312(a126,x105631))),x105631))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,10117,10181,10184,10274,10277,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,4407,10335,2806,3040,3108,3069,3048,3137,3157,10379,4495,4423,10172,3104,10237,3987,4504,3121,3571,3513,3274,10256,10372,10443,10487,10490,3656,3189,4475,10149,10152,10178,4491,3643,3419,3793,3232,3234,3207,4472,4417,3910,3204,10267,10361,10440,3205,3206,10348,4471,10215,10300,10351,3364,3268,10531,3299,3721,3661,10218,4484,10169,10525,4031,4483,4462,3182,3183,4464,4467,4498,10140,10143,10397,10446,4503,3481,10496,10499,4501,3682,4499,10191,10194,10519,3654,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229])).
% 155.94/155.67 cnf(10564,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x105641),f312(f312(f90(a853),x105641),x105641)))),
% 155.94/155.67 inference(rename_variables,[],[3481])).
% 155.94/155.67 cnf(10568,plain,
% 155.94/155.67 (E(f312(f165(x105681),f37(x105682,f312(f312(f129(x105681),f312(f165(x105681),x105683)),f312(f312(f147(x105681),x105684),f127(x105681))),x105685,x105686,x105687,x105688,x105689,x1056810,x1056811,a23)),f312(f312(f147(x105681),x105684),x105683))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,10117,10181,10184,10274,10277,10558,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,4407,10335,2806,3040,3108,3069,3048,3137,3157,10379,4495,4423,10172,3104,10237,3987,4504,3121,3571,3513,3274,10256,10372,10443,10487,10490,3656,3189,4475,10149,10152,10178,4491,3643,3419,3793,3232,3234,3207,4472,4417,3910,3204,10267,10361,10440,3205,3206,10348,4471,10215,10300,10351,3364,3268,10531,3299,3721,3661,10218,4484,10169,10525,4031,4483,4462,3182,3183,4464,4467,4498,10140,10143,10397,10446,4503,3481,10496,10499,4501,3682,4499,10191,10194,10519,3654,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270])).
% 155.94/155.67 cnf(10569,plain,
% 155.94/155.67 (E(f37(x105691,x105692,x105693,x105694,x105695,x105696,x105697,x105698,x105699,a23),x105692)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(10581,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,f312(a126,f312(f312(f89(a853),x105811),x105812)))),f312(a126,x105812)))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,10117,10181,10184,10274,10277,10558,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,4407,10335,2806,3040,3108,3069,3048,3137,3157,10379,4495,4423,10172,3104,10237,3987,4504,3121,3571,3513,3274,10256,10372,10443,10487,10490,10537,3656,3189,4475,10149,10152,10178,4491,3643,3419,3793,3232,3234,3207,4472,4417,3910,3204,10267,10361,10440,3205,3206,10348,4471,10215,10300,10351,3364,3268,10531,3299,3721,3661,10218,4484,10169,10525,4031,4483,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,4503,3481,10496,10499,4501,3682,4499,10191,10194,10519,3654,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278])).
% 155.94/155.67 cnf(10606,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x106061),x106061))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(10619,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x106191),f312(a126,x106191)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(10622,plain,
% 155.94/155.67 (~P22(f312(f312(f189(f861(x106221,f861(x106222,a846))),x106223),x106224))),
% 155.94/155.67 inference(rename_variables,[],[4502])).
% 155.94/155.67 cnf(10624,plain,
% 155.94/155.67 (P22(f312(f312(f228(a1),f312(f312(f21(a1),x106241),f87(a1))),x106241))),
% 155.94/155.67 inference(scs_inference,[],[4361,10105,10108,10117,10181,10184,10274,10277,10558,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,4407,10335,2806,3040,3108,3069,3048,3137,3157,10379,4495,4423,10172,3104,10237,3987,3843,4504,3121,3571,3513,3274,10256,10372,10443,10487,10490,10537,3656,3189,4475,10149,10152,10178,4491,3643,3419,3793,3232,3234,3207,4472,4417,3910,3204,10267,10361,10440,3205,10606,3206,10348,10549,4471,10215,10300,10351,3364,4487,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,4031,4483,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,4503,3481,10496,10499,4501,4502,3682,4499,10191,10194,10519,3654,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527])).
% 155.94/155.67 cnf(10625,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x106251),x106251))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(10630,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x106301),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(10643,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x106431),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(10646,plain,
% 155.94/155.67 (~P22(f312(f312(f228(f861(x106461,a846)),x106462),f189(f861(x106461,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4496])).
% 155.94/155.67 cnf(10649,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x106491),x106491))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(10652,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x106521),x106521))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(10666,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x106661),f312(f312(f21(a853),x106661),x106662)))),
% 155.94/155.67 inference(scs_inference,[],[4463,4361,10105,10108,10117,10181,10184,10274,10277,10558,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,4407,10335,2806,3040,3108,3069,3048,3137,3157,10379,4495,4423,10172,3104,10237,3987,3843,4504,3121,3571,3513,3274,10256,10372,10443,10487,10490,10537,3656,3189,4475,10149,10152,10178,10630,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3910,4496,3204,10267,10361,10440,3205,10606,10649,10652,3206,10348,10549,4471,10215,10300,10351,10435,3364,4487,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,4031,4483,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,4503,3481,10496,10499,4501,4502,3682,4499,10191,10194,10519,3654,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690])).
% 155.94/155.67 cnf(10667,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x106671),x106671))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(10676,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x106761),x106762),f189(f861(x106761,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(10685,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x106851),x106851))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(10688,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x106881),x106882),f189(f861(x106881,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(10691,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x106911,a846)),f312(f290(x106912,x106911,x106913),f312(f291(x106912,x106911,x106913),x106914))),x106914))),
% 155.94/155.67 inference(rename_variables,[],[4092])).
% 155.94/155.67 cnf(10700,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x107001,a846)),f312(f168(x107001),f312(f132(x107001,x107002),x107003))),f312(f168(x107001),x107003)))),
% 155.94/155.67 inference(rename_variables,[],[3853])).
% 155.94/155.67 cnf(10703,plain,
% 155.94/155.67 (E(f312(f290(x107031,x107031,f5(x107031)),x107032),x107032)),
% 155.94/155.67 inference(rename_variables,[],[3264])).
% 155.94/155.67 cnf(10708,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f2(a853)),x107081))),
% 155.94/155.67 inference(rename_variables,[],[3226])).
% 155.94/155.67 cnf(10711,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x107111),x107111))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(10714,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x107141),x107141))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(10717,plain,
% 155.94/155.67 (~P22(f312(f312(f189(f861(x107171,f861(x107172,a846))),x107173),x107174))),
% 155.94/155.67 inference(rename_variables,[],[4502])).
% 155.94/155.67 cnf(10724,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x107241),x107241))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(10735,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x107351),f312(a126,f312(f312(f89(a853),x107352),x107351))))),
% 155.94/155.67 inference(rename_variables,[],[3654])).
% 155.94/155.67 cnf(10738,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x107381),f312(f312(f90(a853),x107381),x107381)))),
% 155.94/155.67 inference(rename_variables,[],[3481])).
% 155.94/155.67 cnf(10748,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x107481),x107481))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(10751,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x107511),x107511))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(10754,plain,
% 155.94/155.67 (~E(f312(a126,x107541),x107541)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10759,plain,
% 155.94/155.67 (P22(f312(f312(f314(x107591),x107592),f235(f861(x107591,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3364])).
% 155.94/155.67 cnf(10764,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x107641),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(10766,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x107661,a846)),x107662),f48(f861(x107661,a846),f312(f288(x107661),x107662))))),
% 155.94/155.67 inference(scs_inference,[],[4463,4361,10105,10108,10117,10181,10184,10274,10277,10558,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,4407,10335,2806,3040,3108,3069,3048,3264,3137,3157,10379,4495,4423,10172,3104,10237,3987,3843,4504,3121,3411,3571,3513,3274,10256,10372,10443,10487,10490,10537,10619,3656,3189,4475,10149,10152,10178,10630,10643,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3572,3910,4496,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,4487,10676,10688,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,3226,4031,4483,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,4503,3481,10496,10499,10564,10738,4501,4502,10622,4092,3682,4499,10191,10194,10519,3654,10493,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386])).
% 155.94/155.67 cnf(10779,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f2(a853)),x107791))),
% 155.94/155.67 inference(rename_variables,[],[3226])).
% 155.94/155.67 cnf(10786,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x107861),x107861))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(10795,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x107951),x107952),f189(f861(x107951,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(10799,plain,
% 155.94/155.67 (E(f312(f312(f115(f861(x107991,a846)),f312(f312(f115(f861(x107991,a846)),x107992),f312(f88(f861(x107991,a846)),x107993))),x107993),f189(f861(x107991,a846)))),
% 155.94/155.67 inference(scs_inference,[],[4463,4361,10105,10108,10117,10181,10184,10274,10277,10558,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,4407,10335,2806,3040,3108,3069,3048,3264,3137,3157,10379,4495,4423,10172,3104,10237,3987,3843,4504,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,3656,3189,4475,10149,10152,10178,10630,10643,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3572,3910,4496,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,4487,10676,10688,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,4503,3481,10496,10499,10564,10738,4501,4502,10622,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662])).
% 155.94/155.67 cnf(10803,plain,
% 155.94/155.67 (P22(f312(f312(f314(x108031),x108032),f235(f861(x108031,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3364])).
% 155.94/155.67 cnf(10806,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x108061),f854(x108061))),f312(f312(f239(f854(x108061),f854(x108061)),x108062),f127(x108061))),f141(x108061,x108063)))),
% 155.94/155.67 inference(rename_variables,[],[4504])).
% 155.94/155.67 cnf(10812,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(x108121,x108121)),x108122),f237(x108121,f189(f861(x108121,a846)))))),
% 155.94/155.67 inference(scs_inference,[],[4463,4361,10105,10108,10117,10181,10184,10274,10277,10558,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,4407,10335,2806,3040,3108,3069,3048,3264,3137,3157,10379,4495,4423,10172,3104,10237,3987,3843,4504,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,3656,3189,4475,10149,10152,10178,10630,10643,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3572,3910,4496,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,4487,10676,10688,10795,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,4503,3481,10496,10499,10564,10738,4501,4502,10622,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801])).
% 155.94/155.67 cnf(10813,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x108131),x108132),f189(f861(x108131,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(10815,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x108151),x108152),f312(f291(x108151,x108153,x108154),f189(f861(x108153,a846)))))),
% 155.94/155.67 inference(scs_inference,[],[4463,4361,10105,10108,10117,10181,10184,10274,10277,10558,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,4407,10335,2806,3040,3108,3069,3048,3264,3137,3157,10379,4495,4423,10172,3104,10237,3987,3843,4504,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,3656,3189,4475,10149,10152,10178,10630,10643,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3572,3910,4496,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,4487,10676,10688,10795,10813,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,4503,3481,10496,10499,10564,10738,4501,4502,10622,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831])).
% 155.94/155.67 cnf(10816,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x108161),x108162),f189(f861(x108161,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(10819,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x108191,a846)),x108192),f312(f312(f289(x108191),x108193),x108192)))),
% 155.94/155.67 inference(rename_variables,[],[3650])).
% 155.94/155.67 cnf(10822,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x108221),x108221))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(10825,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x108251,a846)),x108252),f312(f312(f289(x108251),x108253),x108252)))),
% 155.94/155.67 inference(rename_variables,[],[3650])).
% 155.94/155.67 cnf(10827,plain,
% 155.94/155.67 (P39(x108271,x108272,x108273,f37(x108274,f127(x108271),x108275,x108276,x108277,x108278,x108279,x1082710,x1082711,a23),f127(x108272))),
% 155.94/155.67 inference(scs_inference,[],[4463,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,4407,10335,2806,3040,3108,3069,3048,3264,3137,3157,10379,4495,4423,10172,3104,10237,3987,3843,4504,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,3656,3189,4475,10149,10152,10178,10630,10643,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3572,3910,4496,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,4487,10676,10688,10795,10813,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,4503,3650,10819,3481,10496,10499,10564,10738,4501,4502,10622,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938])).
% 155.94/155.67 cnf(10828,plain,
% 155.94/155.67 (E(f37(x108281,x108282,x108283,x108284,x108285,x108286,x108287,x108288,x108289,a23),x108282)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(10831,plain,
% 155.94/155.67 (E(f37(x108311,x108312,x108313,x108314,x108315,x108316,x108317,x108318,x108319,a23),x108312)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(10842,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x108421,a846)),x108422),f312(f312(f289(x108421),x108423),x108422)))),
% 155.94/155.67 inference(rename_variables,[],[3650])).
% 155.94/155.67 cnf(10845,plain,
% 155.94/155.67 (P36(x108451,x108452,x108453,f180(x108451,x108452,x108454,x108453))),
% 155.94/155.67 inference(rename_variables,[],[3769])).
% 155.94/155.67 cnf(10853,plain,
% 155.94/155.67 (~P22(f312(f71(x108531,x108532,f189(f861(x108531,a846))),x108533))),
% 155.94/155.67 inference(rename_variables,[],[4498])).
% 155.94/155.67 cnf(10857,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(a853,a853)),f312(f312(f239(a853,a853),f312(a126,x108571)),x108571)),f287(a853,a302)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,4407,10335,2806,3933,3040,3108,3069,3048,3264,3137,3157,10379,4495,4423,10172,3104,10237,3987,3843,4504,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,3656,3189,4475,10149,10152,10178,10630,10643,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3572,3910,4496,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3481,10496,10499,10564,10738,4501,4502,10622,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267])).
% 155.94/155.67 cnf(10868,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x108681),f312(a126,x108681)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(10878,plain,
% 155.94/155.67 (~E(f312(f290(x108781,f861(x108781,a846),x108782),x108783),f312(f288(x108781),x108783))),
% 155.94/155.67 inference(rename_variables,[],[4485])).
% 155.94/155.67 cnf(10881,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x108811),x108812),f189(f861(x108811,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(10884,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(x108841,x108841)),f312(f312(f239(x108841,x108841),x108842),x108842)),f287(x108841,x108843)))),
% 155.94/155.67 inference(rename_variables,[],[3843])).
% 155.94/155.67 cnf(10887,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x108871,a846)),x108872),f235(f861(x108871,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(10890,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x108901,a846)),f312(f168(x108901),f166(x108901,x108902,x108903))),f312(f168(x108901),x108903)))),
% 155.94/155.67 inference(rename_variables,[],[3904])).
% 155.94/155.67 cnf(10906,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x109061,a846)),f189(f861(x109061,a846))),x109062))),
% 155.94/155.67 inference(rename_variables,[],[3652])).
% 155.94/155.67 cnf(10920,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x109201),f854(x109201))),f312(f312(f239(f854(x109201),f854(x109201)),x109202),f127(x109201))),f143(x109201,x109203)))),
% 155.94/155.67 inference(rename_variables,[],[4505])).
% 155.94/155.67 cnf(10931,plain,
% 155.94/155.67 (~E(f312(a126,x109311),x109311)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10934,plain,
% 155.94/155.67 (~E(f312(a126,x109341),x109341)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(10936,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(f854(x109361),f854(x109361))),f312(f312(f239(f854(x109361),f854(x109361)),f127(x109361)),f127(x109361))),f312(f312(f267(f854(x109361),f854(x109361),f854(x109361)),f154(x109361,x109362)),f287(f854(x109361),f154(x109361,x109362)))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,4407,10335,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,4495,3841,4423,10172,4485,3104,10237,3987,3843,10884,4504,10806,4505,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,3656,3189,4475,10149,10152,10178,10630,10643,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3904,3572,3910,3588,4496,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3652,3481,10496,10499,10564,10738,4501,4502,10622,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509])).
% 155.94/155.67 cnf(10946,plain,
% 155.94/155.67 (P19(x109461,x109461,f5(x109461),x109462)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(10951,plain,
% 155.94/155.67 (~E(f312(f290(x109511,f861(x109511,a846),x109512),x109513),f312(f288(x109511),x109513))),
% 155.94/155.67 inference(rename_variables,[],[4485])).
% 155.94/155.67 cnf(10956,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x109561,a846)),x109562),f235(f861(x109561,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(10970,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x109701),x109702),f189(f861(x109701,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(10973,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x109731)),x109731))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(10978,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x109781),x109782),f189(f861(x109781,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(10990,plain,
% 155.94/155.67 (~P22(f312(f312(f314(a853),f312(a126,f312(f138(a853,a853,f89(a853),f2(a853)),x109901))),f312(f168(a853),x109901)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,4495,3841,4423,10172,4485,10878,3313,3104,10237,3987,3843,10884,4504,10806,4505,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3904,3572,3910,3588,10887,4496,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,10881,10970,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3652,3481,10496,10499,10564,10738,4501,4502,10622,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720])).
% 155.94/155.67 cnf(10991,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x109911)),x109911))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(10994,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x109941),x109942),f189(f861(x109941,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11004,plain,
% 155.94/155.67 (E(f312(x110041,f740(f312(x110041,x110042),f312(f219(x110043),x110042),x110041,x110044,x110043)),f312(x110041,x110042))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,4485,10878,3313,3104,10237,3987,3843,10884,4504,10806,4505,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3904,3572,3910,3588,10887,4496,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,10881,10970,10978,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3652,3481,10496,10499,10564,10738,4501,4502,10622,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792])).
% 155.94/155.67 cnf(11013,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(x110131,x110131)),f312(f312(f239(x110131,x110131),x110132),x110132)),f287(x110131,x110133)))),
% 155.94/155.67 inference(rename_variables,[],[3843])).
% 155.94/155.67 cnf(11018,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x110181),f854(x110181))),f312(f312(f239(f854(x110181),f854(x110181)),x110182),f127(x110181))),f141(x110181,x110183)))),
% 155.94/155.67 inference(rename_variables,[],[4504])).
% 155.94/155.67 cnf(11021,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x110211),f854(x110211))),f312(f312(f239(f854(x110211),f854(x110211)),x110212),f127(x110211))),f143(x110211,x110213)))),
% 155.94/155.67 inference(rename_variables,[],[4505])).
% 155.94/155.67 cnf(11024,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x110241),f854(x110241))),f312(f312(f239(f854(x110241),f854(x110241)),x110242),f127(x110241))),f153(x110241,x110243)))),
% 155.94/155.67 inference(rename_variables,[],[4506])).
% 155.94/155.67 cnf(11026,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x110261),f854(x110261))),f312(f312(f239(f854(x110261),f854(x110261)),f127(x110261)),x110262)),f312(f265(f854(x110261),f854(x110261)),f141(x110261,x110263))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,4485,10878,3313,3104,10237,3987,3843,10884,4504,10806,11018,4505,10920,4506,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3904,3572,3910,3588,10887,4496,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,10881,10970,10978,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3652,3481,10496,10499,10564,10738,4501,4502,10622,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943])).
% 155.94/155.67 cnf(11029,plain,
% 155.94/155.67 (~P22(f312(f312(f228(f861(x110291,a846)),x110292),f189(f861(x110291,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4496])).
% 155.94/155.67 cnf(11032,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x110321),x110322),f189(f861(x110321,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11036,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x110361,a846)),x110362),f312(f312(f124(f861(x110361,a846)),x110363),f235(f861(x110361,a846)))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,4485,10878,3313,3104,10237,3987,3843,10884,4504,10806,11018,4505,10920,4506,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,10764,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3904,3572,3910,3588,10887,10956,4496,10646,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3652,3481,10496,10499,10564,10738,4501,4502,10622,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992])).
% 155.94/155.67 cnf(11037,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x110371,a846)),x110372),f235(f861(x110371,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(11040,plain,
% 155.94/155.67 (~P22(f312(f312(f189(f861(x110401,f861(x110402,a846))),x110403),x110404))),
% 155.94/155.67 inference(rename_variables,[],[4502])).
% 155.94/155.67 cnf(11044,plain,
% 155.94/155.67 (~P57(f854(x110441),f154(x110441,x110442))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,4485,10878,3313,3104,10237,3987,3843,10884,4504,10806,11018,4505,10920,4506,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,10764,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3904,3572,3910,3588,10887,10956,4496,10646,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3652,3481,10496,10499,10564,10738,4501,4502,10622,10717,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062])).
% 155.94/155.67 cnf(11049,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x110491),x110492),f189(f861(x110491,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11052,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(x110521,x110521)),f312(f312(f239(x110521,x110521),x110522),x110523)),f149(x110521,f127(f861(x110521,a853)))))),
% 155.94/155.67 inference(rename_variables,[],[4503])).
% 155.94/155.67 cnf(11055,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x110551,a846)),x110552),x110552))),
% 155.94/155.67 inference(rename_variables,[],[3509])).
% 155.94/155.67 cnf(11058,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x110581),x110582),f189(f861(x110581,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11061,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x110611,a846)),f189(f861(x110611,a846))),x110612))),
% 155.94/155.67 inference(rename_variables,[],[3652])).
% 155.94/155.67 cnf(11064,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(x110641,x110641)),f312(f312(f239(x110641,x110641),x110642),x110642)),f287(x110641,x110643)))),
% 155.94/155.67 inference(rename_variables,[],[3843])).
% 155.94/155.67 cnf(11066,plain,
% 155.94/155.67 (~P39(x110661,x110662,x110663,f312(f312(f150(x110664,x110661),x110665),f312(a126,f127(x110664))),f127(x110662))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,4485,10878,3313,3104,10237,3987,3843,10884,11013,4504,10806,11018,4505,10920,4506,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,10764,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3904,3572,3910,3588,10887,10956,4496,10646,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3509,3652,10906,3481,10496,10499,10564,10738,4501,4502,10622,10717,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172])).
% 155.94/155.67 cnf(11070,plain,
% 155.94/155.67 (P39(x110701,x110702,x110703,f312(f312(f150(x110704,x110701),x110705),f37(x110706,f127(x110704),x110707,x110708,x110709,x1107010,x1107011,x1107012,x1107013,a23)),f127(x110702))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,4485,10878,3313,3104,10237,3987,3843,10884,11013,4504,10806,11018,4505,10920,4506,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,10764,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3904,3572,3910,3588,10887,10956,4496,10646,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3509,3652,10906,3481,10496,10499,10564,10738,4501,4502,10622,10717,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196])).
% 155.94/155.67 cnf(11075,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x110751),f854(x110751))),f312(f312(f239(f854(x110751),f854(x110751)),x110752),f127(x110751))),f153(x110751,x110753)))),
% 155.94/155.67 inference(rename_variables,[],[4506])).
% 155.94/155.67 cnf(11078,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x110781),f854(x110781))),f312(f312(f239(f854(x110781),f854(x110781)),f127(x110781)),x110782)),f141(x110781,x110783)))),
% 155.94/155.67 inference(rename_variables,[],[4507])).
% 155.94/155.67 cnf(11083,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f861(x110831,a846),f861(x110831,a846))),f312(f312(f239(f861(x110831,a846),f861(x110831,a846)),x110832),f189(f861(x110831,a846)))),f286(x110831)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,4485,10878,3313,3104,10237,3987,3843,10884,11013,4504,10806,11018,4505,10920,4506,11024,4507,4508,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,10764,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3904,3572,3910,3588,10887,10956,4496,10646,11029,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3509,3652,10906,3481,10496,10499,10564,10738,4501,4502,10622,10717,4092,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320])).
% 155.94/155.67 cnf(11086,plain,
% 155.94/155.67 (P22(f312(f312(f314(x110861),x110862),f235(f861(x110861,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3364])).
% 155.94/155.67 cnf(11091,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x110911,a846)),f189(f861(x110911,a846))),x110912))),
% 155.94/155.67 inference(rename_variables,[],[3652])).
% 155.94/155.67 cnf(11094,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x110941),x110942),f189(f861(x110941,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11097,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x110971,a846)),x110972),f235(f861(x110971,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(11101,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x111011,a846)),f312(f264(x111012,x111011,x111013),f189(f861(x111012,a846)))),x111014))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,4485,10878,3313,3104,10237,3987,3843,10884,11013,4504,10806,11018,4505,10920,4506,11024,4507,4508,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,10764,4491,3643,3419,3793,3232,3234,3207,4472,4417,3950,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,3268,10531,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3509,3652,10906,11061,11091,3481,10496,10499,10564,10738,4501,4502,10622,10717,4092,3992,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425])).
% 155.94/155.67 cnf(11102,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x111021,a846)),f189(f861(x111021,a846))),x111022))),
% 155.94/155.67 inference(rename_variables,[],[3652])).
% 155.94/155.67 cnf(11115,plain,
% 155.94/155.67 (P22(f312(f235(f861(x111151,a846)),x111152))),
% 155.94/155.67 inference(rename_variables,[],[3268])).
% 155.94/155.67 cnf(11123,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x111231),f854(x111231))),f312(f312(f239(f854(x111231),f854(x111231)),x111232),f127(x111231))),f141(x111231,x111233)))),
% 155.94/155.67 inference(rename_variables,[],[4504])).
% 155.94/155.67 cnf(11126,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x111261),f854(x111261))),f312(f312(f239(f854(x111261),f854(x111261)),x111262),f127(x111261))),f143(x111261,x111263)))),
% 155.94/155.67 inference(rename_variables,[],[4505])).
% 155.94/155.67 cnf(11129,plain,
% 155.94/155.67 (~E(f312(a126,x111291),x111291)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11132,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x111321),x111322),f189(f861(x111321,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11137,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(f854(x111371),f854(x111371))),f312(f312(f239(f854(x111371),f854(x111371)),x111372),x111372)),f154(x111371,f287(x111371,x111373))))),
% 155.94/155.67 inference(rename_variables,[],[3981])).
% 155.94/155.67 cnf(11142,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x111421),f854(x111421))),f312(f312(f239(f854(x111421),f854(x111421)),x111422),f127(x111421))),f141(x111421,x111423)))),
% 155.94/155.67 inference(rename_variables,[],[4504])).
% 155.94/155.67 cnf(11146,plain,
% 155.94/155.67 (E(f312(f312(f147(x111461),f594(f287(x111461,x111462),f312(f312(f147(x111461),x111463),x111464),x111464,x111463,x111461)),f595(f287(x111461,x111462),f312(f312(f147(x111461),x111463),x111464),x111464,x111463,x111461)),f312(f312(f147(x111461),x111463),x111464))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,4485,10878,3313,3104,10237,3987,3843,10884,11013,4504,10806,11018,11123,4505,10920,11021,4506,11024,4507,11078,4508,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,10764,4491,3643,3419,3793,3232,3234,3207,4472,4417,3981,11137,3950,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,3268,10531,10561,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3509,3652,10906,11061,11091,3481,10496,10499,10564,10738,4501,4502,10622,10717,4092,3992,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611])).
% 155.94/155.67 cnf(11151,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x111511),x111512),f181(x111513,x111511,f183(x111513,x111511,x111514,f189(f861(x111513,a846))))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,4485,10878,3313,3104,10237,3987,3843,10884,11013,4504,10806,11018,11123,4505,10920,11021,4506,11024,4507,11078,4508,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,10764,4491,3643,3419,3793,3232,3234,3207,4472,4417,3981,11137,3950,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,3268,10531,10561,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,3810,3650,10819,10825,3509,3652,10906,11061,11091,3481,10496,10499,10564,10738,4501,4502,10622,10717,4092,3992,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635])).
% 155.94/155.67 cnf(11152,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x111521),x111522),f189(f861(x111521,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11155,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x111551),x111552),f189(f861(x111551,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11158,plain,
% 155.94/155.67 (P22(f312(f312(f314(x111581),x111582),f235(f861(x111581,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3364])).
% 155.94/155.67 cnf(11163,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(x111631,x111631)),f312(f312(f239(x111631,x111631),x111632),x111633)),f149(x111631,f127(f861(x111631,a853)))))),
% 155.94/155.67 inference(rename_variables,[],[4503])).
% 155.94/155.67 cnf(11166,plain,
% 155.94/155.67 (~E(f312(f290(x111661,f861(x111661,a846),x111662),x111663),f312(f288(x111661),x111663))),
% 155.94/155.67 inference(rename_variables,[],[4485])).
% 155.94/155.67 cnf(11169,plain,
% 155.94/155.67 (~E(f312(f290(x111691,f861(x111691,a846),x111692),x111693),f312(f288(x111691),x111693))),
% 155.94/155.67 inference(rename_variables,[],[4485])).
% 155.94/155.67 cnf(11172,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x111721),f854(x111721))),f312(f312(f239(f854(x111721),f854(x111721)),x111722),f127(x111721))),f141(x111721,x111723)))),
% 155.94/155.67 inference(rename_variables,[],[4504])).
% 155.94/155.67 cnf(11178,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x111781),f854(x111781))),f312(f312(f239(f854(x111781),f854(x111781)),x111782),f127(x111781))),f141(x111781,x111783)))),
% 155.94/155.67 inference(rename_variables,[],[4504])).
% 155.94/155.67 cnf(11181,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x111811),x111812),f189(f861(x111811,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11184,plain,
% 155.94/155.67 (~P22(f312(f312(f189(f861(x111841,f861(x111842,a846))),x111843),x111844))),
% 155.94/155.67 inference(rename_variables,[],[4502])).
% 155.94/155.67 cnf(11187,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x111871),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(11191,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(x111911,x111912)),f312(f312(f239(x111911,x111912),f312(x111913,x111914)),f312(x111915,x111914))),f312(f290(f860(x111916,x111916),f860(x111911,x111912),f250(x111916,x111911,x111916,x111912,x111913,x111915)),f287(x111916,x111917))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,4407,10335,10426,2806,3933,3664,3040,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,4485,10878,10951,11166,3313,3104,10237,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,3513,3717,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,10764,4491,3643,3419,3793,3232,3234,3207,4472,4417,3981,11137,3950,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,11086,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,3268,10531,10561,3299,3721,3661,10218,4484,10169,10525,10528,10973,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,4503,11052,3810,3650,10819,10825,3509,3652,10906,11061,11091,3481,10496,10499,10564,10738,4501,4502,10622,10717,11040,4092,3992,3682,4499,10191,10194,10519,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941])).
% 155.94/155.67 cnf(11194,plain,
% 155.94/155.67 (P22(f312(f312(f314(x111941),f312(x111942,x111943)),f312(f290(x111944,x111941,x111942),f235(f861(x111944,a846)))))),
% 155.94/155.67 inference(rename_variables,[],[3810])).
% 155.94/155.67 cnf(11197,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(x111971,x111971)),f312(f312(f239(x111971,x111971),x111972),x111973)),f149(x111971,f127(f861(x111971,a853)))))),
% 155.94/155.67 inference(rename_variables,[],[4503])).
% 155.94/155.67 cnf(11203,plain,
% 155.94/155.67 (E(f37(x112031,x112032,x112033,x112034,x112035,x112036,x112037,x112038,x112039,a23),x112032)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11206,plain,
% 155.94/155.67 (E(f37(x112061,x112062,x112063,x112064,x112065,x112066,x112067,x112068,x112069,a23),x112062)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11209,plain,
% 155.94/155.67 (~E(f312(a126,x112091),x112091)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11216,plain,
% 155.94/155.67 (~E(f312(a126,x112161),x112161)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11221,plain,
% 155.94/155.67 (E(f37(x112211,x112212,x112213,x112214,x112215,x112216,x112217,x112218,x112219,a23),x112212)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11222,plain,
% 155.94/155.67 (E(f38(x112221,x112222,x112223,x112224,x112225,x112226,x112227,x112228,x112229,a23),x112222)),
% 155.94/155.67 inference(rename_variables,[],[4362])).
% 155.94/155.67 cnf(11225,plain,
% 155.94/155.67 (E(f37(x112251,x112252,x112253,x112254,x112255,x112256,x112257,x112258,x112259,a23),x112252)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11232,plain,
% 155.94/155.67 (~E(f312(a126,x112321),x112321)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11237,plain,
% 155.94/155.67 (~E(f312(f312(f89(a1),x112371),x112371),a111)),
% 155.94/155.67 inference(rename_variables,[],[4420])).
% 155.94/155.67 cnf(11246,plain,
% 155.94/155.67 (E(f312(f312(f21(a853),f2(a853)),x112461),f2(a853))),
% 155.94/155.67 inference(rename_variables,[],[3122])).
% 155.94/155.67 cnf(11249,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x112491),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(11256,plain,
% 155.94/155.67 (E(f312(f312(f89(a1),f312(f312(f90(a1),x112561),f312(f47(a1,x112562),x112561))),f54(a1,x112562,x112561)),x112562)),
% 155.94/155.67 inference(rename_variables,[],[3725])).
% 155.94/155.67 cnf(11270,plain,
% 155.94/155.67 (E(f37(x112701,x112702,x112703,x112704,x112705,x112706,x112707,x112708,x112709,a23),x112702)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11273,plain,
% 155.94/155.67 (E(f37(x112731,x112732,x112733,x112734,x112735,x112736,x112737,x112738,x112739,a23),x112732)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11276,plain,
% 155.94/155.67 (E(f37(x112761,x112762,x112763,x112764,x112765,x112766,x112767,x112768,x112769,a23),x112762)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11279,plain,
% 155.94/155.67 (E(f37(x112791,x112792,x112793,x112794,x112795,x112796,x112797,x112798,x112799,a23),x112792)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11282,plain,
% 155.94/155.67 (~E(f312(a126,x112821),x112821)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11285,plain,
% 155.94/155.67 (~E(f312(a126,x112851),x112851)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11289,plain,
% 155.94/155.67 (E(f37(x112891,x112892,x112893,x112894,x112895,x112896,x112897,x112898,x112899,a23),x112892)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11308,plain,
% 155.94/155.67 (~E(f312(a126,x113081),x113081)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11311,plain,
% 155.94/155.67 (~E(f312(f312(f147(x113111),x113112),x113113),x113113)),
% 155.94/155.67 inference(rename_variables,[],[4423])).
% 155.94/155.67 cnf(11318,plain,
% 155.94/155.67 (~P22(f312(f71(x113181,x113182,f189(f861(x113181,a846))),x113183))),
% 155.94/155.67 inference(rename_variables,[],[4498])).
% 155.94/155.67 cnf(11321,plain,
% 155.94/155.67 (~P22(f312(f312(f189(f861(x113211,f861(x113212,a846))),x113213),x113214))),
% 155.94/155.67 inference(rename_variables,[],[4502])).
% 155.94/155.67 cnf(11324,plain,
% 155.94/155.67 (P22(f312(f312(f314(x113241),x113242),f235(f861(x113241,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3364])).
% 155.94/155.67 cnf(11332,plain,
% 155.94/155.67 (E(f37(x113321,x113322,x113323,x113324,x113325,x113326,x113327,x113328,x113329,a23),x113322)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11339,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x113391),x113391))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(11346,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x113461),x113461))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(11347,plain,
% 155.94/155.67 (E(f37(x113471,x113472,x113473,x113474,x113475,x113476,x113477,x113478,x113479,a23),x113472)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11360,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),f312(f312(f89(a853),x113601),x113602)),x113602))),
% 155.94/155.67 inference(rename_variables,[],[4499])).
% 155.94/155.67 cnf(11363,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a1),f312(f114(a1),x113631)),f2(a1)))),
% 155.94/155.67 inference(rename_variables,[],[4491])).
% 155.94/155.67 cnf(11374,plain,
% 155.94/155.67 (E(f37(x113741,x113742,x113743,x113744,x113745,x113746,x113747,x113748,x113749,a23),x113742)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11377,plain,
% 155.94/155.67 (E(f37(x113771,x113772,x113773,x113774,x113775,x113776,x113777,x113778,x113779,a23),x113772)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11381,plain,
% 155.94/155.67 (~E(f312(f312(f115(a853),f312(a126,x113811)),x113811),f312(a126,x113811))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,4407,10335,10426,2806,2811,2823,2826,2827,2828,2832,2833,2842,2850,2854,2863,2866,2873,2876,2890,2897,2899,2952,2960,2965,2986,3100,4383,3933,3664,3040,3725,11256,3108,3069,10175,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4420,3513,3717,4108,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,10764,11187,11249,4491,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3950,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,10544,11339,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,3268,10531,10561,3299,3721,3661,10218,4484,10169,10525,10528,10973,10991,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,10853,4503,11052,11163,3810,3650,10819,10825,3509,3652,10906,11061,11091,3481,10496,10499,10564,10738,4501,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295])).
% 155.94/155.67 cnf(11388,plain,
% 155.94/155.67 (E(f37(x113881,x113882,x113883,x113884,x113885,x113886,x113887,x113888,x113889,a23),x113882)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11393,plain,
% 155.94/155.67 (E(f37(x113931,x113932,x113933,x113934,x113935,x113936,x113937,x113938,x113939,a23),x113932)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11396,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a1),f312(f114(a1),x113961)),f2(a1)))),
% 155.94/155.67 inference(rename_variables,[],[4491])).
% 155.94/155.67 cnf(11399,plain,
% 155.94/155.67 (E(f37(x113991,x113992,x113993,x113994,x113995,x113996,x113997,x113998,x113999,a23),x113992)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11402,plain,
% 155.94/155.67 (~E(f312(a126,x114021),x114021)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11405,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x114051),x114051))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11407,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),f2(a1)),a92))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,4407,10335,10426,2806,2811,2823,2826,2827,2828,2832,2833,2842,2850,2854,2863,2866,2873,2876,2890,2891,2897,2899,2952,2960,2965,2986,3100,4383,3933,3664,3040,3725,11256,3108,3069,10175,3063,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4420,3513,3717,4108,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,3189,4475,10149,10152,10178,10630,10643,10764,11187,11249,4491,11363,11396,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3950,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,10544,11339,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,10751,4471,10215,10300,10351,10435,10667,10714,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,3268,10531,10561,3308,3299,3721,3661,10218,4484,10169,10525,10528,10973,10991,3226,10708,4031,4483,3729,4462,4465,3182,3183,4464,4467,4498,10140,10143,10397,10446,10451,10853,4503,11052,11163,3810,3650,10819,10825,3509,3652,10906,11061,11091,3481,10496,10499,10564,10738,4501,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386])).
% 155.94/155.67 cnf(11412,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x114121),x114121))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11433,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a1),f312(f114(a1),x114331)),f2(a1)))),
% 155.94/155.67 inference(rename_variables,[],[4491])).
% 155.94/155.67 cnf(11446,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x114461),x114461))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11449,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x114491)),x114491))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(11450,plain,
% 155.94/155.67 (~E(f312(a126,x114501),x114501)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11456,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x114561)),x114561))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(11457,plain,
% 155.94/155.67 (E(f37(x114571,x114572,x114573,x114574,x114575,x114576,x114577,x114578,x114579,a23),x114572)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11464,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),f312(f312(f89(a853),x114641),x114642)),x114641))),
% 155.94/155.67 inference(rename_variables,[],[4500])).
% 155.94/155.67 cnf(11467,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a1),f312(f114(a1),x114671)),f2(a1)))),
% 155.94/155.67 inference(rename_variables,[],[4491])).
% 155.94/155.67 cnf(11470,plain,
% 155.94/155.67 (~E(f312(a126,x114701),x114701)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11483,plain,
% 155.94/155.67 (P22(f312(f312(f314(x114831),x114832),f312(f312(f289(x114831),x114832),x114833)))),
% 155.94/155.67 inference(rename_variables,[],[3522])).
% 155.94/155.67 cnf(11484,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a1),f2(a1)),f312(f88(a1),f312(f114(a1),f312(a126,x114841)))))),
% 155.94/155.67 inference(rename_variables,[],[4501])).
% 155.94/155.67 cnf(11487,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),f312(f312(f21(a853),x114871),x114872)),f312(a126,x114871)))),
% 155.94/155.67 inference(rename_variables,[],[3656])).
% 155.94/155.67 cnf(11490,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f54(a853,x114901,x114902)),x114901))),
% 155.94/155.67 inference(rename_variables,[],[3661])).
% 155.94/155.67 cnf(11496,plain,
% 155.94/155.67 (E(f312(f312(f129(x114961),x114962),f127(x114961)),x114962)),
% 155.94/155.67 inference(rename_variables,[],[3138])).
% 155.94/155.67 cnf(11499,plain,
% 155.94/155.67 (E(f37(x114991,x114992,x114993,x114994,x114995,x114996,x114997,x114998,x114999,a23),x114992)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11502,plain,
% 155.94/155.67 (E(f37(x115021,x115022,x115023,x115024,x115025,x115026,x115027,x115028,x115029,a23),x115022)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11505,plain,
% 155.94/155.67 (E(f37(x115051,x115052,x115053,x115054,x115055,x115056,x115057,x115058,x115059,a23),x115052)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11514,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x115141),x115141))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11515,plain,
% 155.94/155.67 (E(f37(x115151,x115152,x115153,x115154,x115155,x115156,x115157,x115158,x115159,a23),x115152)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11518,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f54(a853,x115181,x115182)),x115181))),
% 155.94/155.67 inference(rename_variables,[],[3661])).
% 155.94/155.67 cnf(11519,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f2(a853)),x115191))),
% 155.94/155.67 inference(rename_variables,[],[3226])).
% 155.94/155.67 cnf(11534,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x115341),x115341))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11537,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x115371),x115371))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11540,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x115401),x115401))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11543,plain,
% 155.94/155.67 (P22(f312(f312(f314(x115431),f312(x115432,x115433)),f312(f290(x115434,x115431,x115432),f235(f861(x115434,a846)))))),
% 155.94/155.67 inference(rename_variables,[],[3810])).
% 155.94/155.67 cnf(11544,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),f312(f312(f89(a853),x115441),x115442)),x115442))),
% 155.94/155.67 inference(rename_variables,[],[4499])).
% 155.94/155.67 cnf(11547,plain,
% 155.94/155.67 (P22(f312(f312(f314(x115471),f312(x115472,x115473)),f312(f290(x115474,x115471,x115472),f235(f861(x115474,a846)))))),
% 155.94/155.67 inference(rename_variables,[],[3810])).
% 155.94/155.67 cnf(11548,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x115481)),x115481))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(11552,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),f312(f47(a853,x115521),f37(x115522,f2(a853),x115523,x115524,x115525,x115526,x115527,x115528,x115529,a23))),f2(a853)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,4407,10335,10426,2806,2811,2823,2826,2827,2828,2832,2833,2842,2850,2854,2856,2863,2865,2866,2873,2874,2876,2890,2891,2897,2899,2952,2958,2960,2965,2986,3100,4383,3247,3933,3138,11496,3664,3040,3725,11256,3108,3069,10175,3063,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,11487,3189,4475,10149,10152,10178,10630,10643,10764,11187,11249,4491,11363,11396,11433,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3950,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,10751,11405,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,3268,10531,10561,3308,3299,3721,3661,10218,11490,4484,10169,10525,10528,10973,10991,11449,11456,3226,10708,10779,4031,4483,3729,4462,4465,3182,3183,4464,4467,3522,4498,10140,10143,10397,10446,10451,10853,4503,11052,11163,3810,11194,11543,3650,10819,10825,3509,3652,10906,11061,11091,3481,10496,10499,10564,10738,4501,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775])).
% 155.94/155.67 cnf(11553,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x115531),x115531))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(11554,plain,
% 155.94/155.67 (E(f37(x115541,x115542,x115543,x115544,x115545,x115546,x115547,x115548,x115549,a23),x115542)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11557,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),f312(f312(f89(a853),x115571),x115572)),x115571))),
% 155.94/155.67 inference(rename_variables,[],[4500])).
% 155.94/155.67 cnf(11560,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x115601),x115601))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11563,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x115631),x115631))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(11569,plain,
% 155.94/155.67 (P22(f312(f312(f314(x115691),x115692),f312(f312(f289(x115691),x115692),x115693)))),
% 155.94/155.67 inference(rename_variables,[],[3522])).
% 155.94/155.67 cnf(11572,plain,
% 155.94/155.67 (~P22(f312(f71(x115721,x115722,f189(f861(x115721,a846))),x115723))),
% 155.94/155.67 inference(rename_variables,[],[4498])).
% 155.94/155.67 cnf(11575,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x115751),x115751))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(11588,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x115881),x115882),f189(f861(x115881,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11591,plain,
% 155.94/155.67 (E(f312(f312(f16(x115911,x115912),x115913),x115914),x115913)),
% 155.94/155.67 inference(rename_variables,[],[3194])).
% 155.94/155.67 cnf(11594,plain,
% 155.94/155.67 (E(f312(f312(f16(x115941,x115942),x115943),x115944),x115943)),
% 155.94/155.67 inference(rename_variables,[],[3194])).
% 155.94/155.67 cnf(11603,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f312(f47(a853,x116031),x116032)),x116031))),
% 155.94/155.67 inference(rename_variables,[],[3581])).
% 155.94/155.67 cnf(11604,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),f2(a853)),f312(a126,x116041)))),
% 155.94/155.67 inference(rename_variables,[],[3286])).
% 155.94/155.67 cnf(11607,plain,
% 155.94/155.67 (P22(f312(f312(f314(x116071),f312(x116072,x116073)),f312(f290(x116074,x116071,x116072),f235(f861(x116074,a846)))))),
% 155.94/155.67 inference(rename_variables,[],[3810])).
% 155.94/155.67 cnf(11610,plain,
% 155.94/155.67 (P22(f312(f70(x116101),f312(f168(x116101),x116102)))),
% 155.94/155.67 inference(rename_variables,[],[3246])).
% 155.94/155.67 cnf(11613,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),f312(f88(a1),f312(f114(a1),x116131))),f312(f114(a1),x116132)))),
% 155.94/155.67 inference(rename_variables,[],[3683])).
% 155.94/155.67 cnf(11616,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x116161),x116162),f189(f861(x116161,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11628,plain,
% 155.94/155.67 (~P22(f312(f312(f314(a853),x116281),f312(f279(a853),f2(a853))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4433,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,4407,10335,10426,2806,2811,2823,2826,2827,2828,2832,2833,2842,2850,2854,2856,2863,2865,2866,2873,2874,2876,2890,2891,2893,2897,2899,2952,2958,2960,2965,2986,3100,4383,3247,3933,3138,11496,3664,3040,3725,11256,3108,3069,10175,3063,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,11487,3189,3286,4475,10149,10152,10178,10630,10643,10764,11187,11249,4491,11363,11396,11433,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,3950,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,10751,11405,3282,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,3268,10531,10561,3308,3299,3721,3661,10218,11490,4484,10169,10525,10528,10973,10991,11449,11456,3226,10708,10779,3683,4031,4483,3729,4462,4465,3182,3183,4464,4467,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,3509,3652,10906,11061,11091,3581,3481,10496,10499,10564,10738,4501,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052])).
% 155.94/155.67 cnf(11635,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x116351),x116351))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(11636,plain,
% 155.94/155.67 (E(f37(x116361,x116362,x116363,x116364,x116365,x116366,x116367,x116368,x116369,a23),x116362)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11639,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x116391),x116391))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11652,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x116521),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(11655,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x116551),x116551))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11660,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x116601),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(11665,plain,
% 155.94/155.67 (P22(f312(f235(f861(x116651,a846)),x116652))),
% 155.94/155.67 inference(rename_variables,[],[3268])).
% 155.94/155.67 cnf(11670,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f2(a853)),x116701))),
% 155.94/155.67 inference(rename_variables,[],[3226])).
% 155.94/155.67 cnf(11671,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x116711)),x116711))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(11674,plain,
% 155.94/155.67 (~P22(f312(f71(x116741,x116742,f189(f861(x116741,a846))),x116743))),
% 155.94/155.67 inference(rename_variables,[],[4498])).
% 155.94/155.67 cnf(11691,plain,
% 155.94/155.67 (P22(f312(f312(f228(a1),f312(f88(a1),f87(a1))),f2(a1)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4433,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,4407,10335,10426,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2890,2891,2893,2897,2899,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,3664,3040,3725,11256,3108,3069,10175,3063,3048,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,11487,3189,3286,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,3950,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,10751,11405,11446,11639,3282,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,3268,10531,10561,11115,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,3226,10708,10779,11519,3683,4031,4483,3729,4462,4465,3182,3183,4464,4467,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,3509,3652,10906,11061,11091,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354])).
% 155.94/155.67 cnf(11696,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x116961),x116961))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11699,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x116991),x116991))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11702,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x117021),x117021))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11705,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x117051),x117051))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11708,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x117081)),x117081))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(11711,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x117111)),x117111))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(11714,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x117141)),x117141))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(11717,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x117171)),x117171))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(11735,plain,
% 155.94/155.67 (E(f312(f190(f854(x117351)),f312(f164(x117351),x117352)),f312(f190(f854(x117351)),x117352))),
% 155.94/155.67 inference(rename_variables,[],[3218])).
% 155.94/155.67 cnf(11738,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x117381),x117381))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(11744,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x117441),x117441))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(11745,plain,
% 155.94/155.67 (~E(f312(a126,x117451),x117451)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11747,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x117471),f312(f84(a1),x117471)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4433,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,4407,10335,10426,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2890,2891,2893,2897,2899,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,3259,3664,3040,3725,11256,3108,3069,10175,3063,3048,3218,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3274,10256,10372,10443,10487,10490,10537,10619,10868,3656,11487,3189,3286,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,3950,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,3205,10606,10649,10652,10685,10711,10748,10786,3206,10348,10549,10625,10751,11405,11446,11639,11655,3282,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,3268,10531,10561,11115,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,3226,10708,10779,11519,3683,4031,4483,3729,4462,4465,3182,3183,4464,4467,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,3509,3652,10906,11061,11091,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448])).
% 155.94/155.67 cnf(11748,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x117481),x117481))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11759,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x117591),x117591))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11762,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(f860(f854(x117621),f854(x117621)),a846)),f154(x117621,x117622)),f287(f854(x117621),f153(x117621,x117622))))),
% 155.94/155.67 inference(rename_variables,[],[3909])).
% 155.94/155.67 cnf(11769,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x117691),f312(a126,x117691)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(11772,plain,
% 155.94/155.67 (P22(f312(f312(f314(f861(x117721,a846)),x117722),f312(f288(x117721),x117722)))),
% 155.94/155.67 inference(rename_variables,[],[3572])).
% 155.94/155.67 cnf(11773,plain,
% 155.94/155.67 (~E(f312(a126,x117731),x117731)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11780,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x117801),x117801))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11785,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x117851),x117851))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11792,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x117921),x117921))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11793,plain,
% 155.94/155.67 (~E(f312(a126,x117931),x117931)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11798,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x117981,a846)),x117982),f312(f312(f289(x117981),x117983),x117982)))),
% 155.94/155.67 inference(rename_variables,[],[3650])).
% 155.94/155.67 cnf(11801,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x118011),x118011))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11812,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x118121),x118121))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11813,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x118131),f312(a126,x118131)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(11816,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x118161),x118161))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(11819,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x118191),x118191))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(11822,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x118221),x118221))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(11825,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x118251),x118251))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(11827,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),f312(a118,f2(a1))),f312(a126,x118271)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4433,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,4407,10335,10426,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2890,2891,2893,2897,2899,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,3259,3664,3040,3725,11256,3108,3069,10175,3063,3048,3218,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,3656,11487,3189,3286,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,3950,3909,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,3282,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,3268,10531,10561,11115,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,3226,10708,10779,11519,3683,4031,4483,3729,4462,4465,3182,3183,4464,4467,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,10842,3509,3652,10906,11061,11091,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691])).
% 155.94/155.67 cnf(11828,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x118281),x118281))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11831,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x118311),x118311))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11840,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x118401),x118401))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11841,plain,
% 155.94/155.67 (~E(f312(a126,x118411),x118411)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11846,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x118461),x118461))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11861,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x118611),x118611))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11865,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a1),f2(a1)),f312(f47(a1,f2(a1)),f87(a1))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4433,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,4407,10335,10426,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2890,2891,2893,2897,2899,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,3147,3259,3664,3974,3040,3725,11256,3108,3069,10175,3063,3048,3218,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,3656,11487,3189,3286,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,3950,3909,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,3268,10531,10561,11115,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,3683,4031,4483,3729,4462,4465,3182,3183,4464,4467,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,10842,3509,3652,10906,11061,11091,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826])).
% 155.94/155.67 cnf(11866,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x118661),x118661))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(11871,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f2(a853)),x118711))),
% 155.94/155.67 inference(rename_variables,[],[3226])).
% 155.94/155.67 cnf(11890,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x118901),f312(a126,x118901)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(11893,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x118931),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(11896,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x118961),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(11899,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x118991),x118992),f189(f861(x118991,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11902,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x119021),x119022),f189(f861(x119021,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11905,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x119051),x119051))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11907,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x119071),f312(f312(f115(a853),x119071),x119072)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4433,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,4407,10335,10426,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2890,2891,2893,2897,2899,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,3147,3259,3664,3974,3040,3725,11256,3108,3069,10175,3063,3048,3218,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,3656,11487,3189,3286,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,3950,3909,3853,10700,3904,3572,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,3268,10531,10561,11115,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,10842,3509,3652,10906,11061,11091,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922])).
% 155.94/155.67 cnf(11908,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x119081),x119081))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11911,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x119111),x119111))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11914,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x119141),x119141))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11921,plain,
% 155.94/155.67 (P22(f312(f312(f314(f861(x119211,a846)),x119212),f312(f288(x119211),x119212)))),
% 155.94/155.67 inference(rename_variables,[],[3572])).
% 155.94/155.67 cnf(11933,plain,
% 155.94/155.67 (~P22(f312(f312(f314(a853),f312(a126,f312(f138(a853,a853,f89(a853),f2(a853)),x119331))),f312(f168(a853),f312(f132(a853,x119332),x119331))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,3769,4433,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,4407,10335,10426,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2890,2891,2893,2897,2899,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,3147,3259,3664,3974,3040,3725,11256,3108,3069,10175,3063,3048,3218,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,3656,11487,3189,3286,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,3950,3909,3853,10700,3904,3572,11772,3910,3588,10887,10956,11037,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,3268,10531,10561,11115,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,10842,3509,3652,10906,11061,11091,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021])).
% 155.94/155.67 cnf(11934,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x119341,a846)),f312(f168(x119341),f312(f132(x119341,x119342),x119343))),f312(f168(x119341),x119343)))),
% 155.94/155.67 inference(rename_variables,[],[3853])).
% 155.94/155.67 cnf(11939,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x119391),x119392),f189(f861(x119391,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11944,plain,
% 155.94/155.67 (E(f312(f190(f854(x119441)),f312(f164(x119441),x119442)),f312(f190(f854(x119441)),x119442))),
% 155.94/155.67 inference(rename_variables,[],[3218])).
% 155.94/155.67 cnf(11951,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x119511),f312(a126,x119511)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(11954,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x119541,a846)),x119542),f235(f861(x119541,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(11955,plain,
% 155.94/155.67 (~E(f312(a126,x119551),x119551)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11958,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x119581,a846)),f312(f168(x119581),f312(f132(x119581,x119582),x119583))),f312(f168(x119581),x119583)))),
% 155.94/155.67 inference(rename_variables,[],[3853])).
% 155.94/155.67 cnf(11970,plain,
% 155.94/155.67 (E(f37(x119701,x119702,x119703,x119704,x119705,x119706,x119707,x119708,x119709,a23),x119702)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(11973,plain,
% 155.94/155.67 (~E(f312(a126,x119731),x119731)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(11977,plain,
% 155.94/155.67 (P22(f312(f70(x119771),f189(f861(x119771,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3282])).
% 155.94/155.67 cnf(11978,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x119781),x119782),f189(f861(x119781,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(11983,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x119831),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(11984,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x119841),x119841))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(11989,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x119891,a846)),f312(f168(x119891),f166(x119891,x119892,x119893))),f312(f168(x119891),x119893)))),
% 155.94/155.67 inference(rename_variables,[],[3904])).
% 155.94/155.67 cnf(11992,plain,
% 155.94/155.67 (P19(x119921,x119921,f5(x119921),x119922)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(11997,plain,
% 155.94/155.67 (P22(f312(f312(f314(f861(x119971,a846)),x119972),f312(f288(x119971),x119972)))),
% 155.94/155.67 inference(rename_variables,[],[3572])).
% 155.94/155.67 cnf(12008,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x120081),x120081))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(12011,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x120111),x120112),f189(f861(x120111,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12014,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x120141,a846)),x120142),f312(f312(f289(x120141),x120143),x120142)))),
% 155.94/155.67 inference(rename_variables,[],[3650])).
% 155.94/155.67 cnf(12015,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x120151,a846)),x120152),f235(f861(x120151,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(12022,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x120221),f312(a126,x120221)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12025,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x120251),f312(a126,x120251)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12028,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x120281),x120281))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12031,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x120311),x120311))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12034,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x120341),x120341))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12037,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x120371),x120371))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12040,plain,
% 155.94/155.67 (~E(f312(a126,x120401),x120401)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(12044,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a1),f312(f312(f21(a1),a92),a111)),f2(a1)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,3769,4433,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,4407,10335,10426,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2890,2891,2893,2894,2897,2899,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,3147,3259,3664,3974,3040,3725,11256,3108,3069,10175,3063,3048,3218,11735,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,11610,3950,3909,3853,10700,11934,3904,10890,3572,11772,11921,3910,3588,10887,10956,11037,11097,11954,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,11977,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,3268,10531,10561,11115,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,10842,11798,3509,3652,10906,11061,11091,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524])).
% 155.94/155.67 cnf(12047,plain,
% 155.94/155.67 (P22(f312(f312(f314(f861(x120471,a846)),x120472),f312(f288(x120471),x120472)))),
% 155.94/155.67 inference(rename_variables,[],[3572])).
% 155.94/155.67 cnf(12051,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a1),f312(f312(f89(a1),a92),a92)),f2(a1)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,3769,4433,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,4407,10335,10426,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2890,2891,2893,2894,2897,2899,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,3147,3259,3664,3974,3040,3725,11256,3108,3069,10175,3063,3048,3218,11735,3264,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,11178,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,11610,3950,3909,3853,10700,11934,3904,10890,3572,11772,11921,11997,3910,3588,10887,10956,11037,11097,11954,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,11977,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,3268,10531,10561,11115,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,10842,11798,3509,3652,10906,11061,11091,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558])).
% 155.94/155.67 cnf(12056,plain,
% 155.94/155.67 (~E(f312(a126,x120561),x120561)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(12057,plain,
% 155.94/155.67 (E(f312(f290(x120571,x120571,f5(x120571)),x120572),x120572)),
% 155.94/155.67 inference(rename_variables,[],[3264])).
% 155.94/155.67 cnf(12060,plain,
% 155.94/155.67 (P37(x120601,x120602,f127(x120601),f127(x120601))),
% 155.94/155.67 inference(rename_variables,[],[3456])).
% 155.94/155.67 cnf(12063,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x120631,a846)),f312(f168(x120631),f166(x120631,x120632,x120633))),f312(f168(x120631),x120633)))),
% 155.94/155.67 inference(rename_variables,[],[3904])).
% 155.94/155.67 cnf(12064,plain,
% 155.94/155.67 (P22(f312(f70(x120641),f312(f168(x120641),x120642)))),
% 155.94/155.67 inference(rename_variables,[],[3246])).
% 155.94/155.67 cnf(12071,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x120711),x120711))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(12074,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x120741),x120741))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(12079,plain,
% 155.94/155.67 (E(f312(f190(f854(x120791)),f312(f164(x120791),x120792)),f312(f190(f854(x120791)),x120792))),
% 155.94/155.67 inference(rename_variables,[],[3218])).
% 155.94/155.67 cnf(12082,plain,
% 155.94/155.67 (~P22(f312(f312(f189(f861(x120821,f861(x120822,a846))),x120823),x120824))),
% 155.94/155.67 inference(rename_variables,[],[4502])).
% 155.94/155.67 cnf(12088,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),f2(a1)),f336(x120881,f189(f861(x120882,f861(x120883,a846))),f87(a1))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,3456,3769,4433,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,4407,10335,10426,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2890,2891,2893,2894,2897,2899,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,3147,3259,3664,3974,3040,3725,11256,3108,3069,10175,3063,3048,3053,3218,11735,11944,3264,10703,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,11178,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,11610,3950,3909,3853,10700,11934,3904,10890,11989,3572,11772,11921,11997,3910,3588,10887,10956,11037,11097,11954,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,11977,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,3364,10504,10759,10803,11086,11158,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,3268,10531,10561,11115,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,10842,11798,3509,3652,10906,11061,11091,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,11321,12082,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2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% 155.94/155.67 cnf(12089,plain,
% 155.94/155.67 (~P22(f312(f312(f189(f861(x120891,f861(x120892,a846))),x120893),x120894))),
% 155.94/155.67 inference(rename_variables,[],[4502])).
% 155.94/155.67 cnf(12092,plain,
% 155.94/155.67 (P33(a853,f312(f165(a853),f312(f312(f150(f854(x120921),a853),f190(f854(x120921))),f175(x120921,x120922))))),
% 155.94/155.67 inference(rename_variables,[],[3763])).
% 155.94/155.67 cnf(12095,plain,
% 155.94/155.67 (P19(x120951,x120951,f5(x120951),x120952)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12098,plain,
% 155.94/155.67 (P22(f312(f312(f314(f854(x120981)),f127(x120981)),f157(x120981,x120982)))),
% 155.94/155.67 inference(rename_variables,[],[3411])).
% 155.94/155.67 cnf(12103,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x121031),x121031))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12104,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f2(a853)),x121041))),
% 155.94/155.67 inference(rename_variables,[],[3226])).
% 155.94/155.67 cnf(12107,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(f860(f854(x121071),f854(x121071)),a846)),f154(x121071,x121072)),f287(f854(x121071),f153(x121071,x121072))))),
% 155.94/155.67 inference(rename_variables,[],[3909])).
% 155.94/155.67 cnf(12112,plain,
% 155.94/155.67 (P22(f312(f312(f228(f861(x121121,a846)),f189(f861(x121121,a846))),f235(f861(x121121,a846))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,11992,3456,3769,4433,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,4407,10335,10426,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2890,2891,2893,2894,2897,2899,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,3147,3259,3664,3974,3040,3725,11256,3108,3069,10175,3063,3048,3053,3084,3218,11735,11944,3264,10703,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,11178,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,3571,4269,4270,4420,3513,3717,4108,3763,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,11610,3950,3909,11762,12107,3853,10700,11934,3904,10890,11989,3572,11772,11921,11997,12047,3910,3588,10887,10956,11037,11097,11954,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,11977,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,3364,10504,10759,10803,11086,11158,11324,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,3268,10531,10561,11115,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,11871,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,10842,11798,3509,3652,10906,11061,11091,11102,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,11321,12082,4092,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,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% 155.94/155.67 cnf(12113,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x121131,a846)),f189(f861(x121131,a846))),x121132))),
% 155.94/155.67 inference(rename_variables,[],[3652])).
% 155.94/155.67 cnf(12116,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x121161,a846)),f312(f290(x121162,x121161,x121163),f312(f291(x121162,x121161,x121163),x121164))),x121164))),
% 155.94/155.67 inference(rename_variables,[],[4092])).
% 155.94/155.67 cnf(12119,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x121191,a846)),f312(f168(x121191),f166(x121191,x121192,x121193))),f312(f168(x121191),x121193)))),
% 155.94/155.67 inference(rename_variables,[],[3904])).
% 155.94/155.67 cnf(12120,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x121201,a846)),f312(f168(x121201),f312(f132(x121201,x121202),x121203))),f312(f168(x121201),x121203)))),
% 155.94/155.67 inference(rename_variables,[],[3853])).
% 155.94/155.67 cnf(12123,plain,
% 155.94/155.67 (P19(x121231,f857(x121231),f219(x121231),x121232)),
% 155.94/155.67 inference(rename_variables,[],[3457])).
% 155.94/155.67 cnf(12128,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x121281,a846)),f312(f290(x121282,x121281,x121283),f312(f291(x121282,x121281,x121283),x121284))),x121284))),
% 155.94/155.67 inference(rename_variables,[],[4092])).
% 155.94/155.67 cnf(12131,plain,
% 155.94/155.67 (P22(f312(f70(f857(x121311)),f312(f290(x121312,f857(x121311),f312(f173(x121312,x121311),x121313)),f235(f861(x121312,a846)))))),
% 155.94/155.67 inference(rename_variables,[],[3916])).
% 155.94/155.67 cnf(12136,plain,
% 155.94/155.67 (~P22(f312(f312(f189(f861(x121361,f861(x121362,a846))),x121363),x121364))),
% 155.94/155.67 inference(rename_variables,[],[4502])).
% 155.94/155.67 cnf(12139,plain,
% 155.94/155.67 (P22(f312(f312(f314(f854(x121391)),f127(x121391)),f157(x121391,x121392)))),
% 155.94/155.67 inference(rename_variables,[],[3411])).
% 155.94/155.67 cnf(12142,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x121421),f854(x121421))),f312(f312(f239(f854(x121421),f854(x121421)),x121422),f127(x121421))),f141(x121421,x121423)))),
% 155.94/155.67 inference(rename_variables,[],[4504])).
% 155.94/155.67 cnf(12145,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x121451),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12147,plain,
% 155.94/155.67 (~P22(f312(f70(x121471),f235(f861(x121471,a846))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,11992,3456,3457,3769,3175,4433,3078,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,4407,10335,10426,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2890,2891,2893,2894,2897,2899,2943,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,3147,3259,3664,3974,3040,3725,11256,3108,3069,10175,3063,3048,3053,3084,3218,11735,11944,3264,10703,3137,3157,10379,3312,4495,3841,4423,10172,10332,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,3843,10884,11013,11064,4504,10806,11018,11123,11142,11172,11178,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,12098,12139,3571,4269,4270,4420,3513,3717,4108,3763,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3403,4492,3981,11137,3531,3246,11610,3950,3909,11762,12107,3853,10700,11934,11958,3904,10890,11989,12063,3572,11772,11921,11997,12047,3910,3588,10887,10956,11037,11097,11954,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,11977,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,3364,10504,10759,10803,11086,11158,11324,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,3268,10531,10561,11115,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,11871,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,3916,3810,11194,11543,11547,3650,10819,10825,10842,11798,3509,11055,3652,10906,11061,11091,11102,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,11321,12082,12089,4092,10691,12116,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052])).
% 155.94/155.67 cnf(12148,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x121481,a846)),x121482),x121482))),
% 155.94/155.67 inference(rename_variables,[],[3509])).
% 155.94/155.67 cnf(12151,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x121511),x121512),f189(f861(x121511,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12154,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x121541,a846)),f312(f290(x121542,x121541,x121543),f312(f291(x121542,x121541,x121543),x121544))),x121544))),
% 155.94/155.67 inference(rename_variables,[],[4092])).
% 155.94/155.67 cnf(12155,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x121551,a846)),x121552),x121552))),
% 155.94/155.67 inference(rename_variables,[],[3509])).
% 155.94/155.67 cnf(12160,plain,
% 155.94/155.67 (E(f37(x121601,x121602,x121603,x121604,x121605,x121606,x121607,x121608,x121609,a23),x121602)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12163,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x121631,a846)),f312(f168(x121631),f166(x121631,x121632,x121633))),f312(f168(x121631),x121633)))),
% 155.94/155.67 inference(rename_variables,[],[3904])).
% 155.94/155.67 cnf(12164,plain,
% 155.94/155.67 (P22(f312(f70(x121641),f312(f168(x121641),x121642)))),
% 155.94/155.67 inference(rename_variables,[],[3246])).
% 155.94/155.67 cnf(12167,plain,
% 155.94/155.67 (P22(f312(f312(f195(a23),x121671),x121671))),
% 155.94/155.67 inference(rename_variables,[],[3204])).
% 155.94/155.67 cnf(12170,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x121701),x121701))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(12173,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x121731),x121731))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(12184,plain,
% 155.94/155.67 (P19(x121841,x121841,f5(x121841),x121842)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12191,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x121911),x121912),f189(f861(x121911,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12194,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(x121941,x121941)),f312(f312(f239(x121941,x121941),x121942),x121942)),f287(x121941,x121943)))),
% 155.94/155.67 inference(rename_variables,[],[3843])).
% 155.94/155.67 cnf(12197,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x121971),x121972),f189(f861(x121971,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12200,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(x122001,x122001)),f312(f312(f239(x122001,x122001),x122002),x122002)),f287(x122001,x122003)))),
% 155.94/155.67 inference(rename_variables,[],[3843])).
% 155.94/155.67 cnf(12210,plain,
% 155.94/155.67 (~E(f312(f312(f147(x122101),x122102),x122103),x122103)),
% 155.94/155.67 inference(rename_variables,[],[4423])).
% 155.94/155.67 cnf(12213,plain,
% 155.94/155.67 (P22(f312(f312(f314(x122131),x122132),f235(f861(x122131,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3364])).
% 155.94/155.67 cnf(12214,plain,
% 155.94/155.67 (~E(f312(a126,x122141),x122141)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(12217,plain,
% 155.94/155.67 (P22(f312(f312(f314(f854(x122171)),f127(x122171)),f157(x122171,x122172)))),
% 155.94/155.67 inference(rename_variables,[],[3411])).
% 155.94/155.67 cnf(12218,plain,
% 155.94/155.67 (~E(f312(f312(f147(x122181),x122182),x122183),f127(x122181))),
% 155.94/155.67 inference(rename_variables,[],[4432])).
% 155.94/155.67 cnf(12221,plain,
% 155.94/155.67 (P22(f312(f312(f314(x122211),f312(x122212,x122213)),f312(f290(x122214,x122211,x122212),f235(f861(x122214,a846)))))),
% 155.94/155.67 inference(rename_variables,[],[3810])).
% 155.94/155.67 cnf(12222,plain,
% 155.94/155.67 (P19(x122221,x122221,f5(x122221),x122222)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12225,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x122251,a846)),f189(f861(x122251,a846))),x122252))),
% 155.94/155.67 inference(rename_variables,[],[3652])).
% 155.94/155.67 cnf(12226,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x122261,a846)),x122262),x122262))),
% 155.94/155.67 inference(rename_variables,[],[3509])).
% 155.94/155.67 cnf(12229,plain,
% 155.94/155.67 (P22(f312(f312(f314(x122291),f312(x122292,x122293)),f312(f290(x122294,x122291,x122292),f235(f861(x122294,a846)))))),
% 155.94/155.67 inference(rename_variables,[],[3810])).
% 155.94/155.67 cnf(12230,plain,
% 155.94/155.67 (P19(x122301,x122301,f5(x122301),x122302)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12233,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(f854(x122331),f854(x122331))),f312(f312(f239(f854(x122331),f854(x122331)),f127(x122331)),f127(x122331))),f154(x122331,x122332)))),
% 155.94/155.67 inference(rename_variables,[],[3987])).
% 155.94/155.67 cnf(12236,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x122361),x122361))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(12237,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x122371),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12243,plain,
% 155.94/155.67 (P19(x122431,x122431,f5(x122431),x122432)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12246,plain,
% 155.94/155.67 (E(f312(f312(f129(x122461),x122462),f127(x122461)),x122462)),
% 155.94/155.67 inference(rename_variables,[],[3138])).
% 155.94/155.67 cnf(12247,plain,
% 155.94/155.67 (~E(f312(f312(f147(x122471),x122472),x122473),x122473)),
% 155.94/155.67 inference(rename_variables,[],[4423])).
% 155.94/155.67 cnf(12250,plain,
% 155.94/155.67 (E(f312(f312(f129(x122501),x122502),f127(x122501)),x122502)),
% 155.94/155.67 inference(rename_variables,[],[3138])).
% 155.94/155.67 cnf(12251,plain,
% 155.94/155.67 (~E(f312(f312(f147(x122511),x122512),x122513),x122513)),
% 155.94/155.67 inference(rename_variables,[],[4423])).
% 155.94/155.67 cnf(12254,plain,
% 155.94/155.67 (E(f312(f312(f129(x122541),x122542),f127(x122541)),x122542)),
% 155.94/155.67 inference(rename_variables,[],[3138])).
% 155.94/155.67 cnf(12261,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x122611,a846)),x122612),f235(f861(x122611,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(12265,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x122651),x122651))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(12266,plain,
% 155.94/155.67 (~E(f312(a126,x122661),x122661)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(12269,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x122691,a846)),f189(f861(x122691,a846))),x122692))),
% 155.94/155.67 inference(rename_variables,[],[3652])).
% 155.94/155.67 cnf(12272,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x122721),x122721))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12275,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x122751,a846)),x122752),x122752))),
% 155.94/155.67 inference(rename_variables,[],[3509])).
% 155.94/155.67 cnf(12280,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x122801,a846)),x122802),f312(f312(f289(x122801),x122803),x122802)))),
% 155.94/155.67 inference(rename_variables,[],[3650])).
% 155.94/155.67 cnf(12283,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x122831,a846)),x122832),x122832))),
% 155.94/155.67 inference(rename_variables,[],[3509])).
% 155.94/155.67 cnf(12284,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x122841),x122842),f189(f861(x122841,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12287,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x122871),x122872),f189(f861(x122871,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12292,plain,
% 155.94/155.67 (P19(x122921,x122921,f5(x122921),x122922)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12295,plain,
% 155.94/155.67 (E(f312(f190(f854(x122951)),f312(f164(x122951),x122952)),f312(f190(f854(x122951)),x122952))),
% 155.94/155.67 inference(rename_variables,[],[3218])).
% 155.94/155.67 cnf(12298,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x122981),x122981))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(12299,plain,
% 155.94/155.67 (P22(f312(f235(f861(x122991,a846)),x122992))),
% 155.94/155.67 inference(rename_variables,[],[3268])).
% 155.94/155.67 cnf(12302,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x123021),x123022),f189(f861(x123021,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12305,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x123051,a846)),x123052),f312(f312(f289(x123051),x123053),x123052)))),
% 155.94/155.67 inference(rename_variables,[],[3650])).
% 155.94/155.67 cnf(12308,plain,
% 155.94/155.67 (P22(f312(f312(f314(x123081),f312(x123082,x123083)),f312(f290(x123084,x123081,x123082),f235(f861(x123084,a846)))))),
% 155.94/155.67 inference(rename_variables,[],[3810])).
% 155.94/155.67 cnf(12309,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(x123091,x123091)),f312(f312(f239(x123091,x123091),x123092),x123092)),f287(x123091,x123093)))),
% 155.94/155.67 inference(rename_variables,[],[3843])).
% 155.94/155.67 cnf(12312,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(x123121,x123121)),f312(f312(f239(x123121,x123121),x123122),x123122)),f287(x123121,x123123)))),
% 155.94/155.67 inference(rename_variables,[],[3843])).
% 155.94/155.67 cnf(12315,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x123151),x123151))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12316,plain,
% 155.94/155.67 (P22(f312(f235(f861(x123161,a846)),x123162))),
% 155.94/155.67 inference(rename_variables,[],[3268])).
% 155.94/155.67 cnf(12319,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x123191,a846)),f189(f861(x123191,a846))),x123192))),
% 155.94/155.67 inference(rename_variables,[],[3652])).
% 155.94/155.67 cnf(12322,plain,
% 155.94/155.67 (P22(f312(f70(x123221),f312(f168(x123221),x123222)))),
% 155.94/155.67 inference(rename_variables,[],[3246])).
% 155.94/155.67 cnf(12329,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(x123291,x123291)),f312(f312(f239(x123291,x123291),x123292),x123292)),f312(f312(f267(x123291,x123291,x123291),f287(x123291,x123293)),f287(x123291,f287(x123291,x123293)))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,11992,12095,12184,12222,12230,12243,3456,3457,3769,3175,4433,3078,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,4407,10335,10426,3263,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2943,2952,2958,2960,2961,2965,2986,3100,4383,3247,3933,3138,11496,12246,12250,12254,3147,3259,3664,3974,3040,4403,3725,11256,3108,3069,10175,3063,3048,3053,3084,3218,11735,11944,12079,3264,10703,12057,3136,3137,3157,10379,3312,4495,3841,4423,10172,10332,11311,12210,12247,4432,12218,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,12233,3843,10884,11013,11064,12194,12200,12309,12312,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,4420,11237,3513,3717,4108,3763,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3597,3403,4492,3981,11137,3531,3246,11610,12064,12164,3950,3909,11762,12107,3853,10700,11934,11958,3904,10890,11989,12063,12119,12163,3572,11772,11921,11997,12047,3910,3588,10887,10956,11037,11097,11954,12015,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,11977,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,3364,10504,10759,10803,11086,11158,11324,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,3268,10531,10561,11115,11665,12299,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,11871,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,3810,11194,11543,11547,11607,12221,12229,3650,10819,10825,10842,11798,12014,12280,3509,11055,12148,12155,12226,12275,3652,10906,11061,11091,11102,12113,12225,12269,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,11321,12082,12089,4092,10691,12116,12128,3992,3682,4499,10191,10194,10519,10522,11360,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322])).
% 155.94/155.67 cnf(12332,plain,
% 155.94/155.67 (~P22(f312(f312(f189(f861(x123321,f861(x123322,a846))),x123323),x123324))),
% 155.94/155.67 inference(rename_variables,[],[4502])).
% 155.94/155.67 cnf(12335,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x123351,a846)),x123352),f235(f861(x123351,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(12338,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(x123381,x123381)),f312(f312(f239(x123381,x123381),x123382),x123382)),f287(x123381,x123383)))),
% 155.94/155.67 inference(rename_variables,[],[3843])).
% 155.94/155.67 cnf(12341,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),f312(f312(f89(a853),x123411),x123412)),x123412))),
% 155.94/155.67 inference(rename_variables,[],[4499])).
% 155.94/155.67 cnf(12342,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x123421),f312(a126,x123421)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12345,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x123451,a846)),f312(f168(x123451),f312(f132(x123451,x123452),x123453))),f312(f168(x123451),x123453)))),
% 155.94/155.67 inference(rename_variables,[],[3853])).
% 155.94/155.67 cnf(12348,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x123481,a846)),x123482),f235(f861(x123481,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(12351,plain,
% 155.94/155.67 (E(f37(x123511,x123512,x123513,x123514,x123515,x123516,x123517,x123518,x123519,a23),x123512)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12358,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(f860(f854(x123581),f854(x123581)),f860(f854(x123581),f854(x123581)))),f420(f287(f860(f854(x123581),f854(x123581)),x123582),f141(x123581,x123583),f860(f854(x123581),f854(x123581)))),f287(f860(f854(x123581),f854(x123581)),x123582)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,11992,12095,12184,12222,12230,12243,3456,3457,3769,3175,4433,3078,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,4407,10335,10426,3263,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2943,2952,2958,2960,2961,2965,2986,3100,4383,3546,3247,3933,3138,11496,12246,12250,12254,3147,3259,3664,3974,3040,4403,3725,11256,3108,3069,10175,3063,3048,3053,3084,3218,11735,11944,12079,3264,10703,12057,3136,3137,3157,10379,3312,4495,3841,4423,10172,10332,11311,12210,12247,4432,12218,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,12233,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,4420,11237,3513,3717,4108,3763,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3597,4123,3403,4492,3981,11137,3531,3246,11610,12064,12164,3950,3909,11762,12107,3853,10700,11934,11958,12120,3904,10890,11989,12063,12119,12163,3572,11772,11921,11997,12047,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,11977,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,3364,10504,10759,10803,11086,11158,11324,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,3268,10531,10561,11115,11665,12299,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,11871,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,3810,11194,11543,11547,11607,12221,12229,3650,10819,10825,10842,11798,12014,12280,3509,11055,12148,12155,12226,12275,3985,3652,10906,11061,11091,11102,12113,12225,12269,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,11321,12082,12089,12136,4092,10691,12116,12128,3992,3682,4499,10191,10194,10519,10522,11360,11544,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322,9326,9329,9330,9345,9359,9368,9379,9392,9393,9397])).
% 155.94/155.67 cnf(12362,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x123621),x123622),f189(f861(x123621,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12363,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(f854(x123631),f854(x123631))),f312(f312(f239(f854(x123631),f854(x123631)),f127(x123631)),f127(x123631))),f154(x123631,x123632)))),
% 155.94/155.67 inference(rename_variables,[],[3987])).
% 155.94/155.67 cnf(12365,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(a853,a853)),f312(f312(f239(a853,a853),f312(a126,x123651)),f312(a126,f312(a126,x123651)))),f312(f312(f267(a853,a853,a853),f287(a853,a302)),f287(a853,f287(a853,a302)))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,11992,12095,12184,12222,12230,12243,3456,3457,3769,3175,4433,3078,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,4407,10335,10426,3263,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2943,2952,2958,2960,2961,2965,2986,3100,4383,3546,3247,3933,3138,11496,12246,12250,12254,3147,3259,3664,3974,3040,4403,3725,11256,3108,3069,10175,3063,3048,3053,3084,3218,11735,11944,12079,3264,10703,12057,3136,3137,3157,10379,3312,4495,3841,4423,10172,10332,11311,12210,12247,4432,12218,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,12233,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,4420,11237,3513,3717,4108,3763,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3597,4123,3403,4492,3981,11137,3531,3246,11610,12064,12164,3950,3909,11762,12107,3853,10700,11934,11958,12120,3904,10890,11989,12063,12119,12163,3572,11772,11921,11997,12047,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,11977,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,3364,10504,10759,10803,11086,11158,11324,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,3268,10531,10561,11115,11665,12299,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,11871,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,3810,11194,11543,11547,11607,12221,12229,3650,10819,10825,10842,11798,12014,12280,3509,11055,12148,12155,12226,12275,3985,3652,10906,11061,11091,11102,12113,12225,12269,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,11321,12082,12089,12136,4092,10691,12116,12128,3992,3682,4499,10191,10194,10519,10522,11360,11544,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322,9326,9329,9330,9345,9359,9368,9379,9392,9393,9397,9399,9423])).
% 155.94/155.67 cnf(12368,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x123681),x123682),f189(f861(x123681,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12371,plain,
% 155.94/155.67 (E(f312(f190(f854(x123711)),f312(f164(x123711),x123712)),f312(f190(f854(x123711)),x123712))),
% 155.94/155.67 inference(rename_variables,[],[3218])).
% 155.94/155.67 cnf(12374,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x123741),x123742),f189(f861(x123741,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12381,plain,
% 155.94/155.67 (~P22(f312(f312(f314(f860(f854(x123811),f854(x123811))),f312(f312(f239(f854(x123811),f854(x123811)),x123812),x123812)),f143(x123811,f149(x123811,f127(f861(x123811,a853))))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,11992,12095,12184,12222,12230,12243,3456,3457,3769,3175,4433,3078,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,4407,10335,10426,3263,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2943,2952,2958,2960,2961,2965,2986,3100,4383,3546,3247,3933,3138,11496,12246,12250,12254,3147,3259,3664,3974,3040,4403,3725,11256,3108,3069,10175,3063,3048,3053,3084,3218,11735,11944,12079,12295,3264,10703,12057,3136,3137,3157,10379,3312,4495,3841,4423,10172,10332,11311,12210,12247,4432,12218,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,4420,11237,3513,3717,4108,3763,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3597,4123,3403,4492,3981,11137,3531,3246,11610,12064,12164,3950,3909,11762,12107,3853,10700,11934,11958,12120,3904,10890,11989,12063,12119,12163,3572,11772,11921,11997,12047,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,11977,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,3364,10504,10759,10803,11086,11158,11324,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,3268,10531,10561,11115,11665,12299,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,11871,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,3810,11194,11543,11547,11607,12221,12229,3650,10819,10825,10842,11798,12014,12280,3509,11055,12148,12155,12226,12275,3985,3652,10906,11061,11091,11102,12113,12225,12269,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,11321,12082,12089,12136,4092,10691,12116,12128,3992,3682,4499,10191,10194,10519,10522,11360,11544,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322,9326,9329,9330,9345,9359,9368,9379,9392,9393,9397,9399,9423,9541,9584,9628,9672,9788,9789])).
% 155.94/155.67 cnf(12383,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x123831),x123831))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(12385,plain,
% 155.94/155.67 (P22(f312(f312(f314(f860(f854(x123851),f854(x123851))),f312(f312(f239(f854(x123851),f854(x123851)),f312(f164(x123851),x123852)),x123852)),f154(x123851,f235(f861(f860(x123851,x123851),a846)))))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,11992,12095,12184,12222,12230,12243,3456,3457,3769,3175,4433,3078,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,4362,11222,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,4407,10335,10426,3263,3418,2806,2811,2823,2826,2827,2828,2832,2833,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2943,2952,2958,2960,2961,2965,2986,3100,4383,3546,3247,3933,3138,11496,12246,12250,12254,3147,3259,3664,3974,3040,4403,3725,11256,3108,3069,10175,3063,3048,3053,3084,3218,11735,11944,12079,12295,12371,3264,10703,12057,3136,3137,3157,10379,3312,4495,3841,4423,10172,10332,11311,12210,12247,4432,12218,3194,11591,4485,10878,10951,11166,11169,3313,3103,3104,10237,10534,3370,3018,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,4420,11237,3513,3717,4108,3763,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,4491,11363,11396,11433,11467,3643,3419,3793,3232,3234,3207,4472,4417,3597,4123,3403,4492,3981,11137,3531,3246,11610,12064,12164,3950,3909,11762,12107,3853,10700,11934,11958,12120,3904,10890,11989,12063,12119,12163,3572,11772,11921,11997,12047,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,3282,11977,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,3364,10504,10759,10803,11086,11158,11324,12213,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,3268,10531,10561,11115,11665,12299,3308,3299,3721,3661,10218,11490,11518,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,11871,3683,4031,4483,3692,3729,4462,4465,3182,3183,4464,4467,3700,3522,11483,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,3810,11194,11543,11547,11607,12221,12229,3650,10819,10825,10842,11798,12014,12280,3509,11055,12148,12155,12226,12275,3985,3652,10906,11061,11091,11102,12113,12225,12269,3581,3481,10496,10499,10564,10738,4501,11484,4502,10622,10717,11040,11184,11321,12082,12089,12136,4092,10691,12116,12128,3992,3682,4499,10191,10194,10519,10522,11360,11544,4500,11464,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322,9326,9329,9330,9345,9359,9368,9379,9392,9393,9397,9399,9423,9541,9584,9628,9672,9788,9789,9848])).
% 155.94/155.67 cnf(12386,plain,
% 155.94/155.67 (P22(f312(f312(f314(x123861),x123862),f235(f861(x123861,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3364])).
% 155.94/155.67 cnf(12393,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x123931,a846)),x123932),x123932))),
% 155.94/155.67 inference(rename_variables,[],[3509])).
% 155.94/155.67 cnf(12396,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x123961),x123962),f189(f861(x123961,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12399,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),f2(a1)),f312(f312(f240(a1),f312(f84(a1),x123991)),x123992)))),
% 155.94/155.67 inference(rename_variables,[],[3682])).
% 155.94/155.67 cnf(12402,plain,
% 155.94/155.67 (E(f37(x124021,x124022,x124023,x124024,x124025,x124026,x124027,x124028,x124029,a23),x124022)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12404,plain,
% 155.94/155.67 (E(f37(x124041,x124042,x124043,x124044,x124045,x124046,x124047,x124048,x124049,a23),x124042)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12408,plain,
% 155.94/155.67 (E(f37(x124081,x124082,x124083,x124084,x124085,x124086,x124087,x124088,x124089,a23),x124082)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12410,plain,
% 155.94/155.67 (P19(x124101,x124101,f5(x124101),x124102)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12412,plain,
% 155.94/155.67 (P19(x124121,x124121,f5(x124121),x124122)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12418,plain,
% 155.94/155.67 (E(f37(x124181,x124182,x124183,x124184,x124185,x124186,x124187,x124188,x124189,a23),x124182)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12420,plain,
% 155.94/155.67 (P11(x124201,f861(x124201,a846),f289(x124201))),
% 155.94/155.67 inference(rename_variables,[],[3179])).
% 155.94/155.67 cnf(12424,plain,
% 155.94/155.67 (E(f37(x124241,x124242,x124243,x124244,x124245,x124246,x124247,x124248,x124249,a23),x124242)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12429,plain,
% 155.94/155.67 (E(f37(x124291,x124292,x124293,x124294,x124295,x124296,x124297,x124298,x124299,a23),x124292)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12431,plain,
% 155.94/155.67 (P36(x124311,x124312,x124313,f180(x124311,x124312,x124314,x124313))),
% 155.94/155.67 inference(rename_variables,[],[3769])).
% 155.94/155.67 cnf(12433,plain,
% 155.94/155.67 (P36(x124331,x124332,x124333,f180(x124331,x124332,x124334,x124333))),
% 155.94/155.67 inference(rename_variables,[],[3769])).
% 155.94/155.67 cnf(12435,plain,
% 155.94/155.67 (P36(x124351,x124352,x124353,f180(x124351,x124352,x124354,x124353))),
% 155.94/155.67 inference(rename_variables,[],[3769])).
% 155.94/155.67 cnf(12437,plain,
% 155.94/155.67 (P36(x124371,x124372,x124373,f180(x124371,x124372,x124374,x124373))),
% 155.94/155.67 inference(rename_variables,[],[3769])).
% 155.94/155.67 cnf(12439,plain,
% 155.94/155.67 (E(f37(x124391,x124392,x124393,x124394,x124395,x124396,x124397,x124398,x124399,a23),x124392)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12444,plain,
% 155.94/155.67 (E(f37(x124441,x124442,x124443,x124444,x124445,x124446,x124447,x124448,x124449,a23),x124442)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12446,plain,
% 155.94/155.67 (P18(x124461,x124462,f189(f861(f852(x124461),a846)))),
% 155.94/155.67 inference(rename_variables,[],[3262])).
% 155.94/155.67 cnf(12452,plain,
% 155.94/155.67 (E(f189(f861(f860(x124521,x124521),a846)),f237(x124521,f189(f861(x124521,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3277])).
% 155.94/155.67 cnf(12458,plain,
% 155.94/155.67 (P41(x124581,f149(x124581,x124582))),
% 155.94/155.67 inference(rename_variables,[],[3078])).
% 155.94/155.67 cnf(12465,plain,
% 155.94/155.67 (E(f37(x124651,x124652,x124653,x124654,x124655,x124656,x124657,x124658,x124659,a23),x124652)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12468,plain,
% 155.94/155.67 (P55(x124681,f189(f861(x124681,a846)),x124682)),
% 155.94/155.67 inference(rename_variables,[],[3224])).
% 155.94/155.67 cnf(12472,plain,
% 155.94/155.67 (E(f37(x124721,x124722,x124723,x124724,x124725,x124726,x124727,x124728,x124729,a23),x124722)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12474,plain,
% 155.94/155.67 (P50(x124741,x124742,f237(x124741,x124742))),
% 155.94/155.67 inference(rename_variables,[],[3174])).
% 155.94/155.67 cnf(12476,plain,
% 155.94/155.67 (P50(x124761,x124762,f237(x124761,x124762))),
% 155.94/155.67 inference(rename_variables,[],[3174])).
% 155.94/155.67 cnf(12480,plain,
% 155.94/155.67 (P34(x124801,f2(a853),f312(f312(f312(f100(x124801),x124802),f312(a27,x124803)),x124804))),
% 155.94/155.67 inference(rename_variables,[],[3579])).
% 155.94/155.67 cnf(12486,plain,
% 155.94/155.67 (E(f37(x124861,x124862,x124863,x124864,x124865,x124866,x124867,x124868,x124869,a23),x124862)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12492,plain,
% 155.94/155.67 (E(f37(x124921,x124922,x124923,x124924,x124925,x124926,x124927,x124928,x124929,a23),x124922)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12494,plain,
% 155.94/155.67 (P54(x124941,x124941,f237(x124941,x124942))),
% 155.94/155.67 inference(rename_variables,[],[3175])).
% 155.94/155.67 cnf(12502,plain,
% 155.94/155.67 (P45(x125021,x125022,x125023,x125024,f189(f861(x125021,a846)),x125024)),
% 155.94/155.67 inference(rename_variables,[],[4152])).
% 155.94/155.67 cnf(12505,plain,
% 155.94/155.67 (P45(x125051,x125052,x125053,x125054,f189(f861(x125051,a846)),x125054)),
% 155.94/155.67 inference(rename_variables,[],[4152])).
% 155.94/155.67 cnf(12509,plain,
% 155.94/155.67 (P37(x125091,x125092,f127(x125091),f127(x125091))),
% 155.94/155.67 inference(rename_variables,[],[3456])).
% 155.94/155.67 cnf(12511,plain,
% 155.94/155.67 (P37(x125111,x125112,f127(x125111),f127(x125111))),
% 155.94/155.67 inference(rename_variables,[],[3456])).
% 155.94/155.67 cnf(12517,plain,
% 155.94/155.67 (P42(x125171,f192(x125171))),
% 155.94/155.67 inference(rename_variables,[],[3037])).
% 155.94/155.67 cnf(12530,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x125301),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12533,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x125331),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12540,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a1),f312(f114(a1),x125401)),f312(f88(a1),f312(f114(a1),x125402))))),
% 155.94/155.67 inference(rename_variables,[],[4497])).
% 155.94/155.67 cnf(12550,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x125501),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12553,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x125531),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12556,plain,
% 155.94/155.67 (P22(f312(f70(a853),f284(a853,x125561,x125562)))),
% 155.94/155.67 inference(rename_variables,[],[3420])).
% 155.94/155.67 cnf(12559,plain,
% 155.94/155.67 (P22(f312(f70(a853),f284(a853,x125591,x125592)))),
% 155.94/155.67 inference(rename_variables,[],[3420])).
% 155.94/155.67 cnf(12562,plain,
% 155.94/155.67 (P22(f312(f70(a853),f284(a853,x125621,x125622)))),
% 155.94/155.67 inference(rename_variables,[],[3420])).
% 155.94/155.67 cnf(12565,plain,
% 155.94/155.67 (P22(f312(f70(a853),f284(a853,x125651,x125652)))),
% 155.94/155.67 inference(rename_variables,[],[3420])).
% 155.94/155.67 cnf(12572,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),f312(f88(a1),f312(f114(a1),x125721))),f312(f114(a1),x125722)))),
% 155.94/155.67 inference(rename_variables,[],[3683])).
% 155.94/155.67 cnf(12575,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x125751),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12576,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x125761),x125761))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12583,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x125831),f312(a126,x125831)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12586,plain,
% 155.94/155.67 (P22(f312(f312(f314(x125861),f312(x125862,x125863)),f312(f290(x125864,x125861,x125862),f235(f861(x125864,a846)))))),
% 155.94/155.67 inference(rename_variables,[],[3810])).
% 155.94/155.67 cnf(12587,plain,
% 155.94/155.67 (~E(f312(a126,x125871),f2(a853))),
% 155.94/155.67 inference(rename_variables,[],[4401])).
% 155.94/155.67 cnf(12592,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x125921),x125921))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(12595,plain,
% 155.94/155.67 (P22(f312(f70(a853),f284(a853,x125951,x125952)))),
% 155.94/155.67 inference(rename_variables,[],[3420])).
% 155.94/155.67 cnf(12598,plain,
% 155.94/155.67 (P22(f312(f70(a853),f284(a853,x125981,x125982)))),
% 155.94/155.67 inference(rename_variables,[],[3420])).
% 155.94/155.67 cnf(12601,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x126011),x126011))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12614,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x126141),f312(a126,x126141)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12619,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f54(a853,x126191,x126192)),x126191))),
% 155.94/155.67 inference(rename_variables,[],[3661])).
% 155.94/155.67 cnf(12626,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x126261),f312(a126,x126261)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12627,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x126271),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12636,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a1),f312(f114(a1),x126361)),f2(a1)))),
% 155.94/155.67 inference(rename_variables,[],[4491])).
% 155.94/155.67 cnf(12637,plain,
% 155.94/155.67 (P22(f312(f235(f861(x126371,a846)),x126372))),
% 155.94/155.67 inference(rename_variables,[],[3268])).
% 155.94/155.67 cnf(12640,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a1),f312(f114(a1),x126401)),f2(a1)))),
% 155.94/155.67 inference(rename_variables,[],[4491])).
% 155.94/155.67 cnf(12641,plain,
% 155.94/155.67 (P22(f312(f235(f861(x126411,a846)),x126412))),
% 155.94/155.67 inference(rename_variables,[],[3268])).
% 155.94/155.67 cnf(12644,plain,
% 155.94/155.67 (P22(f312(f235(f861(x126441,a846)),x126442))),
% 155.94/155.67 inference(rename_variables,[],[3268])).
% 155.94/155.67 cnf(12655,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x126551),x126552),f189(f861(x126551,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12656,plain,
% 155.94/155.67 (P22(f312(f70(x126561),f189(f861(x126561,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3282])).
% 155.94/155.67 cnf(12665,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f2(a853)),x126651))),
% 155.94/155.67 inference(rename_variables,[],[3226])).
% 155.94/155.67 cnf(12668,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x126681),f312(a126,x126681)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12669,plain,
% 155.94/155.67 (~E(f312(a126,x126691),x126691)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(12672,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x126721),x126722),f189(f861(x126721,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12675,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x126751),x126752),f189(f861(x126751,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12678,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x126781),x126781))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12685,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x126851),x126851))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12688,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x126881),x126881))),
% 155.94/155.67 inference(rename_variables,[],[4471])).
% 155.94/155.67 cnf(12689,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x126891),f312(a126,x126891)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12692,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x126921),x126921))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12697,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x126971),x126971))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12700,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x127001),x127001))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12703,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x127031),x127031))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12706,plain,
% 155.94/155.67 (E(f312(f312(f21(f861(x127061,a846)),f189(f861(x127061,a846))),x127062),f189(f861(x127061,a846)))),
% 155.94/155.67 inference(rename_variables,[],[3483])).
% 155.94/155.67 cnf(12707,plain,
% 155.94/155.67 (P22(f312(f70(x127071),f189(f861(x127071,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3282])).
% 155.94/155.67 cnf(12710,plain,
% 155.94/155.67 (E(f312(f312(f21(f861(x127101,a846)),f189(f861(x127101,a846))),x127102),f189(f861(x127101,a846)))),
% 155.94/155.67 inference(rename_variables,[],[3483])).
% 155.94/155.67 cnf(12711,plain,
% 155.94/155.67 (P22(f312(f70(x127111),f189(f861(x127111,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3282])).
% 155.94/155.67 cnf(12714,plain,
% 155.94/155.67 (E(f312(f312(f21(f861(x127141,a846)),f189(f861(x127141,a846))),x127142),f189(f861(x127141,a846)))),
% 155.94/155.67 inference(rename_variables,[],[3483])).
% 155.94/155.67 cnf(12715,plain,
% 155.94/155.67 (P22(f312(f70(x127151),f189(f861(x127151,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3282])).
% 155.94/155.67 cnf(12718,plain,
% 155.94/155.67 (E(f312(f312(f21(f861(x127181,a846)),f189(f861(x127181,a846))),x127182),f189(f861(x127181,a846)))),
% 155.94/155.67 inference(rename_variables,[],[3483])).
% 155.94/155.67 cnf(12719,plain,
% 155.94/155.67 (P22(f312(f70(x127191),f189(f861(x127191,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3282])).
% 155.94/155.67 cnf(12723,plain,
% 155.94/155.67 (E(f37(x127231,x127232,x127233,x127234,x127235,x127236,x127237,x127238,x127239,a23),x127232)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12728,plain,
% 155.94/155.67 (E(f312(f312(f21(f861(x127281,a846)),f189(f861(x127281,a846))),x127282),f189(f861(x127281,a846)))),
% 155.94/155.67 inference(rename_variables,[],[3483])).
% 155.94/155.67 cnf(12729,plain,
% 155.94/155.67 (P22(f312(f70(x127291),f189(f861(x127291,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3282])).
% 155.94/155.67 cnf(12733,plain,
% 155.94/155.67 (P22(f312(f70(x127331),f189(f861(x127331,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3282])).
% 155.94/155.67 cnf(12736,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x127361),x127361))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12742,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x127421),x127421))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(12745,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x127451),f312(a126,x127451)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12748,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x127481),x127481))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12751,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x127511),f312(a126,x127511)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12766,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x127661),x127661))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(12771,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x127711),x127712),f189(f861(x127711,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12782,plain,
% 155.94/155.67 (P22(f312(f312(f314(x127821),x127822),f235(f861(x127821,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3364])).
% 155.94/155.67 cnf(12786,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x127861,a846)),f312(f168(x127861),f312(f132(x127861,x127862),x127863))),f312(f168(x127861),x127863)))),
% 155.94/155.67 inference(rename_variables,[],[3853])).
% 155.94/155.67 cnf(12792,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x127921),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12793,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x127931),x127931))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(12797,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x127971),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12798,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x127981),x127981))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(12803,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x128031,a846)),x128032),f235(f861(x128031,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(12808,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x128081),x128081))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12815,plain,
% 155.94/155.67 (E(f312(f312(f16(x128151,x128152),x128153),x128154),x128153)),
% 155.94/155.67 inference(rename_variables,[],[3194])).
% 155.94/155.67 cnf(12818,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x128181,a846)),f312(f168(x128181),f166(x128181,x128182,x128183))),f312(f168(x128181),x128183)))),
% 155.94/155.67 inference(rename_variables,[],[3904])).
% 155.94/155.67 cnf(12820,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f842(f312(x128201,f2(a853)),x128201,f2(a853))),f2(a853)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,11992,12095,12184,12222,12230,12243,12292,12410,3456,12060,12509,12511,3457,12123,3769,10845,12431,12433,12435,3174,12474,12476,3175,12494,4433,4152,12502,12505,3179,12420,3015,3037,12517,3078,12458,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,12351,12402,12404,12408,12418,12424,12429,12439,12444,12465,12472,12486,12492,4362,11222,3511,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,12266,4407,10335,10426,3263,3224,12468,3418,4401,2806,2811,2823,2826,2827,2828,2832,2833,2841,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2905,2909,2917,2928,2939,2943,2952,2957,2958,2959,2960,2961,2962,2965,2986,3100,3077,4383,3546,3187,3247,3933,3159,3533,3784,4374,3138,11496,12246,12250,12254,3147,3259,3664,3974,3040,4403,4421,3725,11256,3262,12446,3108,3069,10175,3579,12480,3063,3876,3586,4348,3048,3027,3053,3084,3218,11735,11944,12079,12295,12371,3264,10703,12057,3136,3137,3157,10379,3312,4495,10307,3841,4423,10172,10332,11311,12210,12247,4432,12218,3194,11591,11594,4485,10878,10951,11166,11169,3313,3532,3277,12452,3103,3104,10237,10534,3370,3094,3018,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,4420,11237,3513,3549,3717,4108,3483,12706,12710,12714,12718,12728,3763,12092,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,12342,12583,12614,12626,12668,12689,12745,12751,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,12237,12530,12533,12550,12553,12575,12627,12792,12797,4491,11363,11396,11433,11467,12636,12640,3643,3419,3420,12556,12559,12562,12565,12595,3793,3232,3234,3207,4472,3102,4417,3597,4123,3911,3403,4492,3981,11137,3531,3246,11610,12064,12164,12322,3950,3909,11762,12107,3853,10700,11934,11958,12120,12345,3904,10890,11989,12063,12119,12163,3572,11772,11921,11997,12047,3873,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,12348,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,12315,12576,12601,12678,12685,12692,12697,12700,12703,12736,12748,12808,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,11866,12592,12742,12766,12793,12798,3282,11977,12656,12707,12711,12715,12719,12729,12733,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,12383,12688,3364,10504,10759,10803,11086,11158,11324,12213,12386,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,12374,12396,12655,12672,12675,3268,10531,10561,11115,11665,12299,12316,12637,12641,12644,3308,3299,3721,3661,10218,11490,11518,12619,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,11871,12104,3683,11613,12572,4031,3425,4483,3692,3729,4462,4465,4466,3182,3183,4464,4467,3700,3522,11483,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,12131,3810,11194,11543,11547,11607,12221,12229,12308,3650,10819,10825,10842,11798,12014,12280,3509,11055,12148,12155,12226,12275,12283,3985,3652,10906,11061,11091,11102,12113,12225,12269,3581,11603,3481,10496,10499,10564,10738,3480,4501,11484,4497,12540,4502,10622,10717,11040,11184,11321,12082,12089,12136,12332,4092,10691,12116,12128,3992,3682,12399,4499,10191,10194,10519,10522,11360,11544,12341,4500,11464,11557,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322,9326,9329,9330,9345,9359,9368,9379,9392,9393,9397,9399,9423,9541,9584,9628,9672,9788,9789,9848,9918,9992,10007,10012,3,2560,2563,2566,2570,2571,2572,2573,2577,2582,2584,2586,2587,2588,2589,2592,2594,2595,2596,2597,2603,2606,2607,2608,2613,2615,2616,2617,2619,2621,2624,2625,2627,2628,2630,2631,2638,2662,2663,2665,2667,2673,2674,2682,2686,2687,2688,2697,2698,2699,2710,2724,2727,2728,2734,2735,2736,2737,2746,2748,2750,2753,2754,2755,2759,2761,2762,2764,2769,2770,2783,2790,2791,5222,5394,5400,5401,5475,5521,5550,5579,5655,5657,5663,5720,5721,5722,5723,5729,5758,5889,5941,5960,5994,6031,6176,6183,6217,6218,6234,6238,6240,6247,6248,6249,6250,6251,6252,6253,6254,6335,6401,6402,6483,6517,6518,6559,6560,6697,6726,6778,6779,6783,6805,6830,6838,6840,6889,6917,6918,6934,6935,6936,6971,7015,7016,7115,7173,7174,7175,7176,7189,7216,7272,7273,7281,7289,7291,7303,7333,7334,7335,7336,7478,7479,7486,7488,7489,7490,7700,7702,7703,7719,7758,7869,7925,7946,7947,7962,8024,8126,8196,8197,8199,8237,8299])).
% 155.94/155.67 cnf(12822,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x128221),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12823,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x128231),x128231))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(12827,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a853),x128271),f2(a853)))),
% 155.94/155.67 inference(rename_variables,[],[4475])).
% 155.94/155.67 cnf(12828,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x128281),x128281))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(12830,plain,
% 155.94/155.67 (~P22(f312(f312(f228(f861(a853,a846)),f283(a853,f312(a126,x128301),f312(a126,x128301))),f283(a853,x128302,x128301)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,11992,12095,12184,12222,12230,12243,12292,12410,3456,12060,12509,12511,3457,12123,3769,10845,12431,12433,12435,3174,12474,12476,3175,12494,4433,4152,12502,12505,3179,12420,3015,3037,12517,3078,12458,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,12351,12402,12404,12408,12418,12424,12429,12439,12444,12465,12472,12486,12492,4362,11222,3511,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,12266,4407,10335,10426,3263,3224,12468,3418,4401,2806,2811,2823,2826,2827,2828,2832,2833,2841,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2905,2909,2917,2928,2939,2943,2952,2957,2958,2959,2960,2961,2962,2965,2986,3100,3077,4383,3546,3187,3247,3933,3159,3533,3784,4374,3138,11496,12246,12250,12254,3147,3259,3664,3974,3040,4403,4421,3725,11256,3262,12446,3108,3069,10175,3579,12480,3063,3876,3586,4348,3048,3027,3053,3084,3218,11735,11944,12079,12295,12371,3264,10703,12057,3136,3137,3157,10379,3312,4495,10307,3841,4423,10172,10332,11311,12210,12247,4432,12218,3194,11591,11594,4485,10878,10951,11166,11169,3313,3532,3277,12452,3103,3104,10237,10534,3370,3094,3018,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,4420,11237,3513,3549,3717,4108,3483,12706,12710,12714,12718,12728,3763,12092,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,12342,12583,12614,12626,12668,12689,12745,12751,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,12237,12530,12533,12550,12553,12575,12627,12792,12797,12822,4491,11363,11396,11433,11467,12636,12640,3643,3419,3420,12556,12559,12562,12565,12595,3793,3232,3234,3207,4472,3102,4417,3597,4123,3911,3403,4492,3981,11137,3531,3246,11610,12064,12164,12322,3950,3909,11762,12107,3853,10700,11934,11958,12120,12345,3904,10890,11989,12063,12119,12163,3572,11772,11921,11997,12047,3873,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,12348,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,12315,12576,12601,12678,12685,12692,12697,12700,12703,12736,12748,12808,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,11866,12592,12742,12766,12793,12798,12823,3282,11977,12656,12707,12711,12715,12719,12729,12733,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,12383,12688,3364,10504,10759,10803,11086,11158,11324,12213,12386,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,12374,12396,12655,12672,12675,3268,10531,10561,11115,11665,12299,12316,12637,12641,12644,3308,3299,3721,3661,10218,11490,11518,12619,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,11871,12104,3683,11613,12572,4031,3425,4483,3692,3729,4462,4465,4466,3182,3183,4464,4467,3700,3522,11483,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,12131,3810,11194,11543,11547,11607,12221,12229,12308,3650,10819,10825,10842,11798,12014,12280,3509,11055,12148,12155,12226,12275,12283,3985,3652,10906,11061,11091,11102,12113,12225,12269,3581,11603,3481,10496,10499,10564,10738,3480,4501,11484,4497,12540,4502,10622,10717,11040,11184,11321,12082,12089,12136,12332,4092,10691,12116,12128,3992,3682,12399,4499,10191,10194,10519,10522,11360,11544,12341,4500,11464,11557,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322,9326,9329,9330,9345,9359,9368,9379,9392,9393,9397,9399,9423,9541,9584,9628,9672,9788,9789,9848,9918,9992,10007,10012,3,2560,2563,2566,2570,2571,2572,2573,2577,2582,2584,2586,2587,2588,2589,2592,2594,2595,2596,2597,2603,2606,2607,2608,2613,2615,2616,2617,2619,2621,2624,2625,2627,2628,2630,2631,2638,2662,2663,2665,2667,2673,2674,2682,2686,2687,2688,2697,2698,2699,2710,2724,2727,2728,2734,2735,2736,2737,2746,2748,2750,2753,2754,2755,2759,2761,2762,2764,2769,2770,2783,2790,2791,5222,5394,5400,5401,5475,5521,5550,5579,5655,5657,5663,5720,5721,5722,5723,5729,5758,5889,5941,5960,5994,6031,6176,6183,6217,6218,6234,6238,6240,6247,6248,6249,6250,6251,6252,6253,6254,6335,6401,6402,6483,6517,6518,6559,6560,6697,6726,6778,6779,6783,6805,6830,6838,6840,6889,6917,6918,6934,6935,6936,6971,7015,7016,7115,7173,7174,7175,7176,7189,7216,7272,7273,7281,7289,7291,7303,7333,7334,7335,7336,7478,7479,7486,7488,7489,7490,7700,7702,7703,7719,7758,7869,7925,7946,7947,7962,8024,8126,8196,8197,8199,8237,8299,8300,8399])).
% 155.94/155.67 cnf(12831,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x128311),x128311))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12833,plain,
% 155.94/155.67 (~P22(f312(f312(f227(f861(a853,a846)),f283(a853,f312(a126,x128331),f312(a126,x128331))),f283(a853,x128332,x128331)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3449,10946,11992,12095,12184,12222,12230,12243,12292,12410,3456,12060,12509,12511,3457,12123,3769,10845,12431,12433,12435,3174,12474,12476,3175,12494,4433,4152,12502,12505,3179,12420,3015,3037,12517,3078,12458,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,12351,12402,12404,12408,12418,12424,12429,12439,12444,12465,12472,12486,12492,4362,11222,3511,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,12266,4407,10335,10426,3263,3224,12468,3418,4401,2806,2811,2823,2826,2827,2828,2832,2833,2841,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2905,2909,2917,2928,2939,2943,2952,2957,2958,2959,2960,2961,2962,2965,2986,3100,3077,4383,3546,3187,3247,3933,3159,3533,3784,4374,3138,11496,12246,12250,12254,3147,3259,3664,3974,3040,4403,4421,3725,11256,3262,12446,3108,3069,10175,3579,12480,3063,3876,3586,4348,3048,3027,3053,3084,3218,11735,11944,12079,12295,12371,3264,10703,12057,3136,3137,3157,10379,3312,4495,10307,3841,4423,10172,10332,11311,12210,12247,4432,12218,3194,11591,11594,4485,10878,10951,11166,11169,3313,3532,3277,12452,3103,3104,10237,10534,3370,3094,3018,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,4420,11237,3513,3549,3717,4108,3483,12706,12710,12714,12718,12728,3763,12092,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,12342,12583,12614,12626,12668,12689,12745,12751,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,12237,12530,12533,12550,12553,12575,12627,12792,12797,12822,4491,11363,11396,11433,11467,12636,12640,3643,3419,3420,12556,12559,12562,12565,12595,3793,3232,3234,3207,4472,3102,4417,3597,4123,3911,3403,4492,3981,11137,3531,3246,11610,12064,12164,12322,3950,3909,11762,12107,3853,10700,11934,11958,12120,12345,3904,10890,11989,12063,12119,12163,3572,11772,11921,11997,12047,3873,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,12348,4496,10646,11029,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,12315,12576,12601,12678,12685,12692,12697,12700,12703,12736,12748,12808,12831,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,11866,12592,12742,12766,12793,12798,12823,3282,11977,12656,12707,12711,12715,12719,12729,12733,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,12383,12688,3364,10504,10759,10803,11086,11158,11324,12213,12386,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,12374,12396,12655,12672,12675,3268,10531,10561,11115,11665,12299,12316,12637,12641,12644,3308,3299,3721,3661,10218,11490,11518,12619,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,3226,10708,10779,11519,11670,11871,12104,3683,11613,12572,4031,3425,4483,3692,3729,4462,4465,4466,3182,3183,4464,4467,3700,3522,11483,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,12131,3810,11194,11543,11547,11607,12221,12229,12308,3650,10819,10825,10842,11798,12014,12280,3509,11055,12148,12155,12226,12275,12283,3985,3652,10906,11061,11091,11102,12113,12225,12269,3581,11603,3481,10496,10499,10564,10738,3480,4501,11484,4497,12540,4502,10622,10717,11040,11184,11321,12082,12089,12136,12332,4092,10691,12116,12128,3992,3682,12399,4499,10191,10194,10519,10522,11360,11544,12341,4500,11464,11557,3654,10493,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322,9326,9329,9330,9345,9359,9368,9379,9392,9393,9397,9399,9423,9541,9584,9628,9672,9788,9789,9848,9918,9992,10007,10012,3,2560,2563,2566,2570,2571,2572,2573,2577,2582,2584,2586,2587,2588,2589,2592,2594,2595,2596,2597,2603,2606,2607,2608,2613,2615,2616,2617,2619,2621,2624,2625,2627,2628,2630,2631,2638,2662,2663,2665,2667,2673,2674,2682,2686,2687,2688,2697,2698,2699,2710,2724,2727,2728,2734,2735,2736,2737,2746,2748,2750,2753,2754,2755,2759,2761,2762,2764,2769,2770,2783,2790,2791,5222,5394,5400,5401,5475,5521,5550,5579,5655,5657,5663,5720,5721,5722,5723,5729,5758,5889,5941,5960,5994,6031,6176,6183,6217,6218,6234,6238,6240,6247,6248,6249,6250,6251,6252,6253,6254,6335,6401,6402,6483,6517,6518,6559,6560,6697,6726,6778,6779,6783,6805,6830,6838,6840,6889,6917,6918,6934,6935,6936,6971,7015,7016,7115,7173,7174,7175,7176,7189,7216,7272,7273,7281,7289,7291,7303,7333,7334,7335,7336,7478,7479,7486,7488,7489,7490,7700,7702,7703,7719,7758,7869,7925,7946,7947,7962,8024,8126,8196,8197,8199,8237,8299,8300,8399,8400])).
% 155.94/155.67 cnf(12834,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x128341),x128341))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12837,plain,
% 155.94/155.67 (~P22(f312(f312(f227(a853),f312(a126,x128371)),x128371))),
% 155.94/155.67 inference(rename_variables,[],[4484])).
% 155.94/155.67 cnf(12843,plain,
% 155.94/155.67 (P22(f312(f312(f314(x128431),f312(x128432,x128433)),f312(f290(x128434,x128431,x128432),f235(f861(x128434,a846)))))),
% 155.94/155.67 inference(rename_variables,[],[3810])).
% 155.94/155.67 cnf(12844,plain,
% 155.94/155.67 (P19(x128441,x128441,f5(x128441),x128442)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12848,plain,
% 155.94/155.67 (P22(f312(f312(f314(x128481),x128482),f235(f861(x128481,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3364])).
% 155.94/155.67 cnf(12849,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x128491),x128492),f189(f861(x128491,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12853,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x128531,a846)),x128532),f235(f861(x128531,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(12854,plain,
% 155.94/155.67 (P19(x128541,x128541,f5(x128541),x128542)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12858,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x128581,a846)),x128582),f235(f861(x128581,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3588])).
% 155.94/155.67 cnf(12859,plain,
% 155.94/155.67 (P19(x128591,x128591,f5(x128591),x128592)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12865,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x128651,a846)),f312(f290(x128652,x128651,x128653),f312(f291(x128652,x128651,x128653),x128654))),x128654))),
% 155.94/155.67 inference(rename_variables,[],[4092])).
% 155.94/155.67 cnf(12866,plain,
% 155.94/155.67 (P19(x128661,x128661,f5(x128661),x128662)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12869,plain,
% 155.94/155.67 (~P22(f312(f312(f228(f861(x128691,a846)),x128692),f189(f861(x128691,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4496])).
% 155.94/155.67 cnf(12872,plain,
% 155.94/155.67 (P19(x128721,x128721,f5(x128721),x128722)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12875,plain,
% 155.94/155.67 (P19(x128751,x128751,f5(x128751),x128752)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12878,plain,
% 155.94/155.67 (P22(f312(f312(f314(x128781),x128782),f312(f312(f289(x128781),x128782),x128783)))),
% 155.94/155.67 inference(rename_variables,[],[3522])).
% 155.94/155.67 cnf(12886,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x128861,a846)),f189(f861(x128861,a846))),x128862))),
% 155.94/155.67 inference(rename_variables,[],[3652])).
% 155.94/155.67 cnf(12890,plain,
% 155.94/155.67 (E(f37(x128901,x128902,x128903,x128904,x128905,x128906,x128907,x128908,x128909,a23),x128902)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12894,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x128941),x128942),f189(f861(x128941,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12897,plain,
% 155.94/155.67 (~P22(f312(f312(f228(a1),f312(f114(a1),x128971)),f2(a1)))),
% 155.94/155.67 inference(rename_variables,[],[4491])).
% 155.94/155.67 cnf(12898,plain,
% 155.94/155.67 (~E(f312(a126,x128981),x128981)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(12902,plain,
% 155.94/155.67 (P22(f312(f312(f314(x129021),f312(x129022,x129023)),f312(f290(x129024,x129021,x129022),f235(f861(x129024,a846)))))),
% 155.94/155.67 inference(rename_variables,[],[3810])).
% 155.94/155.67 cnf(12903,plain,
% 155.94/155.67 (P19(x129031,x129031,f5(x129031),x129032)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(12906,plain,
% 155.94/155.67 (P22(f312(f312(f314(x129061),x129062),f235(f861(x129061,a846))))),
% 155.94/155.67 inference(rename_variables,[],[3364])).
% 155.94/155.67 cnf(12913,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x129131),x129132),f189(f861(x129131,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12916,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x129161),x129162),f189(f861(x129161,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12919,plain,
% 155.94/155.67 (E(f37(x129191,x129192,x129193,x129194,x129195,x129196,x129197,x129198,x129199,a23),x129192)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(12921,plain,
% 155.94/155.67 (~E(f312(a126,x129211),x129211)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(12925,plain,
% 155.94/155.67 (E(f312(f312(f16(x129251,x129252),x129253),x129254),x129253)),
% 155.94/155.67 inference(rename_variables,[],[3194])).
% 155.94/155.67 cnf(12928,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x129281),f312(a126,x129281)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12929,plain,
% 155.94/155.67 (~E(f312(a126,x129291),x129291)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(12932,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x129321),f312(a126,f312(f312(f89(a853),x129322),x129321))))),
% 155.94/155.67 inference(rename_variables,[],[3654])).
% 155.94/155.67 cnf(12933,plain,
% 155.94/155.67 (P22(f312(f312(f228(a853),x129331),f312(a126,x129331)))),
% 155.94/155.67 inference(rename_variables,[],[3274])).
% 155.94/155.67 cnf(12935,plain,
% 155.94/155.67 (~E(f312(f312(f90(a853),f312(a126,f2(a853))),f40(x129351)),f312(f312(f90(a853),f312(a126,f2(a853))),f41(x129352)))),
% 155.94/155.67 inference(scs_inference,[],[4463,3431,3449,10946,11992,12095,12184,12222,12230,12243,12292,12410,12412,12844,12854,12859,12866,12872,12875,3456,12060,12509,12511,3457,12123,3769,10845,12431,12433,12435,12437,3174,12474,12476,3175,12494,4433,4152,12502,12505,3179,12420,3015,3037,12517,3078,12458,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,12351,12402,12404,12408,12418,12424,12429,12439,12444,12465,12472,12486,12492,12723,12890,4362,11222,3511,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,12266,12669,12898,12921,12929,4407,10335,10426,3263,3224,12468,3418,4401,2806,2811,2820,2823,2826,2827,2828,2832,2833,2841,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2905,2909,2917,2925,2928,2939,2943,2952,2957,2958,2959,2960,2961,2962,2965,2986,3100,3077,4383,3546,3187,3247,3933,3159,3533,3784,4374,3138,11496,12246,12250,12254,3147,3259,3664,3974,3039,3040,4403,4421,3725,11256,3262,12446,3108,3069,10175,3579,12480,3063,3876,3085,3586,4348,3048,3027,3053,3084,3218,11735,11944,12079,12295,12371,3264,10703,12057,3136,3137,3157,10379,3312,4495,10307,3841,4423,10172,10332,11311,12210,12247,12251,4432,12218,3194,11591,11594,12815,4485,10878,10951,11166,11169,3190,3313,3532,3277,12452,3103,3104,10237,10534,4469,3370,3094,3018,3146,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,11075,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,4420,11237,3513,3549,3717,4108,3483,12706,12710,12714,12718,12728,3763,12092,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,12342,12583,12614,12626,12668,12689,12745,12751,12928,3656,11487,3189,3286,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,12237,12530,12533,12550,12553,12575,12627,12792,12797,12822,4491,11363,11396,11433,11467,12636,12640,3643,3419,3420,12556,12559,12562,12565,12595,3422,3793,3232,3234,3207,4472,3102,4417,3597,4123,3911,3403,4492,3981,11137,3531,3246,11610,12064,12164,12322,3950,3909,11762,12107,3853,10700,11934,11958,12120,12345,3904,10890,11989,12063,12119,12163,3572,11772,11921,11997,12047,3873,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,12348,12803,12853,12858,4496,10646,11029,12869,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,12315,12576,12601,12678,12685,12692,12697,12700,12703,12736,12748,12808,12831,12834,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,11866,12592,12742,12766,12793,12798,12823,3282,11977,12656,12707,12711,12715,12719,12729,12733,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,12383,12688,3364,10504,10759,10803,11086,11158,11324,12213,12386,12782,12848,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,12374,12396,12655,12672,12675,12771,12849,12894,12913,3268,10531,10561,11115,11665,12299,12316,12637,12641,12644,3308,3299,3721,3661,10218,11490,11518,12619,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,12837,3226,10708,10779,11519,11670,11871,12104,3683,11613,12572,4031,3425,4483,3692,3729,4462,4465,4466,3182,3183,4464,4467,3700,3522,11483,11569,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,12131,3810,11194,11543,11547,11607,12221,12229,12308,12586,12843,12902,3650,10819,10825,10842,11798,12014,12280,12305,3509,11055,12148,12155,12226,12275,12283,3985,3652,10906,11061,11091,11102,12113,12225,12269,12319,3581,11603,3481,10496,10499,10564,10738,3480,4501,11484,4497,12540,4502,10622,10717,11040,11184,11321,12082,12089,12136,12332,4092,10691,12116,12128,12154,3992,3682,12399,4499,10191,10194,10519,10522,11360,11544,12341,4500,11464,11557,3654,10493,10735,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322,9326,9329,9330,9345,9359,9368,9379,9392,9393,9397,9399,9423,9541,9584,9628,9672,9788,9789,9848,9918,9992,10007,10012,3,2560,2563,2566,2570,2571,2572,2573,2577,2582,2584,2586,2587,2588,2589,2592,2594,2595,2596,2597,2603,2606,2607,2608,2613,2615,2616,2617,2619,2621,2624,2625,2627,2628,2630,2631,2638,2662,2663,2665,2667,2673,2674,2682,2686,2687,2688,2697,2698,2699,2710,2724,2727,2728,2734,2735,2736,2737,2746,2748,2750,2753,2754,2755,2759,2761,2762,2764,2769,2770,2783,2790,2791,5222,5394,5400,5401,5475,5521,5550,5579,5655,5657,5663,5720,5721,5722,5723,5729,5758,5889,5941,5960,5994,6031,6176,6183,6217,6218,6234,6238,6240,6247,6248,6249,6250,6251,6252,6253,6254,6335,6401,6402,6483,6517,6518,6559,6560,6697,6726,6778,6779,6783,6805,6830,6838,6840,6889,6917,6918,6934,6935,6936,6971,7015,7016,7115,7173,7174,7175,7176,7189,7216,7272,7273,7281,7289,7291,7303,7333,7334,7335,7336,7478,7479,7486,7488,7489,7490,7700,7702,7703,7719,7758,7869,7925,7946,7947,7962,8024,8126,8196,8197,8199,8237,8299,8300,8399,8400,8401,8402,8545,8754,8777,8778,8827,8856,8871,8929,8930,9044,9077,9100,9135,9178,9335,9366,9622,9817,9875,9878,5547,5955,6316,6317,6405])).
% 155.94/155.67 cnf(12937,plain,
% 155.94/155.67 (~E(f312(a126,x129371),x129371)),
% 155.94/155.67 inference(rename_variables,[],[4389])).
% 155.94/155.67 cnf(12942,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),f2(a1)),f312(f114(a1),x129421)))),
% 155.94/155.67 inference(rename_variables,[],[3308])).
% 155.94/155.67 cnf(12947,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),f2(a853)),x129471))),
% 155.94/155.67 inference(rename_variables,[],[3226])).
% 155.94/155.67 cnf(12948,plain,
% 155.94/155.67 (P22(f312(f312(f227(a853),x129481),x129481))),
% 155.94/155.67 inference(rename_variables,[],[3205])).
% 155.94/155.67 cnf(12951,plain,
% 155.94/155.67 (~E(f312(a126,x129511),f2(a853))),
% 155.94/155.67 inference(rename_variables,[],[4401])).
% 155.94/155.67 cnf(12956,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x129561),x129562),f189(f861(x129561,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(12959,plain,
% 155.94/155.67 (P22(f312(f70(a853),f284(a853,x129591,x129592)))),
% 155.94/155.67 inference(rename_variables,[],[3420])).
% 155.94/155.67 cnf(12960,plain,
% 155.94/155.67 (E(f312(f312(f226(a853),f312(a126,x129601)),f312(a126,x129602)),f312(a126,f312(f312(f226(a853),x129601),x129602)))),
% 155.94/155.67 inference(rename_variables,[],[3382])).
% 155.94/155.67 cnf(12963,plain,
% 155.94/155.67 (P22(f312(f70(a853),f284(a853,x129631,x129632)))),
% 155.94/155.67 inference(rename_variables,[],[3420])).
% 155.94/155.67 cnf(12964,plain,
% 155.94/155.67 (E(f312(f312(f225(a853),f312(a126,x129641)),f312(a126,x129642)),f312(a126,f312(f312(f225(a853),x129641),x129642)))),
% 155.94/155.67 inference(rename_variables,[],[3381])).
% 155.94/155.67 cnf(12967,plain,
% 155.94/155.67 (P22(f312(f70(a853),f284(a853,x129671,x129672)))),
% 155.94/155.67 inference(rename_variables,[],[3420])).
% 155.94/155.67 cnf(12971,plain,
% 155.94/155.67 (P22(f312(f70(a853),f284(a853,x129711,x129712)))),
% 155.94/155.67 inference(rename_variables,[],[3420])).
% 155.94/155.67 cnf(12975,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x129751,a846)),f312(f168(x129751),f312(f132(x129751,x129752),x129753))),f312(f168(x129751),x129753)))),
% 155.94/155.67 inference(rename_variables,[],[3853])).
% 155.94/155.67 cnf(12976,plain,
% 155.94/155.67 (E(f312(f312(f16(x129761,x129762),x129763),x129764),x129763)),
% 155.94/155.67 inference(rename_variables,[],[3194])).
% 155.94/155.67 cnf(12979,plain,
% 155.94/155.67 (P22(f312(f312(f227(f861(x129791,a846)),f312(f168(x129791),f312(f312(f169(x129791),x129792),x129793))),f312(f168(x129791),x129793)))),
% 155.94/155.67 inference(rename_variables,[],[3899])).
% 155.94/155.67 cnf(12980,plain,
% 155.94/155.67 (E(f312(f312(f16(x129801,x129802),x129803),x129804),x129803)),
% 155.94/155.67 inference(rename_variables,[],[3194])).
% 155.94/155.67 cnf(12984,plain,
% 155.94/155.67 (E(f312(f312(f16(x129841,x129842),x129843),x129844),x129843)),
% 155.94/155.67 inference(rename_variables,[],[3194])).
% 155.94/155.67 cnf(12997,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),f2(a1)),f312(f114(a1),x129971)))),
% 155.94/155.67 inference(rename_variables,[],[3308])).
% 155.94/155.67 cnf(13000,plain,
% 155.94/155.67 (~P22(f312(f312(f314(x130001),x130002),f189(f861(x130001,a846))))),
% 155.94/155.67 inference(rename_variables,[],[4487])).
% 155.94/155.67 cnf(13001,plain,
% 155.94/155.67 (E(f37(x130011,x130012,x130013,x130014,x130015,x130016,x130017,x130018,x130019,a23),x130012)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(13002,plain,
% 155.94/155.67 (P19(x130021,x130021,f5(x130021),x130022)),
% 155.94/155.67 inference(rename_variables,[],[3449])).
% 155.94/155.67 cnf(13006,plain,
% 155.94/155.67 (E(f37(x130061,x130062,x130063,x130064,x130065,x130066,x130067,x130068,x130069,a23),x130062)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(13012,plain,
% 155.94/155.67 (E(f37(x130121,x130122,x130123,x130124,x130125,x130126,x130127,x130128,x130129,a23),x130122)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.67 cnf(13013,plain,
% 155.94/155.67 (P22(f312(f312(f227(a1),x130131),x130131))),
% 155.94/155.67 inference(rename_variables,[],[3206])).
% 155.94/155.67 cnf(13016,plain,
% 155.94/155.67 (E(f37(x130161,x130162,x130163,x130164,x130165,x130166,x130167,x130168,x130169,a23),x130162)),
% 155.94/155.67 inference(rename_variables,[],[4361])).
% 155.94/155.68 cnf(13017,plain,
% 155.94/155.68 (P22(f312(f312(f227(a1),x130171),x130171))),
% 155.94/155.68 inference(rename_variables,[],[3206])).
% 155.94/155.68 cnf(13020,plain,
% 155.94/155.68 (E(f37(x130201,x130202,x130203,x130204,x130205,x130206,x130207,x130208,x130209,a23),x130202)),
% 155.94/155.68 inference(rename_variables,[],[4361])).
% 155.94/155.68 cnf(13024,plain,
% 155.94/155.68 (P22(f312(f312(f228(a853),x130241),f312(a126,x130241)))),
% 155.94/155.68 inference(rename_variables,[],[3274])).
% 155.94/155.68 cnf(13026,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),x130261),x130261))),
% 155.94/155.68 inference(rename_variables,[],[3205])).
% 155.94/155.68 cnf(13027,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),f2(a853)),x130271))),
% 155.94/155.68 inference(rename_variables,[],[3226])).
% 155.94/155.68 cnf(13030,plain,
% 155.94/155.68 (P22(f312(f312(f228(a853),x130301),f312(a126,x130301)))),
% 155.94/155.68 inference(rename_variables,[],[3274])).
% 155.94/155.68 cnf(13032,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),x130321),x130321))),
% 155.94/155.68 inference(rename_variables,[],[3205])).
% 155.94/155.68 cnf(13033,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),f2(a853)),x130331))),
% 155.94/155.68 inference(rename_variables,[],[3226])).
% 155.94/155.68 cnf(13037,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),f2(a853)),x130371))),
% 155.94/155.68 inference(rename_variables,[],[3226])).
% 155.94/155.68 cnf(13038,plain,
% 155.94/155.68 (P22(f312(f312(f228(a853),f2(a853)),f312(a126,x130381)))),
% 155.94/155.68 inference(rename_variables,[],[3286])).
% 155.94/155.68 cnf(13039,plain,
% 155.94/155.68 (E(f37(x130391,x130392,x130393,x130394,x130395,x130396,x130397,x130398,x130399,a23),x130392)),
% 155.94/155.68 inference(rename_variables,[],[4361])).
% 155.94/155.68 cnf(13044,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),f2(a853)),x130441))),
% 155.94/155.68 inference(rename_variables,[],[3226])).
% 155.94/155.68 cnf(13046,plain,
% 155.94/155.68 (E(f37(x130461,x130462,x130463,x130464,x130465,x130466,x130467,x130468,x130469,a23),x130462)),
% 155.94/155.68 inference(rename_variables,[],[4361])).
% 155.94/155.68 cnf(13050,plain,
% 155.94/155.68 (P22(f312(f312(f314(x130501),x130502),f235(f861(x130501,a846))))),
% 155.94/155.68 inference(rename_variables,[],[3364])).
% 155.94/155.68 cnf(13118,plain,
% 155.94/155.68 (P22(f312(f312(f228(a1),f2(a1)),f312(f84(a1),f87(a1))))),
% 155.94/155.68 inference(scs_inference,[],[4463,3431,3449,10946,11992,12095,12184,12222,12230,12243,12292,12410,12412,12844,12854,12859,12866,12872,12875,12903,13002,3456,12060,12509,12511,3457,12123,3769,10845,12431,12433,12435,12437,3174,12474,12476,3175,12494,4433,4152,12502,12505,3179,12420,3015,3037,12517,3078,12458,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,12351,12402,12404,12408,12418,12424,12429,12439,12444,12465,12472,12486,12492,12723,12890,12919,13001,13006,13012,13016,13020,13039,13046,4362,11222,3511,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,12266,12669,12898,12921,12929,4407,10335,10426,3263,3224,12468,3418,4401,12587,12951,2806,2811,2820,2823,2824,2826,2827,2828,2832,2833,2841,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2905,2909,2917,2925,2928,2935,2939,2940,2943,2947,2952,2957,2958,2959,2960,2961,2962,2965,2986,3100,3077,4383,3546,3187,3247,3933,3159,3533,3784,4374,3138,11496,12246,12250,12254,3147,3259,3664,3974,3039,3040,4403,4421,3725,11256,3262,12446,3108,3069,10175,3579,12480,3063,3876,3085,3586,4348,3048,3027,3053,3084,3218,11735,11944,12079,12295,12371,3264,10703,12057,3136,3137,3157,10379,3312,4495,10307,3841,4423,10172,10332,11311,12210,12247,12251,4432,12218,3194,11591,11594,12815,12925,12976,12980,12984,4485,10878,10951,11166,11169,3190,3313,3532,3302,3277,12452,3103,3104,10237,10534,4469,3370,3094,3018,3146,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,11075,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,3394,4420,11237,3513,3549,3717,4108,3483,12706,12710,12714,12718,12728,3763,12092,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,12342,12583,12614,12626,12668,12689,12745,12751,12928,12933,13024,13030,3656,11487,3189,3286,11604,13038,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,12237,12530,12533,12550,12553,12575,12627,12792,12797,12822,12827,4491,11363,11396,11433,11467,12636,12640,12897,3643,3419,3420,12556,12559,12562,12565,12595,12598,12959,12963,12967,3422,3793,3381,12964,3382,12960,3232,3234,3207,4472,3102,4417,3597,4123,3911,3403,4492,3981,11137,3531,3246,11610,12064,12164,12322,3950,3909,11762,12107,3853,10700,11934,11958,12120,12345,12786,12975,3899,12979,3904,10890,11989,12063,12119,12163,12818,3905,3572,11772,11921,11997,12047,3873,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,12348,12803,12853,12858,4496,10646,11029,12869,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,12315,12576,12601,12678,12685,12692,12697,12700,12703,12736,12748,12808,12831,12834,12948,13026,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,11866,12592,12742,12766,12793,12798,12823,12828,13013,13017,3282,11977,12656,12707,12711,12715,12719,12729,12733,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,12383,12688,3364,10504,10759,10803,11086,11158,11324,12213,12386,12782,12848,12906,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,12374,12396,12655,12672,12675,12771,12849,12894,12913,12916,12956,13000,3268,10531,10561,11115,11665,12299,12316,12637,12641,12644,3308,12942,12997,3299,3721,3661,10218,11490,11518,12619,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,12837,3226,10708,10779,11519,11670,11871,12104,12665,12947,13027,13033,13037,13044,3683,11613,12572,4031,3425,4483,3692,3729,4462,4465,4466,3182,3183,4464,4467,4207,3700,3522,11483,11569,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,12131,3810,11194,11543,11547,11607,12221,12229,12308,12586,12843,12902,3650,10819,10825,10842,11798,12014,12280,12305,3509,11055,12148,12155,12226,12275,12283,12393,3985,3652,10906,11061,11091,11102,12113,12225,12269,12319,12886,3581,11603,3481,10496,10499,10564,10738,3480,4501,11484,4497,12540,4502,10622,10717,11040,11184,11321,12082,12089,12136,12332,4092,10691,12116,12128,12154,3992,3682,12399,4499,10191,10194,10519,10522,11360,11544,12341,4500,11464,11557,3654,10493,10735,12932,3923,4511,4512,4520,4525,4532,4548,4597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% 155.94/155.68 cnf(13136,plain,
% 155.94/155.68 (~P22(f312(f312(f228(a853),f312(a126,f312(f312(f89(a853),x131361),x131362))),f312(a126,x131362)))),
% 155.94/155.68 inference(scs_inference,[],[4463,3431,3449,10946,11992,12095,12184,12222,12230,12243,12292,12410,12412,12844,12854,12859,12866,12872,12875,12903,13002,3456,12060,12509,12511,3457,12123,3769,10845,12431,12433,12435,12437,3174,12474,12476,3175,12494,4433,4152,12502,12505,3179,12420,3015,3037,12517,3078,12458,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,12351,12402,12404,12408,12418,12424,12429,12439,12444,12465,12472,12486,12492,12723,12890,12919,13001,13006,13012,13016,13020,13039,13046,4362,11222,3511,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,12266,12669,12898,12921,12929,4407,10335,10426,3263,3224,12468,3418,4401,12587,12951,2806,2811,2820,2823,2824,2826,2827,2828,2832,2833,2841,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2905,2909,2917,2925,2928,2935,2939,2940,2943,2947,2952,2957,2958,2959,2960,2961,2962,2965,2986,3100,3077,4383,3546,3187,3247,3933,3159,3533,3784,4374,3138,11496,12246,12250,12254,3147,3259,3664,3974,3039,3040,4403,4421,3725,11256,3262,12446,3108,3069,10175,3579,12480,3063,3876,3085,3586,4348,3048,3027,3053,3084,3218,11735,11944,12079,12295,12371,3264,10703,12057,3136,3137,3157,10379,3312,4495,10307,3841,4423,10172,10332,11311,12210,12247,12251,4432,12218,3194,11591,11594,12815,12925,12976,12980,12984,4485,10878,10951,11166,11169,3190,3313,3532,3302,3277,12452,3103,3104,10237,10534,4469,3370,3094,3018,3146,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,11075,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,3394,4420,11237,3513,3549,3717,4108,3483,12706,12710,12714,12718,12728,3763,12092,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,12342,12583,12614,12626,12668,12689,12745,12751,12928,12933,13024,13030,3656,11487,3189,3286,11604,13038,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,12237,12530,12533,12550,12553,12575,12627,12792,12797,12822,12827,4491,11363,11396,11433,11467,12636,12640,12897,3643,3419,3420,12556,12559,12562,12565,12595,12598,12959,12963,12967,3422,3793,3381,12964,3382,12960,3232,3234,3207,4472,3102,4417,3597,4123,3911,3403,4492,3981,11137,3531,3246,11610,12064,12164,12322,3950,3909,11762,12107,3853,10700,11934,11958,12120,12345,12786,12975,3899,12979,3904,10890,11989,12063,12119,12163,12818,3905,3572,11772,11921,11997,12047,3873,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,12348,12803,12853,12858,4496,10646,11029,12869,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,12315,12576,12601,12678,12685,12692,12697,12700,12703,12736,12748,12808,12831,12834,12948,13026,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,11866,12592,12742,12766,12793,12798,12823,12828,13013,13017,3282,11977,12656,12707,12711,12715,12719,12729,12733,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,12383,12688,3364,10504,10759,10803,11086,11158,11324,12213,12386,12782,12848,12906,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,12374,12396,12655,12672,12675,12771,12849,12894,12913,12916,12956,13000,3268,10531,10561,11115,11665,12299,12316,12637,12641,12644,3308,12942,12997,3299,3721,3661,10218,11490,11518,12619,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,12837,3226,10708,10779,11519,11670,11871,12104,12665,12947,13027,13033,13037,13044,3683,11613,12572,4031,3425,4483,3692,3729,4462,4465,4466,3182,3183,4464,4467,4207,3700,3522,11483,11569,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,12131,3810,11194,11543,11547,11607,12221,12229,12308,12586,12843,12902,3650,10819,10825,10842,11798,12014,12280,12305,3509,11055,12148,12155,12226,12275,12283,12393,3985,3652,10906,11061,11091,11102,12113,12225,12269,12319,12886,3581,11603,3481,10496,10499,10564,10738,3480,4501,11484,4497,12540,4502,10622,10717,11040,11184,11321,12082,12089,12136,12332,4092,10691,12116,12128,12154,3992,3682,12399,4499,10191,10194,10519,10522,11360,11544,12341,4500,11464,11557,3654,10493,10735,12932,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322,9326,9329,9330,9345,9359,9368,9379,9392,9393,9397,9399,9423,9541,9584,9628,9672,9788,9789,9848,9918,9992,10007,10012,3,2560,2563,2566,2570,2571,2572,2573,2577,2582,2584,2586,2587,2588,2589,2592,2594,2595,2596,2597,2603,2606,2607,2608,2613,2615,2616,2617,2619,2621,2624,2625,2627,2628,2630,2631,2638,2662,2663,2665,2667,2673,2674,2682,2686,2687,2688,2697,2698,2699,2710,2724,2727,2728,2734,2735,2736,2737,2746,2748,2750,2753,2754,2755,2759,2761,2762,2764,2769,2770,2783,2790,2791,5222,5394,5400,5401,5475,5521,5550,5579,5655,5657,5663,5720,5721,5722,5723,5729,5758,5889,5941,5960,5994,6031,6176,6183,6217,6218,6234,6238,6240,6247,6248,6249,6250,6251,6252,6253,6254,6335,6401,6402,6483,6517,6518,6559,6560,6697,6726,6778,6779,6783,6805,6830,6838,6840,6889,6917,6918,6934,6935,6936,6971,7015,7016,7115,7173,7174,7175,7176,7189,7216,7272,7273,7281,7289,7291,7303,7333,7334,7335,7336,7478,7479,7486,7488,7489,7490,7700,7702,7703,7719,7758,7869,7925,7946,7947,7962,8024,8126,8196,8197,8199,8237,8299,8300,8399,8400,8401,8402,8545,8754,8777,8778,8827,8856,8871,8929,8930,9044,9077,9100,9135,9178,9335,9366,9622,9817,9875,9878,5547,5955,6316,6317,6405,6424,6425,6476,6829,7050,8473,8695,8884,8885,8956,8957,9225,9226,9227,9228,9426,9691,10055,10056,6386,7268,7520,7521,8290,8291,8744,8761,9555,9692,10054,4558,4589,4591,4592,4651,4661,4794,4808,4809,4839,4840,4870,4922,4978,4982,5042,5094,5122,5158,5161,5165,5167,5168,5193,5263,5284,5415,5482,5483,5605,5606,5628,5629,5633,5683,5689,5698,5704,5771])).
% 155.94/155.68 cnf(13142,plain,
% 155.94/155.68 (~E(f312(f183(x131421,a1,x131422,f189(f861(x131421,a846))),x131423),f312(f219(a1),f318(f181(x131421,a1,f183(x131421,a1,x131422,f189(f861(x131421,a846)))))))),
% 155.94/155.68 inference(scs_inference,[],[4463,3431,3449,10946,11992,12095,12184,12222,12230,12243,12292,12410,12412,12844,12854,12859,12866,12872,12875,12903,13002,3456,12060,12509,12511,3457,12123,3769,10845,12431,12433,12435,12437,3174,12474,12476,3175,12494,4433,4152,12502,12505,3179,12420,3015,3037,12517,3078,12458,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,12351,12402,12404,12408,12418,12424,12429,12439,12444,12465,12472,12486,12492,12723,12890,12919,13001,13006,13012,13016,13020,13039,13046,4362,11222,3511,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,12266,12669,12898,12921,12929,4407,10335,10426,3263,3224,12468,3418,4401,12587,12951,2806,2811,2820,2823,2824,2826,2827,2828,2832,2833,2841,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2905,2909,2917,2925,2928,2935,2939,2940,2943,2947,2952,2957,2958,2959,2960,2961,2962,2965,2986,3100,3077,4383,3546,3187,3247,3933,3159,3533,3784,4374,3138,11496,12246,12250,12254,3147,3259,3664,3974,3039,3040,4403,4421,3725,11256,3262,12446,3108,3069,10175,3579,12480,3063,3876,3085,3586,4348,3048,3027,3053,3084,3218,11735,11944,12079,12295,12371,3264,10703,12057,3136,3137,3157,10379,3312,4495,10307,3841,4423,10172,10332,11311,12210,12247,12251,4432,12218,3194,11591,11594,12815,12925,12976,12980,12984,4485,10878,10951,11166,11169,3190,3313,3532,3302,3277,12452,3103,3104,10237,10534,4469,3370,3094,3018,3146,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,11075,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,3394,4420,11237,3513,3549,3717,4108,3483,12706,12710,12714,12718,12728,3763,12092,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,12342,12583,12614,12626,12668,12689,12745,12751,12928,12933,13024,13030,3656,11487,3189,3286,11604,13038,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,12237,12530,12533,12550,12553,12575,12627,12792,12797,12822,12827,4491,11363,11396,11433,11467,12636,12640,12897,3643,3419,3420,12556,12559,12562,12565,12595,12598,12959,12963,12967,3422,3793,3381,12964,3382,12960,3232,3234,3207,4472,3102,4417,3597,4123,3911,3403,4492,3981,11137,3531,3246,11610,12064,12164,12322,3950,3909,11762,12107,3853,10700,11934,11958,12120,12345,12786,12975,3899,12979,3904,10890,11989,12063,12119,12163,12818,3905,3572,11772,11921,11997,12047,3873,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,12348,12803,12853,12858,4496,10646,11029,12869,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,12315,12576,12601,12678,12685,12692,12697,12700,12703,12736,12748,12808,12831,12834,12948,13026,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,11866,12592,12742,12766,12793,12798,12823,12828,13013,13017,3282,11977,12656,12707,12711,12715,12719,12729,12733,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,12383,12688,3364,10504,10759,10803,11086,11158,11324,12213,12386,12782,12848,12906,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,12374,12396,12655,12672,12675,12771,12849,12894,12913,12916,12956,13000,3268,10531,10561,11115,11665,12299,12316,12637,12641,12644,3308,12942,12997,3299,3721,3661,10218,11490,11518,12619,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,12837,3226,10708,10779,11519,11670,11871,12104,12665,12947,13027,13033,13037,13044,3683,11613,12572,4031,3425,4483,3692,3729,4462,4465,4466,3182,3183,4464,4467,4207,3700,3522,11483,11569,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,12131,3810,11194,11543,11547,11607,12221,12229,12308,12586,12843,12902,3650,10819,10825,10842,11798,12014,12280,12305,3509,11055,12148,12155,12226,12275,12283,12393,3985,3652,10906,11061,11091,11102,12113,12225,12269,12319,12886,3581,11603,3481,10496,10499,10564,10738,3480,4501,11484,4497,12540,4502,10622,10717,11040,11184,11321,12082,12089,12136,12332,4092,10691,12116,12128,12154,3992,3682,12399,4499,10191,10194,10519,10522,11360,11544,12341,4500,11464,11557,3654,10493,10735,12932,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322,9326,9329,9330,9345,9359,9368,9379,9392,9393,9397,9399,9423,9541,9584,9628,9672,9788,9789,9848,9918,9992,10007,10012,3,2560,2563,2566,2570,2571,2572,2573,2577,2582,2584,2586,2587,2588,2589,2592,2594,2595,2596,2597,2603,2606,2607,2608,2613,2615,2616,2617,2619,2621,2624,2625,2627,2628,2630,2631,2638,2662,2663,2665,2667,2673,2674,2682,2686,2687,2688,2697,2698,2699,2710,2724,2727,2728,2734,2735,2736,2737,2746,2748,2750,2753,2754,2755,2759,2761,2762,2764,2769,2770,2783,2790,2791,5222,5394,5400,5401,5475,5521,5550,5579,5655,5657,5663,5720,5721,5722,5723,5729,5758,5889,5941,5960,5994,6031,6176,6183,6217,6218,6234,6238,6240,6247,6248,6249,6250,6251,6252,6253,6254,6335,6401,6402,6483,6517,6518,6559,6560,6697,6726,6778,6779,6783,6805,6830,6838,6840,6889,6917,6918,6934,6935,6936,6971,7015,7016,7115,7173,7174,7175,7176,7189,7216,7272,7273,7281,7289,7291,7303,7333,7334,7335,7336,7478,7479,7486,7488,7489,7490,7700,7702,7703,7719,7758,7869,7925,7946,7947,7962,8024,8126,8196,8197,8199,8237,8299,8300,8399,8400,8401,8402,8545,8754,8777,8778,8827,8856,8871,8929,8930,9044,9077,9100,9135,9178,9335,9366,9622,9817,9875,9878,5547,5955,6316,6317,6405,6424,6425,6476,6829,7050,8473,8695,8884,8885,8956,8957,9225,9226,9227,9228,9426,9691,10055,10056,6386,7268,7520,7521,8290,8291,8744,8761,9555,9692,10054,4558,4589,4591,4592,4651,4661,4794,4808,4809,4839,4840,4870,4922,4978,4982,5042,5094,5122,5158,5161,5165,5167,5168,5193,5263,5284,5415,5482,5483,5605,5606,5628,5629,5633,5683,5689,5698,5704,5771,5847,5916,5977])).
% 155.94/155.68 cnf(13146,plain,
% 155.94/155.68 (~P22(f312(f70(x131461),f48(f861(x131461,a846),f235(f861(f861(x131461,a846),a846)))))),
% 155.94/155.68 inference(scs_inference,[],[4463,3431,3449,10946,11992,12095,12184,12222,12230,12243,12292,12410,12412,12844,12854,12859,12866,12872,12875,12903,13002,3456,12060,12509,12511,3457,12123,3769,10845,12431,12433,12435,12437,3174,12474,12476,3175,12494,4433,4152,12502,12505,3179,12420,3015,3037,12517,3078,12458,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,12351,12402,12404,12408,12418,12424,12429,12439,12444,12465,12472,12486,12492,12723,12890,12919,13001,13006,13012,13016,13020,13039,13046,4362,11222,3511,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,12266,12669,12898,12921,12929,4407,10335,10426,3263,3224,12468,3418,4401,12587,12951,2806,2811,2820,2823,2824,2826,2827,2828,2832,2833,2841,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2905,2909,2917,2925,2928,2935,2939,2940,2943,2947,2952,2957,2958,2959,2960,2961,2962,2965,2986,3100,3077,4383,3546,3187,3247,3933,3159,3533,3784,4374,3138,11496,12246,12250,12254,3147,3259,3664,3974,3039,3040,4403,4421,3725,11256,3262,12446,3108,3069,10175,3579,12480,3063,3876,3085,3586,4348,3048,3027,3053,3084,3218,11735,11944,12079,12295,12371,3264,10703,12057,3136,3137,3157,10379,3312,4495,10307,3841,4423,10172,10332,11311,12210,12247,12251,4432,12218,3194,11591,11594,12815,12925,12976,12980,12984,4485,10878,10951,11166,11169,3190,3313,3532,3302,3277,12452,3103,3104,10237,10534,4469,3370,3094,3018,3146,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,11075,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,3394,4420,11237,3513,3549,3717,4108,3483,12706,12710,12714,12718,12728,3763,12092,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,12342,12583,12614,12626,12668,12689,12745,12751,12928,12933,13024,13030,3656,11487,3189,3286,11604,13038,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,12237,12530,12533,12550,12553,12575,12627,12792,12797,12822,12827,4491,11363,11396,11433,11467,12636,12640,12897,3643,3419,3420,12556,12559,12562,12565,12595,12598,12959,12963,12967,3422,3793,3381,12964,3382,12960,3232,3234,3207,4472,3102,4417,3597,4123,3911,3403,4492,3981,11137,3531,3246,11610,12064,12164,12322,3950,3909,11762,12107,3853,10700,11934,11958,12120,12345,12786,12975,3899,12979,3904,10890,11989,12063,12119,12163,12818,3905,3572,11772,11921,11997,12047,3873,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,12348,12803,12853,12858,4496,10646,11029,12869,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,12315,12576,12601,12678,12685,12692,12697,12700,12703,12736,12748,12808,12831,12834,12948,13026,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,11866,12592,12742,12766,12793,12798,12823,12828,13013,13017,3282,11977,12656,12707,12711,12715,12719,12729,12733,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,12383,12688,3364,10504,10759,10803,11086,11158,11324,12213,12386,12782,12848,12906,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,12374,12396,12655,12672,12675,12771,12849,12894,12913,12916,12956,13000,3268,10531,10561,11115,11665,12299,12316,12637,12641,12644,3308,12942,12997,3299,3721,3661,10218,11490,11518,12619,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,12837,3226,10708,10779,11519,11670,11871,12104,12665,12947,13027,13033,13037,13044,3683,11613,12572,4031,3425,4483,3692,3729,4462,4465,4466,3182,3183,4464,4467,4207,3700,3522,11483,11569,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,12131,3810,11194,11543,11547,11607,12221,12229,12308,12586,12843,12902,3650,10819,10825,10842,11798,12014,12280,12305,3509,11055,12148,12155,12226,12275,12283,12393,3985,3652,10906,11061,11091,11102,12113,12225,12269,12319,12886,3581,11603,3481,10496,10499,10564,10738,3480,4501,11484,4497,12540,4502,10622,10717,11040,11184,11321,12082,12089,12136,12332,4092,10691,12116,12128,12154,3992,3682,12399,4499,10191,10194,10519,10522,11360,11544,12341,4500,11464,11557,3654,10493,10735,12932,3923,4511,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4905,4906,4923,4924,4937,4940,4961,4968,4985,4988,4989,4990,4995,4996,5019,5045,5046,5056,5061,5069,5114,5115,5123,5133,5137,5139,5149,5151,5157,5160,5175,5182,5185,5186,5190,5224,5236,5243,5245,5246,5249,5250,5251,5258,5260,5262,5266,5267,5268,5275,5279,5280,5281,5289,5293,5298,5310,5318,5330,5332,5340,5341,5345,5349,5372,5375,5381,5391,5392,5407,5440,5446,5462,5463,5466,5487,5495,5496,5501,5502,5512,5514,5527,5531,5542,5543,5544,5546,5562,5567,5580,5581,5590,5597,5609,5612,5613,5619,5620,5621,5624,5625,5630,5667,5668,5671,5674,5675,5677,5679,5681,5686,5693,5706,5724,5725,5734,5735,5740,5745,5747,5750,5794,5806,5814,5817,5821,5829,5832,5839,5853,5859,5877,5880,5892,5926,5927,5940,5961,5980,5981,5984,5997,5999,6000,6002,6014,6017,6018,6020,6023,6024,6035,6040,6042,6047,6086,6087,6094,6104,6145,6147,6149,6151,6157,6159,6161,6167,6169,6175,6178,6186,6193,6194,6195,6201,6223,6229,6233,6270,6271,6274,6275,6276,6277,6278,6279,6280,6288,6318,6319,6326,6329,6330,6350,6370,6373,6384,6385,6391,6404,6421,6422,6423,6433,6527,6551,6598,6613,6622,6623,6624,6625,6646,6647,6654,6665,6668,6670,6672,6673,6674,6676,6690,6699,6701,6702,6714,6717,6765,6775,6777,6781,6795,6796,6834,6842,6847,6877,6916,6968,7000,7051,7075,7084,7088,7140,7150,7196,7198,7215,7223,7226,7227,7248,7254,7255,7304,7313,7316,7331,7381,7382,7386,7428,7429,7447,7515,7535,7556,7579,7594,7609,7618,7627,7628,7658,7660,7662,7671,7709,7721,7747,7801,7831,7862,7906,7922,7938,7939,8016,8071,8088,8113,8133,8153,8158,8246,8260,8262,8267,8283,8287,8303,8306,8327,8338,8340,8357,8363,8366,8392,8406,8407,8422,8423,8428,8429,8430,8431,8432,8451,8452,8453,8463,8464,8478,8480,8494,8498,8500,8501,8502,8509,8513,8537,8538,8567,8580,8584,8602,8624,8625,8626,8627,8640,8641,8664,8674,8683,8684,8685,8686,8688,8708,8709,8720,8763,8769,8775,8788,8790,8792,8795,8796,8800,8809,8895,8926,8927,8928,8943,8959,8965,8991,8992,9034,9037,9062,9105,9106,9107,9123,9149,9162,9168,9172,9195,9196,9223,9282,9318,9319,9320,9346,9347,9363,9380,9386,9404,9425,9447,9454,9455,9456,9457,9472,9474,9479,9512,9513,9519,9558,9559,9587,9598,9608,9610,9611,9621,9635,9664,9695,9701,9759,9805,9806,9818,9819,9839,9844,9867,9872,9891,9941,10071,10087,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4857,4858,4871,4893,4943,4944,4947,4948,4950,4952,4964,4965,4975,4986,4987,4993,5012,5013,5033,5038,5039,5040,5041,5044,5052,5055,5062,5063,5064,5129,5135,5136,5143,5172,5183,5188,5204,5207,5223,5230,5231,5232,5240,5255,5256,5257,5264,5271,5272,5285,5286,5287,5288,5290,5291,5294,5295,5296,5297,5326,5327,5328,5336,5337,5338,5339,5386,5388,5390,5425,5427,5428,5430,5431,5433,5434,5436,5445,5450,5452,5453,5454,5455,5456,5457,5464,5474,5478,5479,5490,5506,5507,5510,5520,5523,5524,5525,5554,5564,5582,5583,5591,5592,5594,5596,5632,5637,5639,5694,5726,5727,5731,5736,5737,5738,5739,5746,5756,5757,5759,5760,5768,5775,5791,5820,5835,5838,5840,5849,5851,5870,5871,5872,5875,5876,5896,5910,5911,5942,5943,5963,5966,5988,5993,6015,6019,6026,6034,6039,6041,6051,6052,6053,6054,6089,6105,6143,6160,6196,6197,6199,6219,6220,6222,6225,6226,6236,6245,6263,6282,6283,6289,6299,6309,6333,6338,6340,6354,6355,6358,6359,6361,6363,6364,6365,6367,6369,6372,6378,6379,6380,6381,6387,6389,6394,6429,6432,6445,6448,6449,6450,6451,6485,6490,6492,6497,6498,6506,6510,6523,6547,6548,6549,6550,6562,6566,6579,6586,6590,6592,6641,6642,6643,6648,6651,6682,6684,6686,6688,6691,6696,6709,6718,6751,6754,6755,6768,6769,6770,6771,6787,6788,6804,6825,6826,6832,6853,6866,6868,6869,6871,6873,6874,6881,6899,6913,6914,6919,6920,6921,6922,6924,6926,6959,6960,6972,6979,6981,6982,6983,7012,7021,7032,7041,7054,7055,7060,7062,7063,7069,7078,7092,7126,7128,7143,7151,7192,7197,7222,7267,7301,7314,7330,7361,7362,7365,7366,7390,7413,7430,7433,7434,7444,7463,7464,7466,7468,7470,7472,7519,7523,7524,7555,7557,7558,7559,7564,7586,7605,7615,7624,7636,7637,7639,7659,7668,7669,7692,7711,7759,7760,7802,7811,7833,7850,7851,7914,7915,7916,7941,7974,7981,7983,7991,8000,8004,8039,8045,8052,8066,8089,8112,8156,8186,8198,8216,8219,8254,8274,8341,8342,8347,8349,8367,8455,8456,8457,8458,8489,8516,8541,8583,8601,8658,8701,8704,8717,8724,8760,8781,8805,8806,8823,8824,8970,8989,8999,9023,9025,9028,9032,9035,9036,9067,9073,9085,9134,9154,9173,9208,9209,9215,9251,9274,9279,9315,9322,9326,9329,9330,9345,9359,9368,9379,9392,9393,9397,9399,9423,9541,9584,9628,9672,9788,9789,9848,9918,9992,10007,10012,3,2560,2563,2566,2570,2571,2572,2573,2577,2582,2584,2586,2587,2588,2589,2592,2594,2595,2596,2597,2603,2606,2607,2608,2613,2615,2616,2617,2619,2621,2624,2625,2627,2628,2630,2631,2638,2662,2663,2665,2667,2673,2674,2682,2686,2687,2688,2697,2698,2699,2710,2724,2727,2728,2734,2735,2736,2737,2746,2748,2750,2753,2754,2755,2759,2761,2762,2764,2769,2770,2783,2790,2791,5222,5394,5400,5401,5475,5521,5550,5579,5655,5657,5663,5720,5721,5722,5723,5729,5758,5889,5941,5960,5994,6031,6176,6183,6217,6218,6234,6238,6240,6247,6248,6249,6250,6251,6252,6253,6254,6335,6401,6402,6483,6517,6518,6559,6560,6697,6726,6778,6779,6783,6805,6830,6838,6840,6889,6917,6918,6934,6935,6936,6971,7015,7016,7115,7173,7174,7175,7176,7189,7216,7272,7273,7281,7289,7291,7303,7333,7334,7335,7336,7478,7479,7486,7488,7489,7490,7700,7702,7703,7719,7758,7869,7925,7946,7947,7962,8024,8126,8196,8197,8199,8237,8299,8300,8399,8400,8401,8402,8545,8754,8777,8778,8827,8856,8871,8929,8930,9044,9077,9100,9135,9178,9335,9366,9622,9817,9875,9878,5547,5955,6316,6317,6405,6424,6425,6476,6829,7050,8473,8695,8884,8885,8956,8957,9225,9226,9227,9228,9426,9691,10055,10056,6386,7268,7520,7521,8290,8291,8744,8761,9555,9692,10054,4558,4589,4591,4592,4651,4661,4794,4808,4809,4839,4840,4870,4922,4978,4982,5042,5094,5122,5158,5161,5165,5167,5168,5193,5263,5284,5415,5482,5483,5605,5606,5628,5629,5633,5683,5689,5698,5704,5771,5847,5916,5977,5998,6163])).
% 155.94/155.68 cnf(13154,plain,
% 155.94/155.68 (~P22(f312(f312(f228(a853),f2(a853)),f37(x131541,f2(a853),x131542,x131543,x131544,x131545,x131546,x131547,x131548,a23)))),
% 155.94/155.68 inference(scs_inference,[],[4463,3431,3449,10946,11992,12095,12184,12222,12230,12243,12292,12410,12412,12844,12854,12859,12866,12872,12875,12903,13002,3456,12060,12509,12511,3457,12123,3769,10845,12431,12433,12435,12437,3174,12474,12476,3175,12494,4433,4152,12502,12505,3179,12420,3015,3037,12517,3078,12458,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,12351,12402,12404,12408,12418,12424,12429,12439,12444,12465,12472,12486,12492,12723,12890,12919,13001,13006,13012,13016,13020,13039,13046,4362,11222,3511,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,12266,12669,12898,12921,12929,4407,10335,10426,3263,3224,12468,3418,4401,12587,12951,2806,2811,2820,2823,2824,2826,2827,2828,2832,2833,2841,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2905,2909,2917,2925,2928,2935,2939,2940,2943,2947,2952,2957,2958,2959,2960,2961,2962,2965,2986,3100,3077,4383,3546,3187,3247,3933,3159,3533,3784,4374,3138,11496,12246,12250,12254,3147,3259,3664,3974,3039,3040,4403,4421,3725,11256,3262,12446,3108,3069,10175,3579,12480,3063,3876,3085,3586,4348,3048,3027,3053,3084,3218,11735,11944,12079,12295,12371,3264,10703,12057,3136,3137,3157,10379,3312,4495,10307,3841,4423,10172,10332,11311,12210,12247,12251,4432,12218,3194,11591,11594,12815,12925,12976,12980,12984,4485,10878,10951,11166,11169,3190,3313,3532,3302,3277,12452,3103,3104,10237,10534,4469,3370,3094,3018,3146,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,11075,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,3394,4420,11237,3513,3549,3717,4108,3483,12706,12710,12714,12718,12728,3763,12092,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,12342,12583,12614,12626,12668,12689,12745,12751,12928,12933,13024,13030,3656,11487,3189,3286,11604,13038,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,12237,12530,12533,12550,12553,12575,12627,12792,12797,12822,12827,4491,11363,11396,11433,11467,12636,12640,12897,3643,3419,3420,12556,12559,12562,12565,12595,12598,12959,12963,12967,3422,3793,3381,12964,3382,12960,3232,3234,3207,4472,3102,4417,3597,4123,3911,3403,4492,3981,11137,3531,3246,11610,12064,12164,12322,3950,3909,11762,12107,3853,10700,11934,11958,12120,12345,12786,12975,3899,12979,3904,10890,11989,12063,12119,12163,12818,3905,3572,11772,11921,11997,12047,3873,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,12348,12803,12853,12858,4496,10646,11029,12869,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,12315,12576,12601,12678,12685,12692,12697,12700,12703,12736,12748,12808,12831,12834,12948,13026,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,11866,12592,12742,12766,12793,12798,12823,12828,13013,13017,3282,11977,12656,12707,12711,12715,12719,12729,12733,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,12383,12688,3364,10504,10759,10803,11086,11158,11324,12213,12386,12782,12848,12906,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,12374,12396,12655,12672,12675,12771,12849,12894,12913,12916,12956,13000,3268,10531,10561,11115,11665,12299,12316,12637,12641,12644,3308,12942,12997,3299,3721,3661,10218,11490,11518,12619,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,12837,3226,10708,10779,11519,11670,11871,12104,12665,12947,13027,13033,13037,13044,3683,11613,12572,4031,3425,4483,3692,3729,4462,4465,4466,3182,3183,4464,4467,4207,3700,3522,11483,11569,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,12131,3810,11194,11543,11547,11607,12221,12229,12308,12586,12843,12902,3650,10819,10825,10842,11798,12014,12280,12305,3509,11055,12148,12155,12226,12275,12283,12393,3985,3652,10906,11061,11091,11102,12113,12225,12269,12319,12886,3581,11603,3481,10496,10499,10564,10738,3480,4501,11484,4497,12540,4502,10622,10717,11040,11184,11321,12082,12089,12136,12332,4092,10691,12116,12128,12154,3992,3682,12399,4499,10191,10194,10519,10522,11360,11544,12341,4500,11464,11557,3654,10493,10735,12932,3923,4511,4512,4520,4525,4532,4548,4597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50,6251,6252,6253,6254,6335,6401,6402,6483,6517,6518,6559,6560,6697,6726,6778,6779,6783,6805,6830,6838,6840,6889,6917,6918,6934,6935,6936,6971,7015,7016,7115,7173,7174,7175,7176,7189,7216,7272,7273,7281,7289,7291,7303,7333,7334,7335,7336,7478,7479,7486,7488,7489,7490,7700,7702,7703,7719,7758,7869,7925,7946,7947,7962,8024,8126,8196,8197,8199,8237,8299,8300,8399,8400,8401,8402,8545,8754,8777,8778,8827,8856,8871,8929,8930,9044,9077,9100,9135,9178,9335,9366,9622,9817,9875,9878,5547,5955,6316,6317,6405,6424,6425,6476,6829,7050,8473,8695,8884,8885,8956,8957,9225,9226,9227,9228,9426,9691,10055,10056,6386,7268,7520,7521,8290,8291,8744,8761,9555,9692,10054,4558,4589,4591,4592,4651,4661,4794,4808,4809,4839,4840,4870,4922,4978,4982,5042,5094,5122,5158,5161,5165,5167,5168,5193,5263,5284,5415,5482,5483,5605,5606,5628,5629,5633,5683,5689,5698,5704,5771,5847,5916,5977,5998,6163,6281,6430,6776,6882])).
% 155.94/155.68 cnf(13197,plain,
% 155.94/155.68 (P22(f312(f312(f314(x131971),x131972),f235(f861(x131971,a846))))),
% 155.94/155.68 inference(rename_variables,[],[3364])).
% 155.94/155.68 cnf(13213,plain,
% 155.94/155.68 (~P22(f312(f312(f227(a853),f312(a126,f2(a853))),f312(f312(f21(a853),f312(f312(f89(a853),x132131),f2(a853))),f312(f312(f89(a853),x132131),f2(a853)))))),
% 155.94/155.68 inference(scs_inference,[],[4463,3431,3449,10946,11992,12095,12184,12222,12230,12243,12292,12410,12412,12844,12854,12859,12866,12872,12875,12903,13002,3456,12060,12509,12511,3457,12123,3769,10845,12431,12433,12435,12437,3174,12474,12476,3175,12494,4433,4152,12502,12505,3179,12420,3015,3037,12517,3078,12458,4385,3556,4361,10105,10108,10117,10181,10184,10274,10277,10558,10569,10828,10831,11203,11206,11221,11225,11270,11273,11276,11279,11289,11332,11347,11374,11377,11388,11393,11399,11457,11499,11502,11505,11515,11554,11636,11970,12160,12351,12402,12404,12408,12418,12424,12429,12439,12444,12465,12472,12486,12492,12723,12890,12919,13001,13006,13012,13016,13020,13039,13046,4362,11222,3511,4389,10102,10111,10114,10124,10135,10146,10245,10248,10251,10354,10464,10754,10931,10934,11129,11209,11216,11232,11282,11285,11308,11402,11450,11470,11745,11773,11793,11841,11955,11973,12040,12056,12214,12266,12669,12898,12921,12929,12937,4407,10335,10426,3263,3224,12468,3418,4401,12587,12951,2806,2811,2820,2823,2824,2826,2827,2828,2832,2833,2841,2842,2847,2850,2854,2856,2863,2865,2866,2873,2874,2876,2878,2887,2890,2891,2893,2894,2897,2899,2905,2909,2917,2925,2928,2935,2939,2940,2943,2947,2952,2957,2958,2959,2960,2961,2962,2965,2986,3100,3077,4383,3546,3187,3247,3933,3159,3533,3784,4374,3138,11496,12246,12250,12254,3147,3259,3664,3974,3039,3040,4403,4421,3725,11256,3262,12446,3105,3108,3575,3069,10175,3579,12480,3063,3876,3085,3586,4348,3048,3027,3053,3084,3218,11735,11944,12079,12295,12371,3264,10703,12057,3136,3137,3157,10379,3312,4495,10307,3841,4423,10172,10332,11311,12210,12247,12251,4432,12218,3194,11591,11594,12815,12925,12976,12980,12984,4485,10878,10951,11166,11169,3190,3313,3532,3302,3277,12452,3103,3104,10237,10534,4469,3370,3094,3018,3146,3122,11246,3987,12233,12363,3843,10884,11013,11064,12194,12200,12309,12312,12338,4504,10806,11018,11123,11142,11172,11178,12142,4505,10920,11021,11126,4506,11024,11075,4507,11078,4508,3121,3411,12098,12139,12217,3571,4269,4270,3394,4420,11237,3513,3549,3717,4108,3483,12706,12710,12714,12718,12728,3763,12092,3397,3645,3274,10256,10372,10443,10487,10490,10537,10619,10868,11769,11813,11890,11951,12022,12025,12342,12583,12614,12626,12668,12689,12745,12751,12928,12933,13024,13030,3656,11487,3189,3286,11604,13038,3478,4475,10149,10152,10178,10630,10643,10764,11187,11249,11652,11660,11893,11896,11983,12145,12237,12530,12533,12550,12553,12575,12627,12792,12797,12822,12827,4491,11363,11396,11433,11467,12636,12640,12897,3643,3419,3420,12556,12559,12562,12565,12595,12598,12959,12963,12967,12971,3421,3422,3793,3381,12964,3382,12960,3232,3234,3207,4472,3102,4417,3597,4123,3911,3403,4492,3981,11137,3531,3246,11610,12064,12164,12322,3950,3909,11762,12107,3853,10700,11934,11958,12120,12345,12786,12975,3899,12979,3904,10890,11989,12063,12119,12163,12818,3905,3572,11772,11921,11997,12047,3873,3910,3588,10887,10956,11037,11097,11954,12015,12261,12335,12348,12803,12853,12858,4496,10646,11029,12869,3204,10267,10361,10440,10544,11339,11346,11553,11563,11575,11635,11738,11744,12008,12167,3205,10606,10649,10652,10685,10711,10748,10786,10822,11816,11819,11822,11825,12028,12031,12034,12037,12103,12272,12315,12576,12601,12678,12685,12692,12697,12700,12703,12736,12748,12808,12831,12834,12948,13026,13032,3206,10348,10549,10625,10751,11405,11446,11639,11655,11748,11759,11780,11785,11801,11828,11846,11861,11866,12592,12742,12766,12793,12798,12823,12828,13013,13017,3282,11977,12656,12707,12711,12715,12719,12729,12733,4471,10215,10300,10351,10435,10667,10714,10724,11412,11514,11534,11537,11540,11560,11696,11699,11702,11705,11792,11812,11831,11840,11905,11908,11911,11914,11984,12071,12074,12170,12173,12236,12265,12298,12383,12688,3364,10504,10759,10803,11086,11158,11324,12213,12386,12782,12848,12906,13050,13197,4487,10676,10688,10795,10813,10816,10881,10970,10978,10994,11032,11049,11058,11094,11132,11152,11155,11181,11588,11616,11899,11902,11939,11978,12011,12151,12191,12197,12284,12287,12302,12362,12368,12374,12396,12655,12672,12675,12771,12849,12894,12913,12916,12956,13000,3268,10531,10561,11115,11665,12299,12316,12637,12641,12644,3308,12942,12997,3299,3721,3661,10218,11490,11518,12619,4484,10169,10525,10528,10973,10991,11449,11456,11548,11671,11708,11711,11714,11717,12837,3226,10708,10779,11519,11670,11871,12104,12665,12947,13027,13033,13037,13044,3683,11613,12572,4031,3425,4483,3692,3729,4462,4465,4466,3182,3183,4464,4467,4207,3700,3522,11483,11569,12878,4128,4498,10140,10143,10397,10446,10451,10853,11318,11572,11674,4503,11052,11163,11197,3916,12131,3810,11194,11543,11547,11607,12221,12229,12308,12586,12843,12902,3650,10819,10825,10842,11798,12014,12280,12305,3509,11055,12148,12155,12226,12275,12283,12393,3985,3652,10906,11061,11091,11102,12113,12225,12269,12319,12886,3581,11603,3481,10496,10499,10564,10738,3480,4501,11484,4497,12540,4502,10622,10717,11040,11184,11321,12082,12089,12136,12332,4092,10691,12116,12128,12154,12865,3992,3682,12399,4499,10191,10194,10519,10522,11360,11544,12341,4500,11464,11557,3654,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6031,6176,6183,6217,6218,6234,6238,6240,6247,6248,6249,6250,6251,6252,6253,6254,6335,6401,6402,6483,6517,6518,6559,6560,6697,6726,6778,6779,6783,6805,6830,6838,6840,6889,6917,6918,6934,6935,6936,6971,7015,7016,7115,7173,7174,7175,7176,7189,7216,7272,7273,7281,7289,7291,7303,7333,7334,7335,7336,7478,7479,7486,7488,7489,7490,7700,7702,7703,7719,7758,7869,7925,7946,7947,7962,8024,8126,8196,8197,8199,8237,8299,8300,8399,8400,8401,8402,8545,8754,8777,8778,8827,8856,8871,8929,8930,9044,9077,9100,9135,9178,9335,9366,9622,9817,9875,9878,5547,5955,6316,6317,6405,6424,6425,6476,6829,7050,8473,8695,8884,8885,8956,8957,9225,9226,9227,9228,9426,9691,10055,10056,6386,7268,7520,7521,8290,8291,8744,8761,9555,9692,10054,4558,4589,4591,4592,4651,4661,4794,4808,4809,4839,4840,4870,4922,4978,4982,5042,5094,5122,5158,5161,5165,5167,5168,5193,5263,5284,5415,5482,5483,5605,5606,5628,5629,5633,5683,5689,5698,5704,5771,5847,5916,5977,5998,6163,6281,6430,6776,6882,7058,7341,7676,7678,7841,7843,7844,7923,8960,9192,4824,4872,5006,5894,5923,5934,5965,6216,6296,6636,7077,7234,7300,7375,7663])).
% 155.94/155.68 cnf(13275,plain,
% 155.94/155.68 (E(f38(x132751,x132752,x132753,x132754,x132755,x132756,x132757,x132758,x132759,a23),x132752)),
% 155.94/155.68 inference(rename_variables,[],[4362])).
% 155.94/155.68 cnf(13284,plain,
% 155.94/155.68 (~E(f312(f312(f115(a853),f312(a126,x132841)),x132841),f312(a126,x132841))),
% 155.94/155.68 inference(rename_variables,[],[11381])).
% 155.94/155.68 cnf(13287,plain,
% 155.94/155.68 (~P22(f312(f312(f314(f860(x132871,x132871)),x132872),f237(x132871,f189(f861(x132871,a846)))))),
% 155.94/155.68 inference(rename_variables,[],[10812])).
% 155.94/155.68 cnf(13290,plain,
% 155.94/155.68 (~E(f312(f312(f147(x132901),x132902),x132903),x132903)),
% 155.94/155.68 inference(rename_variables,[],[4423])).
% 155.94/155.68 cnf(13293,plain,
% 155.94/155.68 (E(f38(x132931,x132932,x132933,x132934,x132935,x132936,x132937,x132938,x132939,a23),x132932)),
% 155.94/155.68 inference(rename_variables,[],[4362])).
% 155.94/155.68 cnf(13296,plain,
% 155.94/155.68 (~E(f312(a126,x132961),f2(a853))),
% 155.94/155.68 inference(rename_variables,[],[4401])).
% 155.94/155.68 cnf(13299,plain,
% 155.94/155.68 (P22(f312(f312(f227(a1),x132991),x132991))),
% 155.94/155.68 inference(rename_variables,[],[3206])).
% 155.94/155.68 cnf(13302,plain,
% 155.94/155.68 (P22(f312(f312(f227(f861(x133021,a846)),f312(f168(x133021),f166(x133021,x133022,x133023))),f312(f168(x133021),x133023)))),
% 155.94/155.68 inference(rename_variables,[],[3904])).
% 155.94/155.68 cnf(13310,plain,
% 155.94/155.68 (~P22(f312(f312(f314(x133101),x133102),f189(f861(x133101,a846))))),
% 155.94/155.68 inference(rename_variables,[],[4487])).
% 155.94/155.68 cnf(13317,plain,
% 155.94/155.68 (~P22(f312(f312(f314(x133171),x133172),f189(f861(x133171,a846))))),
% 155.94/155.68 inference(rename_variables,[],[4487])).
% 155.94/155.68 cnf(13320,plain,
% 155.94/155.68 (~P22(f312(f312(f228(a853),f312(f312(f89(a853),x133201),x133202)),x133201))),
% 155.94/155.68 inference(rename_variables,[],[4500])).
% 155.94/155.68 cnf(13323,plain,
% 155.94/155.68 (P39(x133231,x133232,x133233,f312(f312(f150(x133234,x133231),x133235),f37(x133236,f127(x133234),x133237,x133238,x133239,x1332310,x1332311,x1332312,x1332313,a23)),f127(x133232))),
% 155.94/155.68 inference(rename_variables,[],[11070])).
% 155.94/155.68 cnf(13328,plain,
% 155.94/155.68 (~P22(f312(f312(f314(x133281),x133282),f189(f861(x133281,a846))))),
% 155.94/155.68 inference(rename_variables,[],[4487])).
% 155.94/155.68 cnf(13335,plain,
% 155.94/155.68 (~P22(f312(f312(f314(x133351),x133352),f189(f861(x133351,a846))))),
% 155.94/155.68 inference(rename_variables,[],[4487])).
% 155.94/155.68 cnf(13338,plain,
% 155.94/155.68 (~P22(f312(f312(f314(a853),x133381),f312(f279(a853),f2(a853))))),
% 155.94/155.68 inference(rename_variables,[],[11628])).
% 155.94/155.68 cnf(13357,plain,
% 155.94/155.68 (P22(f312(f312(f227(f861(x133571,a846)),x133572),x133572))),
% 155.94/155.68 inference(rename_variables,[],[3509])).
% 155.94/155.68 cnf(13364,plain,
% 155.94/155.68 (E(f38(x133641,x133642,x133643,x133644,x133645,x133646,x133647,x133648,x133649,a23),x133642)),
% 155.94/155.68 inference(rename_variables,[],[4362])).
% 155.94/155.68 cnf(13371,plain,
% 155.94/155.68 (E(f38(x133711,x133712,x133713,x133714,x133715,x133716,x133717,x133718,x133719,a23),x133712)),
% 155.94/155.68 inference(rename_variables,[],[4362])).
% 155.94/155.68 cnf(13376,plain,
% 155.94/155.68 (~P22(f312(f312(f189(f861(x133761,f861(x133762,a846))),x133763),x133764))),
% 155.94/155.68 inference(rename_variables,[],[4502])).
% 155.94/155.68 cnf(13379,plain,
% 155.94/155.68 (E(f312(x133791,f740(f312(x133791,x133792),f312(f219(x133793),x133792),x133791,x133794,x133793)),f312(x133791,x133792))),
% 155.94/155.68 inference(rename_variables,[],[11004])).
% 155.94/155.68 cnf(13390,plain,
% 155.94/155.68 (P22(f312(f312(f228(a1),f312(f312(f21(a1),x133901),f87(a1))),x133901))),
% 155.94/155.68 inference(rename_variables,[],[10624])).
% 155.94/155.68 cnf(13397,plain,
% 155.94/155.68 (P22(f312(f312(f228(a1),f312(f312(f21(a1),x133971),f87(a1))),x133971))),
% 155.94/155.68 inference(rename_variables,[],[10624])).
% 155.94/155.68 cnf(13402,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),x134021),x134021))),
% 155.94/155.68 inference(rename_variables,[],[3205])).
% 155.94/155.68 cnf(13412,plain,
% 155.94/155.68 (~P22(f312(f312(f314(x134121),x134122),f189(f861(x134121,a846))))),
% 155.94/155.68 inference(rename_variables,[],[4487])).
% 155.94/155.68 cnf(13432,plain,
% 155.94/155.68 (E(f38(x134321,x134322,x134323,x134324,x134325,x134326,x134327,x134328,x134329,a23),x134322)),
% 155.94/155.68 inference(rename_variables,[],[4362])).
% 155.94/155.68 cnf(13440,plain,
% 155.94/155.68 (E(f312(f312(f89(a1),f312(f312(f89(a1),f312(f312(f90(a1),f312(f47(a1,x134401),x134402)),x134402)),f54(a1,x134401,x134402))),x134403),f312(f312(f89(a1),x134401),x134403))),
% 155.94/155.68 inference(rename_variables,[],[4108])).
% 155.94/155.68 cnf(13450,plain,
% 155.94/155.68 (P22(f312(f312(f228(a1),f312(f312(f21(a1),x134501),f87(a1))),x134501))),
% 155.94/155.68 inference(rename_variables,[],[10624])).
% 155.94/155.68 cnf(13453,plain,
% 155.94/155.68 (~P22(f312(f312(f314(a853),x134531),f312(f279(a853),f2(a853))))),
% 155.94/155.68 inference(rename_variables,[],[11628])).
% 155.94/155.68 cnf(13456,plain,
% 155.94/155.68 (~P22(f312(f312(f227(a853),f312(a126,x134561)),x134561))),
% 155.94/155.68 inference(rename_variables,[],[4484])).
% 155.94/155.68 cnf(13466,plain,
% 155.94/155.68 (P22(f312(f312(f227(f861(x134661,a846)),x134662),x134662))),
% 155.94/155.68 inference(rename_variables,[],[3509])).
% 155.94/155.68 cnf(13469,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),x134691),f312(f312(f89(a853),x134691),x134692)))),
% 155.94/155.68 inference(rename_variables,[],[3480])).
% 155.94/155.68 cnf(13472,plain,
% 155.94/155.68 (~E(f312(f312(f147(x134721),x134722),x134723),x134723)),
% 155.94/155.68 inference(rename_variables,[],[4423])).
% 155.94/155.68 cnf(13486,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),x134861),f312(f312(f90(a853),x134861),x134861)))),
% 155.94/155.68 inference(rename_variables,[],[3481])).
% 155.94/155.68 cnf(13489,plain,
% 155.94/155.68 (~P22(f312(f312(f227(a853),f312(a126,x134891)),x134891))),
% 155.94/155.68 inference(rename_variables,[],[4484])).
% 155.94/155.68 cnf(13496,plain,
% 155.94/155.68 (P22(f312(f312(f314(x134961),f312(x134962,x134963)),f312(f290(x134964,x134961,x134962),f235(f861(x134964,a846)))))),
% 155.94/155.68 inference(rename_variables,[],[3810])).
% 155.94/155.68 cnf(13503,plain,
% 155.94/155.68 (P22(f312(f312(f227(f861(x135031,a846)),f312(f168(x135031),f166(x135031,x135032,x135033))),f312(f168(x135031),x135033)))),
% 155.94/155.68 inference(rename_variables,[],[3904])).
% 155.94/155.68 cnf(13506,plain,
% 155.94/155.68 (~P22(f312(f312(f314(f860(x135061,x135061)),x135062),f237(x135061,f189(f861(x135061,a846)))))),
% 155.94/155.68 inference(rename_variables,[],[10812])).
% 155.94/155.68 cnf(13509,plain,
% 155.94/155.68 (~P22(f312(f312(f314(x135091),x135092),f189(f861(x135091,a846))))),
% 155.94/155.68 inference(rename_variables,[],[4487])).
% 155.94/155.68 cnf(13512,plain,
% 155.94/155.68 (~E(f312(f312(f115(a853),f312(a126,x135121)),x135121),f312(a126,x135121))),
% 155.94/155.68 inference(rename_variables,[],[11381])).
% 155.94/155.68 cnf(13518,plain,
% 155.94/155.68 (~P22(f312(f312(f228(a853),x135181),f312(f312(f115(a853),x135181),x135182)))),
% 155.94/155.68 inference(rename_variables,[],[11907])).
% 155.94/155.68 cnf(13534,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),x135341),f312(f312(f90(a853),x135341),x135341)))),
% 155.94/155.68 inference(rename_variables,[],[3481])).
% 155.94/155.68 cnf(13537,plain,
% 155.94/155.68 (~P22(f312(f312(f314(f860(f854(x135371),f854(x135371))),f312(f312(f239(f854(x135371),f854(x135371)),f127(x135371)),x135372)),f153(x135371,x135373)))),
% 155.94/155.68 inference(rename_variables,[],[4508])).
% 155.94/155.68 cnf(13547,plain,
% 155.94/155.68 (~P22(f312(f312(f189(f861(x135471,f861(x135472,a846))),x135473),x135474))),
% 155.94/155.68 inference(rename_variables,[],[4502])).
% 155.94/155.68 cnf(13550,plain,
% 155.94/155.68 (~P22(f312(f312(f314(a853),x135501),f312(f279(a853),f2(a853))))),
% 155.94/155.68 inference(rename_variables,[],[11628])).
% 155.94/155.68 cnf(13557,plain,
% 155.94/155.68 (~P22(f312(f312(f314(x135571),x135572),f189(f861(x135571,a846))))),
% 155.94/155.68 inference(rename_variables,[],[4487])).
% 155.94/155.68 cnf(13560,plain,
% 155.94/155.68 (~P22(f312(f312(f314(f860(f854(x135601),f854(x135601))),f312(f312(f239(f854(x135601),f854(x135601)),x135602),f127(x135601))),f141(x135601,x135603)))),
% 155.94/155.68 inference(rename_variables,[],[4504])).
% 155.94/155.68 cnf(13563,plain,
% 155.94/155.68 (E(f38(x135631,x135632,x135633,x135634,x135635,x135636,x135637,x135638,x135639,a23),x135632)),
% 155.94/155.68 inference(rename_variables,[],[4362])).
% 155.94/155.68 cnf(13573,plain,
% 155.94/155.68 (~E(f312(a126,x135731),f2(a853))),
% 155.94/155.68 inference(rename_variables,[],[4401])).
% 155.94/155.68 cnf(13585,plain,
% 155.94/155.68 (~P22(f312(f312(f314(x135851),x135852),f189(f861(x135851,a846))))),
% 155.94/155.68 inference(rename_variables,[],[4487])).
% 155.94/155.68 cnf(13588,plain,
% 155.94/155.68 (P22(f312(f312(f227(f861(x135881,a846)),x135882),f312(f312(f124(f861(x135881,a846)),x135883),f235(f861(x135881,a846)))))),
% 155.94/155.68 inference(rename_variables,[],[11036])).
% 155.94/155.68 cnf(13593,plain,
% 155.94/155.68 (E(f312(x135931,f740(f312(x135931,x135932),f312(f219(x135933),x135932),x135931,x135934,x135933)),f312(x135931,x135932))),
% 155.94/155.68 inference(rename_variables,[],[11004])).
% 155.94/155.68 cnf(13602,plain,
% 155.94/155.68 (~P22(f312(f312(f314(a853),x136021),f312(f279(a853),f2(a853))))),
% 155.94/155.68 inference(rename_variables,[],[11628])).
% 155.94/155.68 cnf(13605,plain,
% 155.94/155.68 (P22(f312(f312(f227(f861(x136051,a846)),f312(f168(x136051),f166(x136051,x136052,x136053))),f312(f168(x136051),x136053)))),
% 155.94/155.68 inference(rename_variables,[],[3904])).
% 155.94/155.68 cnf(13615,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),x136151),f312(f312(f90(a853),x136151),x136151)))),
% 155.94/155.68 inference(rename_variables,[],[3481])).
% 155.94/155.68 cnf(13620,plain,
% 155.94/155.68 (~P22(f312(f312(f314(f860(x136201,x136201)),x136202),f237(x136201,f189(f861(x136201,a846)))))),
% 155.94/155.68 inference(rename_variables,[],[10812])).
% 155.94/155.68 cnf(13643,plain,
% 155.94/155.68 (~P22(f312(f312(f189(f861(x136431,f861(x136432,a846))),x136433),x136434))),
% 155.94/155.68 inference(rename_variables,[],[4502])).
% 155.94/155.68 cnf(13651,plain,
% 155.94/155.68 (~E(f312(f312(f147(x136511),x136512),x136513),x136513)),
% 155.94/155.68 inference(rename_variables,[],[4423])).
% 155.94/155.68 cnf(13659,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),f2(a853)),x136591))),
% 155.94/155.68 inference(rename_variables,[],[3226])).
% 155.94/155.68 cnf(13666,plain,
% 155.94/155.68 (~P22(f312(f312(f314(x136661),x136662),f189(f861(x136661,a846))))),
% 155.94/155.68 inference(rename_variables,[],[4487])).
% 155.94/155.68 cnf(13673,plain,
% 155.94/155.68 (~P22(f312(f312(f314(x136731),x136732),f312(f291(x136731,x136733,x136734),f189(f861(x136733,a846)))))),
% 155.94/155.68 inference(rename_variables,[],[10815])).
% 155.94/155.68 cnf(13683,plain,
% 155.94/155.68 (~P22(f312(f312(f314(x136831),x136832),f312(f291(x136831,x136833,x136834),f189(f861(x136833,a846)))))),
% 155.94/155.68 inference(rename_variables,[],[10815])).
% 155.94/155.68 cnf(13692,plain,
% 155.94/155.68 (~P39(x136921,x136922,x136923,f312(f312(f150(x136924,x136921),x136925),f312(a126,f127(x136924))),f127(x136922))),
% 155.94/155.68 inference(rename_variables,[],[11066])).
% 155.94/155.68 cnf(13710,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),x137101),x137101))),
% 155.94/155.68 inference(rename_variables,[],[3205])).
% 155.94/155.68 cnf(13727,plain,
% 155.94/155.68 (~E(f312(f312(f147(x137271),x137272),x137273),x137273)),
% 155.94/155.68 inference(rename_variables,[],[4423])).
% 155.94/155.68 cnf(13743,plain,
% 155.94/155.68 (P22(f312(f312(f227(f861(x137431,a846)),f312(f168(x137431),f166(x137431,x137432,x137433))),f312(f168(x137431),x137433)))),
% 155.94/155.68 inference(rename_variables,[],[3904])).
% 155.94/155.68 cnf(13749,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),x137491),f312(f312(f89(a853),x137491),x137492)))),
% 155.94/155.68 inference(rename_variables,[],[3480])).
% 155.94/155.68 cnf(13755,plain,
% 155.94/155.68 (~E(f312(f312(f147(x137551),x137552),x137553),x137553)),
% 155.94/155.68 inference(rename_variables,[],[4423])).
% 155.94/155.68 cnf(13822,plain,
% 155.94/155.68 (E(f312(x138221,f740(f312(x138221,x138222),f312(f219(x138223),x138222),x138221,x138224,x138223)),f312(x138221,x138222))),
% 155.94/155.68 inference(rename_variables,[],[11004])).
% 155.94/155.68 cnf(13872,plain,
% 155.94/155.68 (P22(f312(f312(f227(a853),f54(a853,x138721,x138722)),x138721))),
% 155.94/155.68 inference(rename_variables,[],[3661])).
% 155.94/155.68 cnf(13875,plain,
% 155.94/155.68 (E(f312(x138751,f740(f312(x138751,x138752),f312(f219(x138753),x138752),x138751,x138754,x138753)),f312(x138751,x138752))),
% 155.94/155.68 inference(rename_variables,[],[11004])).
% 155.94/155.68 cnf(13928,plain,
% 155.94/155.68 ($false),
% 155.94/155.68 inference(scs_inference,[],[3234,3232,3643,3950,3987,3207,4501,3205,13402,13710,4491,3843,3282,4464,3299,3656,4504,13560,4487,13310,13317,13328,13335,13412,13509,13557,13585,13666,3286,3904,13302,13503,13605,13743,3810,13496,3682,3027,3312,4407,4401,13296,13573,4423,13290,13472,13651,13727,13755,3189,3981,3853,3206,13299,3661,13872,3226,13659,3522,3650,3509,13357,13466,3652,3581,3481,13486,13534,13615,3480,13469,13749,4092,3654,4362,13275,13293,13364,13371,13432,13563,3146,3571,4108,13440,4505,4506,4508,13537,4471,4484,13456,13489,4497,4502,13376,13547,13643,4499,4500,13320,3418,11381,13284,13512,10201,12935,10463,13142,10253,11827,11691,11552,12820,11191,13118,10432,12112,12088,11747,10478,11407,10936,12329,12358,12365,11036,13588,10766,10624,13390,13397,13450,4213,12385,11101,4218,11004,13379,13593,13822,13875,10180,10799,11146,10568,3238,10188,11083,10857,12830,12833,13136,10581,12051,12044,11026,11865,13154,12147,10165,11628,13338,13453,13550,13602,10990,10812,13287,13506,13620,10815,13673,13683,13213,10563,10666,11907,13518,11933,11151,12381,13146,11066,13692,11070,13323,10827,11044,2978,6014,6201,8452,6159,8016,8363,9105,4532,5281,5747,6047,8262,8432,9598,9608,5345,8640,9318,5046,8494,5168,9819,5679,9610,4905,8684,9701,5251,8775,9,5186,6422,7662,9425,5892,7215,7939,5667,5332,4525,7428,8260,5689,4659,5151,6281,5771,5542,5725,7841,5734,6702,6968,4651,5677,5806,9839,4923,6674,7721,6385,5980,9192,5839,5998,5280,5609,6163,8463,9320,8327,5139,5440,8685,7140,7196,8430,9123,9162,6024,4650,6274,8800,9195,7831,9519,6777,5149,6086,8071,8340,8688,8795,8537,8763,6598,9806,9818,4922,5482,6271,5613,6040,6278,6834,7906,9282,10071,5496,8567,5853,8664,5275,5620,8602,9844,7938,9891,5706,5977,8513,6842,8392,6670,7381,7709,8624,5122,4599,5298,6326,7248,7801,8406,5466,5245,5310,7000,5633,5483,6916,8641,2,8,6151,5829,7386,6087,8451,4961,4842,7535,6270,4548,6622,9196,6223,6094,5463,6646,7255,7515,7658,6000,4968,9149,6781,6654,8992,9621,4990,5094,5330,6765,7627,8959,5349,6175,6776,7628,6624,9223,6672,8428,9456,5546,7304,5847,8580,4597,5625,7341,8303,8407,6229,6690,4512,5279,5724,8926,6042,9106,9635,4989,6701,4728,6276,9664,6775,5415,5832,6668,6002,5341,6279,7316,8683,9172,5961,9319,8423,9363,6017,5681,5165,8498,4700,5391,5502,5512,6193,8088,4982,5674,6186,5372,8502,9457,5190,8928,5446,5531,8133,5462,5735,6384,4589,5160,7844,8158,5167,7922,4558,4924,5392,6023,7747,5375,6370,6391,8809,5123,5268,6423,6673,9587,9474,5262,9447,4633]),
% 155.94/155.68 ['proof']).
% 155.94/155.68 % SZS output end Proof
% 155.94/155.68 % Total time :140.760000s
%------------------------------------------------------------------------------